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On symmetry-resolved generalized entropies

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Pith's one-line read This paper derives explicit sum formulas for the normalized generalized charged moments of the free compact boson CFT, making symmetry-resolved entanglement computable for arbitrary descendant states and matching XX-chain lattice data.

desk verdict A real technical advance on symmetry-resolved entanglement for descendant states, with a load-bearing boundary-condition approximation that needs scrutiny before the 1/log expansions are trusted. read the letter →

arxiv 2412.14165 v2 pith:2K3KS2D6 submitted 2024-12-18 quant-ph cond-mat.stat-mechcond-mat.str-elhep-th

Fei Yan , Sara Murciano , Pasquale Calabrese , Robert Konik This is my paper · ORCID
classification quant-phcond-mat.stat-mechcond-mat.str-elhep-th MSC 81T40
keywords symmetry-resolvedentanglementgeneralizedRényientropieschargedmomentsfreecompactbosonCFTXXspinchainfullcountingstatisticsconformalfieldtheoryequipartition
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper introduces symmetry-resolved generalized Rényi entropies, which split the entanglement between a subsystem and its complement according to the sector of a global $U(1)$ charge while allowing the replica in- and out-states to be arbitrary excited states. These quantities are the building blocks for studying symmetry-resolved entanglement in excited states and in symmetry-preserving out-of-equilibrium dynamics. The paper claims that in the free massless compact boson CFT these entropies are controlled by normalized generalized charged moments, and it derives explicit sum formulas for the $n=1$ and $n=2$ moments, Eqs. (58) and (81), valid for arbitrary descendant states. At leading order in the chord length the moments are finite polynomials in the Aharonov–Bohm flux $\theta$, and the formulas reproduce known primary-state results and match exact XX-chain lattice computations. This gives a route to the full counting statistics of the subsystem charge and to the time evolution of symmetry-resolved entanglement after symmetric quenches.

What carries the argument

The central object is the normalized generalized charged moment $F_n(\theta;\psi_1,\ldots,\psi_{2n})$, defined in Eq. (19) as the ratio of the trace of $n$ glued generalized density matrices with an insertion of the subsystem charge operator $e^{i\theta Q_A}$ to the ground-state $n$-th charged moment. The computation uses the replica trick: the moment is a partition function on an $n$-fold branched cover of the cylinder, with vertex operators and $\partial\varphi$ insertions at the infinities and the $U(1)$ twist operators at the entanglement cuts. A conformal transformation, Eq. (40) for $n=1$ and Eq. (71) for $n=2$, maps this geometry to a branched cover of the plane, and the correlation-function ratio is expanded into Wick contractions. The sum formulas (58) and (81) organize these contractions into a polynomial in $\theta$: the $n=1$ case simplifies because contractions of $\partial\varphi$ with vertex operators combine into a phase $e^{i\beta\theta r\alpha}$ times mode-dependent factors $L(k_i)$, while the $n=2$ case requires the full functions $L_{k_j}(\theta)$ and $\tilde{L}_{k_j}(\bar{\alpha})$.

What would settle it

Evaluate the full cut-plane correlator in Eq. (47), including the boundary conditions on the two disks, and compare it with the plane-correlator approximation used in the paper: if the difference is not suppressed by at least one power of $1/\log(\ell/\epsilon)$ at the orders retained, the sum formulas for $F_n$ and the derived variance shift would be incomplete. On the lattice side, exact diagonalization of the XX chain at larger flux $\theta$ or for $n=2$ with additional descendant states would expose any missing $\theta$-dependence in the polynomial.

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Extended reading notes

Core claim

For a $(1+1)$-dimensional free massless compact boson with a $U(1)$ winding symmetry, the normalized generalized charged moment $F_n(\theta;\psi_1,\ldots,\psi_{2n})$ — the ratio of a charged replica trace built from $2n$ states to the ground-state charged moment — can be evaluated as an explicit sum over Wick contractions. The central formulas are Eq. (58) for $n=1$ and Eq. (81) for $n=2$: they give $F_n$ for arbitrary descendant states as a finite polynomial in $\theta$ at leading order in the chord length $\ell$, with coefficients that are trigonometric functions of the subsystem size ratio $r$. The $n=1$ formula is organized recursively by a pairing function $R$ and single-mode functions $L(k_i)$, while the $n=2$ formula additionally tracks contractions with the vertex-operator insertions through functions $L_{k_j}(\theta)$ and $\tilde{L}_{k_j}(\bar{\alpha})$. These sums reproduce the known primary-field charged moments from Refs. [18,20] and match exact lattice data in the XX chain for level-2 chiral states in Figures 4 and 5.

Load-bearing premise

The load-bearing premise is that correlation functions on the cut plane can be replaced by ordinary plane correlators, with the entanglement-cut boundary conditions contributing only corrections suppressed by powers of $\log(\ell/\epsilon)$; if that suppression fails at the orders the paper keeps, the polynomial-in-$\theta$ formulas, the $1/\log$ expansions, and the variance shift would be incomplete.

