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REVIEW 2 major objections 1 minor 69 references

Dissipation splits the Mott transition in one dimension

T0 review · 2 major / 1 minor · reviewed 2026-07-02 · grok-4.3

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Pith's one-line read Dissipation creates an intermediate phase that splits the one-dimensional Mott transition into two distinct critical points.

desk verdict The paper claims dissipation splits the 1D Mott transition via a new intermediate gapless compressible phase with zero stiffness, but the control of the bosonized theory for s<3/2 is the untested core. read the letter →

arxiv 2607.00086 v1 pith:OYUQHMKB submitted 2026-06-30 cond-mat.str-el cond-mat.stat-mech

Oscar Bouverot-Dupuis , Alberto Rosso , Laura Foini This is my paper · ORCID
classification cond-mat.str-elcond-mat.stat-mech
keywords Motttransitiondissipativebathsone-dimensionalsystemsLuttingerliquidBerezinskii-Kosterlitz-Thoulesscommensurate-incommensuratebosonisation
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

In isolated one-dimensional systems the Mott transition directly separates a conducting Luttinger liquid from a Mott insulator. When local dissipative baths couple to the density and the bath exponent s lies below 3/2, an intermediate dissipative phase appears that remains compressible and gapless yet possesses zero superfluid stiffness. This phase intervenes between the Luttinger liquid and the Mott insulator, converting the single transition into a Berezinskii-Kosterlitz-Thouless transition followed by a new commensurate-incommensurate transition. The universality class of the second transition depends on s, with continuously varying exponents for 1 < s < 3/2 and a limiting case of vanishing exponents for s < 1. Monte Carlo simulations confirm the analytic predictions obtained from bosonisation after exact integration of the bath.

What carries the argument

Bosonisation combined with exact integration of the bath degrees of freedom, which produces an effective long-range interaction that stabilizes the intermediate dissipative phase and splits the transition.

What would settle it

Quantum Monte Carlo simulations that either find no intermediate compressible gapless phase with zero stiffness or measure critical exponents different from the predicted s-dependent values at the DP-MI transition.

Watch

Extended reading notes

Core claim

Rather than undergoing a direct LL-MI transition, the system develops an intermediate dissipative phase (DP) that is compressible and gapless, yet has zero superfluid stiffness. As a result, the conventional Mott transition splits into two distinct critical phenomena: a Berezinskii-Kosterlitz-Thouless transition from the LL to the DP, followed by a new commensurate-incommensurate transition from the DP to the MI. For 1 < s < 3/2 the critical exponents vary continuously with the bath exponent as β = ν = 1/z = s-1, while for s < 1 the transition is governed by β = ν = 1/z = 0 and the doping vanishes sharper than any power law.

Load-bearing premise

Bosonisation together with exact bath integration remains valid and captures the low-energy physics when the bath exponent satisfies s less than 3/2 and the coupling is strictly local in density.

Editorial extensions

If this is right

  • For bath exponents s below 3/2 the Mott transition splits into a Berezinskii-Kosterlitz-Thouless transition followed by a new commensurate-incommensurate transition.
  • The dissipative phase is compressible and gapless but has vanishing superfluid stiffness.
  • Critical exponents of the dissipative-phase to Mott-insulator transition vary continuously with s when 1 < s < 3/2.
  • For s below 1 the doping vanishes faster than any power law across the second transition.

Reading between the lines

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

  • Similar splitting may occur in other open quantum systems where dissipation couples locally to a conserved density.
  • Cold-atom experiments with tunable engineered baths could directly observe the two separate critical points and the intermediate phase.
  • The new commensurate-incommensurate universality class might appear in related models with long-range interactions generated by baths.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript claims that local dissipative baths coupled to density in one dimension split the conventional Luttinger-liquid to Mott-insulator transition for bath exponents s < 3/2. Bosonization plus exact bath integration yields an intermediate dissipative phase (DP) that remains compressible and gapless but possesses zero superfluid stiffness; the transition therefore decomposes into a Berezinskii-Kosterlitz-Thouless line from LL to DP followed by a new commensurate-incommensurate transition from DP to MI. The paper derives the universality class of the latter transition, obtaining continuously varying exponents β = ν = 1/z = s − 1 for 1 < s < 3/2 and β = ν = 1/z = 0 for s < 1, and reports quantitative agreement with state-of-the-art Monte Carlo simulations.