Editorial extensions

If this is right

  • For any descendant state of the compact boson CFT, the $n=1$ and $n=2$ symmetry-resolved generalized Rényi entropies can be written down directly from the sum formulas, extending previous results that were limited to primary states.
  • The $n=1$ moment is a generating function, so the full counting statistics of the subsystem $U(1)$ charge in an excited state follows immediately, with a mean shifted to $r m$ and a variance shifted by $-2\pi^2 h_2$ relative to the ground state.
  • Entanglement equipartition across charge sectors is broken at order $1/(\log \ell')^2$ by universal terms, and the excited-state symmetry-resolved second Rényi entropy acquires a double-logarithmic correction.
  • The same building blocks combine with a numerical time-evolution scheme to track symmetry-resolved entanglement and charge statistics after quantum quenches that preserve the symmetry.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the same Wick-contraction framework carries over to other CFTs, the natural next test is the Ising model's $\mathbb{Z}_2$ symmetry resolution for descendant states, whose analogous sums should produce polynomial charged moments with different trigonometric coefficients.
  • The predicted variance shift in the subsystem charge distribution is a sharp experimental signature: a quantum-gas microscope measuring charge fluctuations in a one-dimensional Bose gas after exciting a Luttinger-liquid state should see the distribution width deviate from the ground-state Gaussian.
  • The $r=1/2$ simplification in Appendix A.2 suggests that half-system bipartitions may admit closed forms for general $n$, which would provide a cheap diagnostic of the entire construction before more general geometries are attempted.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

1 major / 4 minor

Summary. The manuscript introduces the notion of symmetry-resolved generalized entropies, which are intended as building blocks for studying symmetry-resolved entanglement of excited states and its out-of-equilibrium dynamics. The central technical object is the normalized generalized charged moment F_n(θ; ψ_1, ..., ψ_{2n}) of Eq. (4). For the free compact boson CFT, the authors derive explicit sum formulas for the n=1 and n=2 chiral moments, Eq. (58) and Eq. (81), which at leading order in the chord length ℓ take the form of finite polynomials in the flux θ. These formulas are benchmarked against exact XX-chain lattice computations (Figs. 4 and 5) and against previously known primary-field results (Eqs. (64), (85), (86), (88)). The paper then applies the moments to compute the generalized subsystem charge distribution and the symmetry-resolved generalized second Rényi entropy, obtaining expansions in 1/log(ℓ/ε).

Significance. If the results hold, the paper provides a substantial extension of symmetry-resolved entanglement techniques from primary states to arbitrary descendant states in a CFT, which is directly relevant to Luttinger-liquid physics and to the program of computing entanglement dynamics via generalized entropies. The explicit Wick-contraction sums in Eqs. (58) and (81) are new, and their validation against exact lattice data and against independent published special cases is a genuine strength. The definition of symmetry-resolved generalized entropies is natural and likely to be reused. However, the practical value for out-of-equilibrium settings rests on the 1/log(ℓ/ε) expansions in Sections 6 and 7, and those expansions are the part of the paper that is least supported by derivation or numerics.

major comments (1)
  1. [Sec. 4.1 (below Eq. (47)); Sec. 5.1 (below Eq. (72))] The replacement of correlation functions on C′ (the plane with two disks cut out around 0 and ∞, representing the regularized entanglement cuts) by ordinary plane correlators is asserted with the statement that the effects of the entanglement-cut boundary conditions are 'suppressed by powers of log(ℓ/ε)', but no derivation or quantitative estimate is provided. In the free compact boson, the annulus has a compact zero mode whose contributions to correlators of vertex operators with zero total charge are of order 1/log(ℓ/ε), not exponentially small. Since the twist operators V_{±βθ/(2π)} are inserted at y0 ≈ δ and y0′ ≈ 1/δ, i.e., on the cut boundaries, their OPEs with the bulk insertions are exactly where boundary-condition dependence can enter. A correction of order 1/log(ℓ/ε) carrying an O(θ^2) piece would change h2 in Eq. (92), the variance shift b1 in Eq. (96), and the 1/log expansions in Eqs. (93), (99), (102), and (104), all of which are presented as physical results of the framework. The lattice benchmarks in Figs. 4 and 5 (L=64) test only selected level-2 descendants at two values of θ and cannot isolate a 1/log boundary term from lattice finite-size and parity effects. The authors should either provide an explicit boundary CFT computation showing that the boundary corrections are subleading at the orders kept, or include the 1/log corrections and re-derive the expansions in Sections 6 and 7.
minor comments (4)
  1. [Abstract] The abstract contains formatting artifacts from the LaTeX source ('W e', 'T he', and stray spaces), which should be cleaned before final submission.
  2. [Sec. 3.1, bullet 3] The phrase 'the regularization-dependent corrections are power-law suppressed by log ℓ/ε' is ambiguous; it should read 'suppressed by powers of 1/log(ℓ/ε)'.
  3. [Eq. (58) and similar formulas] The deletion notation R_{k1,...,\emptyset ki,...,kM} is not defined; please describe the deletion operation explicitly, for example by placing a hat over the deleted entry.
  4. [Figs. 4 and 5] The insets showing imaginary parts are small and hard to read; consider enlarging them or presenting the imaginary parts in separate panels.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: central sum formulas are derived by Wick contraction and benchmarked against exact lattice data and independent special cases.

full rationale

The derivation chain is self-contained and non-circular. The central objects F_L^1 and F_L^2 are obtained by explicit free-boson Wick contractions after the conformal maps in Eqs. (44) and (71); Eqs. (50), (58), (74), and (81) are concrete combinatorial sums, not definitions of the answer. The only load-bearing approximation is the replacement of C′ correlators by plane correlators below Eq. (47), with the suppression of entanglement-cut effects asserted rather than proved; this is a correctness and omitted-proof risk, but it is an input assumption, not a fitted or renamed output. The results are benchmarked against exact XX-chain lattice computations in Figs. 4 and 5 and reduce to the independently published special cases of Refs. [18,20] in Eqs. (64), (85), (86), and (88). Self-citations to Refs. [25] and [63] supply the ground-state charged-moment denominator and a ∂ϕ∂ϕ contraction simplification; neither carries the central derivation, and neither is the quantity being predicted. No parameter is fitted to the data used for comparison. Hence no circular step is exhibited, and the appropriate score is 0.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

No parameters are fitted to data. The compactification radius β is a theory input (set to 1 for the XX-chain comparison), r and ℓ are geometric variables, and the regulator ε appears only in logarithms; the coefficients h2, f2, etc., in the expansions are outputs of the derivations. No new particles, fields, or conserved quantities are introduced.

assumptions (5)
  • domain assumption The effects of the entanglement-cut boundary conditions on the correlator ratios are suppressed by powers of log(ℓ/ε), so the cut-plane correlators in C′ can be replaced by complex-plane correlators at leading order.
    Stated in Section 4.1 below Eq. (47); underlies the polynomial-in-θ form of Fn and all 1/log expansions. If the suppression is not strong enough, the derived formulas are incomplete.
  • domain assumption At leading order in the chord length the normalized generalized charged moment Fn is a finite polynomial in θ, with subleading corrections suppressed by 1/log(ℓ/ε).
    Used in Sections 3.1, 6 and 7 to truncate the θ-series at o(θ^4) and to Fourier transform term by term; the decay of coefficients is argued, not proven.
  • standard math Wick's theorem applies to the free boson correlators on the replica surface, and the oscillator-mode integrals reduce to contour integrals around the insertion points, with the two-point functions given by Eq. (48).
    Standard CFT free-field technique; the basis for the sum formulas in Sections 4-5 and the appendices.
  • domain assumption The subsystem-restricted U(1)_w charge operator e^{iθQ_A} is realized by inserting vertex operators at the entangling points, requiring Dirichlet boundary conditions on the compact boson at the entangling surface.
    Used in Eq. (34) and throughout; standard in the symmetry-resolution literature but specific to the U(1)_w resolution.
  • domain assumption The XX spin chain with free-fermion techniques gives a lattice realization of the compact boson CFT at β=1, with the low-energy excited states mapped as in Appendix C.
    Underlies the numerical benchmarks in Figures 4 and 5; the mapping is taken from Refs. [10,67].

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Pith. "Pith review of On symmetry-resolved generalized entropies." pith.science (2026). https://pith.science/paper/2K3KS2D6

@misc{pith2026241214165,
  author       = {Pith},
  title        = {Pith review of: On symmetry-resolved generalized entropies},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2K3KS2D6}},
  note         = {Machine review of arXiv:2412.14165}
}
read the original abstract

Symmetry-resolved entanglement, capturing the refined structure of quantum entanglement in systems with global symmetries, has attracted a lot of attention recently. In this manuscript, introducing the notion of symmetry-resolved generalized entropies, we aim to develop a computational framework suitable for the study of excited state symmetry-resolved entanglement as well as the dynamical evolution of symmetry-resolved entanglement in symmetry-preserving out-of-equilibrium settings. We illustrate our framework using the example of (1+1)-d free massless compact boson theory, and benchmark our results using lattice computation in the XX chain. As a byproduct, our computational framework also provides access to the probability distribution of the symmetry charge contained within a subsystem and the corresponding full counting statistics.

Figures

Figures reproduced from arXiv: 2412.14165 by the authors.

Figure 1
Figure 1. Left: The replica geometry Cn for the computation of the generalized charged moment, as a n-fold branched covering of a cylinder with infinite length. The n sheets are glued together by identifying the edges of cut-open slits with the same color, e.g. the maroon-colored slit edge on sheet 1 is identified with the maroon-colored slit edge on sheet 2 etc. The operator O2i−1 corresponding to |ψ2i−1⟩ are inserted at the… view at source ↗
Figure 2
Figure 2. Left: The replica geometry Cn for computing the chiral normalized charged moment, as a n-fold branched covering of a cylinder with infinite length. The n sheets are glued together by identifying the edges of cut-open slits with the same color, e.g. the maroon-colored slit edge on sheet 1 is identified with the maroon-colored slit edge on sheet 2 etc. The vertex operators Vσiαi and ∂ϕ are inserted at the past and fut… view at source ↗
Figure 3
Figure 3. Left: The cylindrical geometry C1 for computing the chiral n = 1 normalized generalized charged moment, together with locations of various field insertions. Right: After the conformal transformation in Eq. (44), the cylindrical geometry C1 is mapped to the complex place with two disks cut out around 0 and ∞, which we denote as C ′ . To evaluate the chiral normalized n = 1 generalized charged moment, we perform a con… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Benchmark of the CFT results for the generalized charged moments in [PITH_FULL_IMAGE:figures/full_fig_p022_4.png]
Figure 5
Figure 5. Figure 5: The top (bottom) panels are a test of the real (imaginary) part of the [PITH_FULL_IMAGE:figures/full_fig_p026_5.png]

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Works this paper leans on

88 extracted references · 23 canonical work pages

  1. [1]

    Vidal, J

    G. Vidal, J. I. Latorre, E. Rico and A. Kitaev, Entanglement in quantum critical phenomena, Phys. Rev. Lett. 90, 227902 (2003), doi:10.1103/PhysRevLett.90.227902, quant-ph/0211074

    arXiv 2003

  2. [2]

    Calabrese and J

    P. Calabrese and J. L. Cardy, Time-dependence of correlation func- tions following a quantum quench , Phys. Rev. Lett. 96, 136801 (2006), doi:10.1103/PhysRevLett.96.136801, cond-mat/0601225

    arXiv 2006

  3. [3]

    Kitaev and J

    A. Kitaev and J. Preskill, Topological entanglement entropy, Phys. Rev. Lett. 96, 110404 (2006), doi:10.1103/PhysRevLett.96.110404

    doi:10.1103/physrevlett.96.110404 2006

  4. [4]

    Levin and X.-G

    M. Levin and X.-G. Wen, Detecting Topological Order in a Ground State Wave Function, Phys. Rev. Lett. 96, 110405 (2006), doi:10.1103/PhysRevLett.96.110405, cond-mat/0510613

    arXiv 2006

  5. [5]

    D. N. Page, Information in black hole radiation , Phys. Rev. Lett. 71, 3743 (1993), doi:10.1103/PhysRevLett.71.3743, hep-th/9306083

    arXiv 1993

  6. [6]

    Goldstein and E

    M. Goldstein and E. Sela, Symmetry-resolved entanglement in many-body systems , Phys. Rev. Lett. 120(20), 200602 (2018), doi:10.1103/PhysRevLett.120.200602, 1711.09418

    arXiv 2018

  7. [7]

    Laflorencie and S

    N. Laflorencie and S. Rachel, Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids , J. Phys. A 2014(11), P11013 (2014), doi:10.1088/1742- 5468/2014/11/P11013

    doi:10.1088/1742- 2014

  8. [8]

    J. C. Xavier, F. C. Alcaraz and G. Sierra, Equipartition of the entanglement entropy , Phys. Rev. B 98(4), 041106 (2018), doi:10.1103/PhysRevB.98.041106, 1804.06357

    arXiv 2018

Show all 88 references
  1. [9]

    Kiefer-Emmanouilidis, R

    M. Kiefer-Emmanouilidis, R. Unanyan, J. Sirker and M. Fleischhauer, Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems , SciPost Phys. 8, 083 (2020), doi:10.21468/SciPostPhys.8.6.083, 2003.03112

    2020 arXiv

  2. [10]

    Bonsignori, P

    R. Bonsignori, P. Ruggiero and P. Calabrese, Symmetry resolved entanglement in free fermionic systems, J. Phys. A 52(47), 475302 (2019), doi:10.1088/1751-8121/ab4b77, 1907.02084

    2019 arXiv

  3. [11]

    Monkman and J

    K. Monkman and J. Sirker, Operational entanglement of symmetry- protected topological edge states , Phys. Rev. Res. 2(4), 043191 (2020), doi:10.1103/PhysRevResearch.2.043191, 2005.13026

    2020 arXiv

  4. [12]

    Turkeshi, P

    X. Turkeshi, P. Ruggiero, V. Alba and P. Calabrese, Entanglement equipar- tition in critical random spin chains , Phys. Rev. B 102(1), 014455 (2020), doi:10.1103/PhysRevB.102.014455, 2005.03331

    2020 arXiv

  5. [13]

    Oblak, N

    B. Oblak, N. Regnault and B. Estienne, Equipartition of entanglement in quantum Hall states, Phys. Rev. B 105(11), 115131 (2022), doi:10.1103/PhysRevB.105.115131, 2112.13854

    2022 arXiv

  6. [14]

    Estienne, Y

    B. Estienne, Y. Ikhlef and A. Morin-Duchesne, Finite-size corrections in critical symmetry-resolved entanglement , SciPost Phys. 10(3), 054 (2021), doi:10.21468/SciPostPhys.10.3.054, 2010.10515. 37 SciPost Physics Submission

    2021 arXiv

  7. [15]

    Piroli, E

    L. Piroli, E. Vernier, M. Collura and P. Calabrese, Thermodynamic symmetry resolved entanglement entropies in integrable systems (2022), doi:10.1088/1742-5468/ac7a2d, 2203.09158

    2022 arXiv

  8. [16]

    F. Ares, S. Murciano and P. Calabrese, Symmetry-resolved entanglement in a long- range free-fermion chain, J. Stat. Mech. 2206(6), 063104 (2022), doi:10.1088/1742- 5468/ac7644, 2202.05874

    2022 arXiv

  9. [17]

    Belin, L.-Y

    A. Belin, L.-Y. Hung, A. Maloney, S. Matsuura, R. C. Myers and T. Sierens, Holographic Charged Renyi Entropies , JHEP 12, 059 (2013), doi:10.1007/JHEP12(2013)059, 1310.4180

    2013 arXiv

  10. [18]

    Capizzi, P

    L. Capizzi, P. Ruggiero and P. Calabrese, Symmetry resolved entanglement entropy of excited states in a CFT , J. Stat. Mech. 2007, 073101 (2020), doi:10.1088/1742- 5468/ab96b6, 2003.04670

    2020 arXiv

  11. [19]

    Capizzi, D

    L. Capizzi, D. X. Horv´ ath, P. Calabrese and O. A. Castro-Alvaredo, Entanglement of the 3-state Potts model via form factor bootstrap: total and symmetry resolved entropies, JHEP 05, 113 (2022), doi:10.1007/JHEP05(2022)113, 2108.10935

    2022 arXiv

  12. [20]

    Capizzi and P

    L. Capizzi and P. Calabrese, Symmetry resolved relative entropies and distances in conformal field theory , JHEP 10, 195 (2021), doi:10.1007/JHEP10(2021)195, 2105.08596

    2021 arXiv

  13. [21]

    Milekhin and A

    A. Milekhin and A. Tajdini, Charge fluctuation entropy of Hawking radia- tion: A replica-free way to find large entropy , SciPost Phys. 14(6), 172 (2023), doi:10.21468/SciPostPhys.14.6.172, 2109.03841

    2023 arXiv

  14. [22]

    Di Giulio, R

    G. Di Giulio, R. Meyer, C. Northe, H. Scheppach and S. Zhao, On the boundary conformal field theory approach to symmetry-resolved entanglement , SciPost Phys. Core 6, 049 (2023), doi:10.21468/SciPostPhysCore.6.3.049, 2212.09767

    2023

  15. [23]

    Fossati, F

    M. Fossati, F. Ares and P. Calabrese, Symmetry-resolved entanglement in critical non-Hermitian systems , Phys. Rev. B 107(20), 205153 (2023), doi:10.1103/PhysRevB.107.205153, 2303.05232

    2023 arXiv

  16. [24]

    Northe, Entanglement Resolution with Respect to Conformal Symmetry , Phys

    C. Northe, Entanglement Resolution with Respect to Conformal Symmetry , Phys. Rev. Lett. 131(15), 151601 (2023), doi:10.1103/PhysRevLett.131.151601, 2303. 07724

    2023 doi

  17. [25]

    Kusuki, S

    Y. Kusuki, S. Murciano, H. Ooguri and S. Pal, Symmetry-resolved entangle- ment entropy, spectra & boundary conformal field theory , JHEP 11, 216 (2023), doi:10.1007/JHEP11(2023)216, 2309.03287

    2023 arXiv

  18. [26]

    Capizzi, S

    L. Capizzi, S. Murciano and P. Calabrese, Full counting statistics and symmetry resolved entanglement for free conformal theories with interface defects, J. Stat. Mech. 2307, 073102 (2023), doi:10.1088/1742-5468/ace3b8, 2302.08209

    2023 arXiv

  19. [27]

    Chen, Symmetry decomposition of relative entropies in conformal field theory , JHEP 07, 084 (2021), doi:10.1007/JHEP07(2021)084, 2104.03102

    H.-H. Chen, Symmetry decomposition of relative entropies in conformal field theory , JHEP 07, 084 (2021), doi:10.1007/JHEP07(2021)084, 2104.03102

    2021 arXiv

  20. [28]

    Bonsignori and P

    R. Bonsignori and P. Calabrese, Boundary effects on symmetry resolved entanglement, J. Phys. A 54(1), 015005 (2021), doi:10.1088/1751-8121/abcc3a, 2009.08508. 38 SciPost Physics Submission

    2021 arXiv

  21. [29]

    F. Ares, P. Calabrese, G. Di Giulio and S. Murciano, Multi-charged mo- ments of two intervals in conformal field theory , JHEP 09, 051 (2022), doi:10.1007/JHEP09(2022)051, 2206.01534

    2022 arXiv

  22. [30]

    Ghasemi, Universal thermal corrections to symmetry-resolved entan- glement entropy and full counting statistics , JHEP 05, 209 (2023), doi:10.1007/JHEP05(2023)209, 2203.06708

    M. Ghasemi, Universal thermal corrections to symmetry-resolved entan- glement entropy and full counting statistics , JHEP 05, 209 (2023), doi:10.1007/JHEP05(2023)209, 2203.06708

    2023 arXiv

  23. [31]

    Bruno, F

    A. Bruno, F. Ares, S. Murciano and P. Calabrese, Symmetry resolution of the com- putable cross-norm negativity of two disjoint intervals in the massless Dirac field theory, JHEP 02, 009 (2024), doi:10.1007/JHEP02(2024)009, 2312.02926

    2024 arXiv

  24. [32]

    Berthiere and G

    C. Berthiere and G. Parez, Reflected entropy and computable cross-norm negativ- ity: Free theories and symmetry resolution , Phys. Rev. D 108(5), 054508 (2023), doi:10.1103/PhysRevD.108.054508, 2307.11009

    2023 arXiv

  25. [33]

    Foligno, S

    A. Foligno, S. Murciano and P. Calabrese, Entanglement resolution of free Dirac fermions on a torus , JHEP 03, 096 (2023), doi:10.1007/JHEP03(2023)096, 2212. 07261

    2023 doi

  26. [34]

    Chen, Charged R´ enyi negativity of massless free bosons, JHEP 02, 117 (2022), doi:10.1007/JHEP02(2022)117, 2111.11028

    H.-H. Chen, Charged R´ enyi negativity of massless free bosons, JHEP 02, 117 (2022), doi:10.1007/JHEP02(2022)117, 2111.11028

    2022 arXiv

  27. [35]

    Casini, M

    H. Casini, M. Huerta, J. M. Mag´ an and D. Pontello, Entanglement entropy and superselection sectors. Part I. Global symmetries , JHEP 02, 014 (2020), doi:10.1007/JHEP02(2020)014, 1905.10487

    2020 arXiv

  28. [36]

    Murciano, J

    S. Murciano, J. Dubail and P. Calabrese, More on symmetry resolved operator entanglement, J. Phys. A 57(14), 145002 (2024), doi:10.1088/1751-8121/ad30d1, 2309.04032

    2024 arXiv

  29. [37]

    Di Giulio and J

    G. Di Giulio and J. Erdmenger, Symmetry-resolved modular correlation functions in free fermionic theories , JHEP 07, 058 (2023), doi:10.1007/JHEP07(2023)058, 2305.02343

    2023

  30. [38]

    Gaur and U

    H. Gaur and U. A. Yajnik, Multi-charged moments and symmetry-resolved R´ enyi entropy of free compact boson for multiple disjoint intervals , JHEP 01, 042 (2024), doi:10.1007/JHEP01(2024)042, 2310.14186

    2024 arXiv

  31. [39]

    Saura-Bastida, A

    P. Saura-Bastida, A. Das, G. Sierra and J. Molina-Vilaplana, Categorical-symmetry resolved entanglement in conformal field theory, Phys. Rev. D 109(10), 105026 (2024), doi:10.1103/PhysRevD.109.105026, 2402.06322

    2024 arXiv

  32. [40]

    Y. Choi, B. C. Rayhaun and Y. Zheng, Noninvertible Symmetry-Resolved Affleck- Ludwig-Cardy Formula and Entanglement Entropy from the Boundary Tube Algebra (2024), 2409.02806

    2024

  33. [41]

    A. Das, J. Molina-Vilaplana and P. Saura-Bastida, Generalized symmetry resolution of entanglement in conformal field theory for twisted and anyonic sectors , Phys. Rev. D 110(12), 125005 (2024), doi:10.1103/PhysRevD.110.125005, 2409.02162

    2024 arXiv

  34. [42]

    Heymann and T

    J. Heymann and T. Quella, Revisiting the symmetry-resolved entanglement for non- invertible symmetries in 1+1d conformal field theories (2024), 2409.02315. 39 SciPost Physics Submission

    2024

  35. [43]

    Lukin, M

    A. Lukin, M. Rispoli, R. Schittko, M. E. Tai, A. M. Kaufman, S. Choi, V. Khemani, J. L´ eonard and M. Greiner,Probing entanglement in a many-body–localized system , Science 364(6437), 256–260 (2019), doi:10.1126/science.aau0818, 1805.09819

    2019 arXiv

  36. [44]

    Calabrese, J

    P. Calabrese, J. Dubail and S. Murciano, Symmetry-resolved entanglement entropy in Wess-Zumino-Witten models, JHEP 10, 067 (2021), doi:10.1007/JHEP10(2021)067, 2106.15946

    2021 arXiv

  37. [45]

    Murciano, G

    S. Murciano, G. Di Giulio and P. Calabrese, Entanglement and symmetry res- olution in two dimensional free quantum field theories , JHEP 08, 073 (2020), doi:10.1007/JHEP08(2020)073, 2006.09069

    2020 arXiv

  38. [46]

    Murciano, P

    S. Murciano, P. Calabrese and L. Piroli, Symmetry-resolved Page curves, Phys. Rev. D 106(4), 046015 (2022), doi:10.1103/PhysRevD.106.046015, 2206.05083

    2022 arXiv

  39. [47]

    Calabrese, M

    P. Calabrese, M. Collura, G. Di Giulio and S. Murciano, Full counting statis- tics in the gapped XXZ spin chain , EPL 129(6), 60007 (2020), doi:10.1209/0295- 5075/129/60007, 2002.04367

    2020 arXiv

  40. [48]

    Capizzi, O

    L. Capizzi, O. A. Castro-Alvaredo, C. De Fazio, M. Mazzoni and L. Santamar ´ ıa-Sanz, Symmetry resolved entanglement of excited states in quantum field theory. Part I. Free theories, twist fields and qubits, JHEP 12, 127 (2022), doi:10.1007/JHEP12(2022)127, 2203.12556

    2022 arXiv

  41. [49]

    Capizzi, C

    L. Capizzi, C. De Fazio, M. Mazzoni, L. Santamar ´ ıa-Sanz and O. A. Castro-Alvaredo, Symmetry resolved entanglement of excited states in quantum field theory. Part II. Numerics, interacting theories and higher dimensions , JHEP 12, 128 (2022), doi:10.1007/JHEP12(2022)128, 2206.12223

    2022 arXiv

  42. [50]

    Capizzi, M

    L. Capizzi, M. Mazzoni and O. A. Castro-Alvaredo, Symmetry resolved entanglement of excited states in quantum field theory. Part III. Bosonic and fermionic negativity , JHEP 06, 074 (2023), doi:10.1007/JHEP06(2023)074, 2302.02666

    2023 arXiv

  43. [51]

    Voit, One-dimensional fermi liquids , Rep

    J. Voit, One-dimensional fermi liquids , Rep. Progr. Phys. 58(9), 977 (1995), doi:10.1088/0034-4885/58/9/002

    1995 doi

  44. [52]

    A. M. Tsvelik, Quantum Field Theory in Condensed Matter Physics , Cambridge University Press, 2 edn., doi:10.1017/CBO9780511615832 (2003)

    2003 doi

  45. [53]

    Giamarchi, Quantum physics in one dimension , Clarendon Press, Oxford, doi:10.1093/acprof:oso/9780198525004.001.0001 (2004)

    T. Giamarchi, Quantum physics in one dimension , Clarendon Press, Oxford, doi:10.1093/acprof:oso/9780198525004.001.0001 (2004)

    2004

  46. [54]

    Laroche, G

    D. Laroche, G. Gervais, M. P. Lilly and J. L. Reno, 1d-1d coulomb drag signature of a luttinger liquid , Science 343(6171), 631 (2014), doi:10.1126/science.1244152

    2014 doi

  47. [55]

    S. Wang, S. Zhao, Z. Shi, F. Wu, Z. Zhao, L. Jiang, K. Watanabe, T. Taniguchi, A. Zettl, C. Zhou and F. Wang,Nonlinear luttinger liquid plasmons in semiconducting single-walled carbon nanotubes, Nature Mat. 19(9), 986 (2020), doi:10.1038/s41563- 020-0652-5

    2020 doi

  48. [56]

    Caux and P

    J.-S. Caux and P. Calabrese, Dynamical density-density correlations in the one-dimensional bose gas , Phys. Rev. A 74, 031605 (2006), doi:10.1103/PhysRevA.74.031605. 40 SciPost Physics Submission

    2006 doi

  49. [57]

    A. H. van Amerongen, J. J. P. van Es, P. Wicke, K. V. Kheruntsyan and N. J. van Druten, Yang-yang thermodynamics on an atom chip , Phys. Rev. Lett. 100, 090402 (2008), doi:10.1103/PhysRevLett.100.090402

    2008 doi

  50. [58]

    Pigneur, T

    M. Pigneur, T. Berrada, M. Bonneau, T. Schumm, E. Demler and J. Schmiedmayer, Relaxation to a phase-locked equilibrium state in a one- dimensional bosonic josephson junction , Physical Review Letters 120(17) (2018), doi:10.1103/physrevlett.120.173601, 1711.06635

    2018 arXiv

  51. [59]

    Schweigler, V

    T. Schweigler, V. Kasper, S. Erne, I. Mazets, B. Rauer, F. Cataldini, T. Langen, T. Gasenzer, J. Berges and J. Schmiedmayer, On solving quantum many-body prob- lems by experiment , Nature 545, 323 (2017), doi:10.1038/nature22310, 1505.03126

    2017 arXiv

  52. [60]

    Rauer, S

    B. Rauer, S. Erne, T. Schweigler, F. Cataldini, M. Tajik and J. Schmiedmayer, Recur- rences in an isolated quantum many-body system, Science 360(6386), 307–310 (2018), doi:10.1126/science.aan7938, 1705.08231

    2018 arXiv

  53. [61]

    B. Lake, A. M. Tsvelik, S. Notbohm, D. A. Tennant, T. G. Perring, M. Reehuis, C. Sekar, G. Krabbes and B. B¨ uchner, Confinement of fractional quantum number particles in a condensed-matter system , Nature Phys. 6(1), 50 (2009), doi:10.1038/nphys1462

    2009 doi

  54. [62]

    Hirobe, M

    D. Hirobe, M. Sato, T. Kawamata, Y. Shiomi, K. ichi Uchida, R. Iguchi, Y. Koike, S. Maekawa and E. Saitoh, One-dimensional spinon spin currents , Nature Phys. 13(1), 30 (2016), doi:10.1038/nphys3895

    2016 doi

  55. [63]

    Murciano, P

    S. Murciano, P. Calabrese and R. M. Konik, Generalized entanglement en- tropies in two-dimensional conformal field theory , JHEP 05, 152 (2022), doi:10.1007/JHEP05(2022)152, 2112.09000

    2022 arXiv

  56. [64]

    Calabrese, F

    P. Calabrese, F. H. L. Essler and A. M. L¨ auchli,Entanglement entropies of the quarter filled hubbard model , J. Stat. Mech. 2014(9), P09025 (2014), doi:10.1088/1742- 5468/2014/09/p09025, 1406.7477

    2014 arXiv

  57. [65]

    F. H. L. Essler, A. M. L¨ auchli and P. Calabrese, Shell-filling effect in the en- tanglement entropies of spinful fermions , Phys. Rev. Lett. 110, 115701 (2013), doi:10.1103/PhysRevLett.110.115701, 1211.2474

    2013 arXiv

  58. [66]

    F. C. Alcaraz, M. I. Berganza and G. Sierra, Entanglement of low-energy ex- citations in Conformal Field Theory , Phys. Rev. Lett. 106, 201601 (2011), doi:10.1103/PhysRevLett.106.201601, 1101.2881

    2011 arXiv

  59. [67]

    M. I. Berganza, F. C. Alcaraz and G. Sierra, Entanglement of excited states in critical spin chians , J. Stat. Mech. 1201, P01016 (2012), doi:10.1088/1742- 5468/2012/01/P01016, 1109.5673

    2012 arXiv

  60. [68]

    Taddia, F

    L. Taddia, F. Ortolani and T. P´ almai, Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains , J. Stat. Mech. 1609(9), 093104 (2016), doi:10.1088/1742-5468/2016/09/093104, 1606. 02667

    2016 doi

  61. [69]

    P´ almai,Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details , Phys

    T. P´ almai,Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details , Phys. Rev. B 90(16), 161404 (2014), doi:10.1103/PhysRevB.90.161404, 1406.3182. 41 SciPost Physics Submission

    2014 arXiv

  62. [70]

    Palmai, Entanglement Entropy from the Truncated Conformal Space , Phys

    T. Palmai, Entanglement Entropy from the Truncated Conformal Space , Phys. Lett. B 759, 439 (2016), doi:10.1016/j.physletb.2016.06.012, 1605.00444

    2016 arXiv

  63. [71]

    Zhang and M

    J. Zhang and M. A. Rajabpour, Excited state R´ enyi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states , JHEP 08, 106 (2021), doi:10.1007/JHEP08(2021)106, 2011.11006

    2021 arXiv

  64. [72]

    Zhang and M

    J. Zhang and M. A. Rajabpour, Universal R´ enyi entanglement entropy of quasiparticle excitations, EPL 135(6), 60001 (2021), doi:10.1209/0295-5075/ac130e, 2010.13973

    2021 arXiv

  65. [73]

    Zhang and M

    J. Zhang and M. A. Rajabpour, Subsystem distances between quasiparticle excited states, JHEP 07, 119 (2022), doi:10.1007/JHEP07(2022)119, 2202.11448

    2022 arXiv

  66. [74]

    Zhang and M

    J. Zhang and M. A. Rajabpour, Corrections to universal R´ enyi entropy in quasi- particle excited states of quantum chains , J. Stat. Mech. 2109, 093101 (2021), doi:10.1088/1742-5468/ac1f28, 2010.16348

    2021 arXiv

  67. [75]

    Zhang and M

    J. Zhang and M. A. Rajabpour, Entanglement of magnon excitations in spin chains , JHEP 02, 072 (2022), doi:10.1007/JHEP02(2022)072, 2109.12826

    2022 arXiv

  68. [76]

    Chen, W.-Z

    B. Chen, W.-Z. Guo, S. He and J.-q. Wu, Entanglement Entropy for Descendent Local Operators in 2D CFTs , JHEP 10, 173 (2015), doi:10.1007/JHEP10(2015)173, 1507.01157

    2015 arXiv

  69. [77]

    Zhang, P

    J. Zhang, P. Ruggiero and P. Calabrese, Subsystem Trace Distance in Quantum Field Theory , Phys. Rev. Lett. 122(14), 141602 (2019), doi:10.1103/PhysRevLett.122.141602, 1901.10993

    2019 arXiv

  70. [78]

    Ruggiero and P

    P. Ruggiero and P. Calabrese, Relative Entanglement Entropies in 1+1-dimensional conformal field theories, JHEP 02, 039 (2017), doi:10.1007/JHEP02(2017)039, 1612. 00659

    2017 doi

  71. [79]

    Mollabashi, N

    A. Mollabashi, N. Shiba, T. Takayanagi, K. Tamaoka and Z. Wei, Pseudo En- tropy in Free Quantum Field Theories , Phys. Rev. Lett. 126(8), 081601 (2021), doi:10.1103/PhysRevLett.126.081601, 2011.09648

    2021 arXiv

  72. [80]

    Nakata, T

    Y. Nakata, T. Takayanagi, Y. Taki, K. Tamaoka and Z. Wei, New holographic generalization of entanglement entropy , Phys. Rev. D 103(2), 026005 (2021), doi:10.1103/PhysRevD.103.026005, 2005.13801

    2021 arXiv

  73. [81]

    V. P. Yurov and A. B. Zamolodchikov, Truncated conformal space ap- proach to scaling Lee-Yang model , Int. J. Mod. Phys. A 5, 3221 (1990), doi:10.1142/S0217751X9000218X

    1990 doi

  74. [82]

    V. P. Yurov and A. B. Zamolodchikov, Truncated fermionic space approach to the critical 2-D Ising model with magnetic field , Int. J. Mod. Phys. A 6, 4557 (1991), doi:10.1142/S0217751X91002161

    1991 doi

  75. [83]

    A. J. A. James, R. M. Konik, P. Lecheminant, N. J. Robinson and A. M. Tsve- lik, Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods , Reports on Progress in Physics 81(4), 046002 (2018), d...

    2018 arXiv

  76. [84]

    Murciano, P

    S. Murciano, P. Calabrese and R. M. Konik, Postquantum Quench Growth of Renyi Entropies in Low-Dimensional Continuum Bosonic Systems , Phys. Rev. Lett. 129(10), 106802 (2022), doi:10.1103/PhysRevLett.129.106802, 2112.04412. 42 SciPost Physics Submission

    2022 arXiv

  77. [85]

    Haegeman, D

    J. Haegeman, D. Draxler, V. Stojevic, J. I. Cirac, T. J. Osborne and F. Ver- straete, Quantum Gross-Pitaevskii Equation , SciPost Phys. 3, 006 (2017), doi:10.21468/SciPostPhys.3.1.006

    2017 doi

  78. [86]

    Y. Choi, B. C. Rayhaun, Y. Sanghavi and S.-H. Shao, Remarks on boundaries, anomalies, and noninvertible symmetries , Phys. Rev. D 108(12), 125005 (2023), doi:10.1103/PhysRevD.108.125005, 2305.09713

    2023 arXiv

  79. [87]

    Cardy and P

    J. Cardy and P. Calabrese, Unusual Corrections to Scaling in Entanglement Entropy , J. Stat. Mech. 1004, P04023 (2010), doi:10.1088/1742-5468/2010/04/P04023, 1002. 4353

    2010 doi

  80. [88]

    Ohmori and Y

    K. Ohmori and Y. Tachikawa, Physics at the entangling surface , J. Stat. Mech. 1504, P04010 (2015), doi:10.1088/1742-5468/2015/04/P04010, 1406.4167. 43

    2015 arXiv

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