Significance. If the central claims are correct, the work demonstrates that dissipation can qualitatively restructure a paradigmatic quantum phase transition, producing an intermediate phase with unusual transport properties and a new universality class whose exponents vary continuously with the bath spectrum. The exact integration of the bath degrees of freedom and the reported quantitative Monte Carlo support constitute concrete strengths that would make the result a notable addition to the literature on open quantum systems.

major comments (2)
  1. [Abstract / derivation of effective action] Abstract and the bosonization-plus-bath-integration derivation: the existence of the intermediate DP as a stable, compressible, gapless phase with vanishing stiffness rests on the assumption that the dissipative kernel |ω|^s |∂φ(ω)|^2 only renormalizes Luttinger parameters for s < 3/2 without generating relevant operators that would either open a gap or restore finite stiffness. No explicit renormalization-group stability analysis or operator-content check of the resulting quadratic theory is supplied; this is load-bearing for the claimed splitting of the Mott transition.
  2. [Monte Carlo simulations] Monte Carlo section: the quantitative support for the predicted exponents and phase boundaries is presented as independent validation, yet the manuscript does not report the precise fitting procedures, data-exclusion criteria, or finite-size scaling ansatz used to extract β, ν, and z from the simulations. Without these details the claimed agreement cannot be assessed at the level required to confirm the new commensurate-incommensurate universality.
minor comments (1)
  1. The notation for the dissipative kernel and the definition of the bath exponent s could be stated more explicitly in the main text to aid readers who are not already familiar with Caldeira-Leggett-type baths.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each major point below and will revise the manuscript to incorporate the requested clarifications.

read point-by-point responses

  1. Referee: [Abstract / derivation of effective action] Abstract and the bosonization-plus-bath-integration derivation: the existence of the intermediate DP as a stable, compressible, gapless phase with vanishing stiffness rests on the assumption that the dissipative kernel |ω|^s |∂φ(ω)|^2 only renormalizes Luttinger parameters for s < 3/2 without generating relevant operators that would either open a gap or restore finite stiffness. No explicit renormalization-group stability analysis or operator-content check of the resulting quadratic theory is supplied; this is load-bearing for the claimed splitting of the Mott transition.

    Authors: The effective action after exact bath integration is quadratic (Luttinger liquid terms plus the |ω|^s dissipative kernel). Within bosonization the only additional operator is the standard umklapp cosine, whose relevance is controlled by the renormalized K. Dissipation drives the system into a regime where this operator is irrelevant while the |ω|^s term enforces vanishing stiffness, yielding a compressible gapless phase. We acknowledge, however, that an explicit RG stability analysis of the quadratic fixed point was not supplied. We will add a concise RG section (or appendix) deriving the flow equations for K and the dissipative coefficient and confirming the absence of relevant operators for s < 3/2. This will be included in the revised manuscript. revision: yes

  2. Referee: [Monte Carlo simulations] Monte Carlo section: the quantitative support for the predicted exponents and phase boundaries is presented as independent validation, yet the manuscript does not report the precise fitting procedures, data-exclusion criteria, or finite-size scaling ansatz used to extract β, ν, and z from the simulations. Without these details the claimed agreement cannot be assessed at the level required to confirm the new commensurate-incommensurate universality.

    Authors: We agree that the numerical details must be reported for reproducibility. In the revised version we will expand the Monte Carlo section with: (i) the explicit finite-size scaling ansätze used for stiffness, compressibility and order parameter, (ii) the precise data-exclusion criteria (e.g., discarding points within a stated distance of the estimated critical point), and (iii) the fitting protocol, including system-size ranges and the data-collapse or direct-fit procedures employed to extract β, ν and z. These additions will allow independent verification of the reported quantitative agreement. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation relies on standard bosonization and bath integration

full rationale

The paper's central derivation proceeds from bosonization of the 1D bosons plus exact integration of the local dissipative bath, yielding an effective quadratic action with a |ω|^s kernel. This leads to the claimed intermediate dissipative phase and split transitions without any parameter fitting, self-definition of observables, or load-bearing self-citations. Monte Carlo results are presented as an external numerical check rather than as input to the analytic claims. No step reduces the output to the input by construction.

Assumptions & free parameters 1 free parameters · 1 assumptions · 0 invented entities

The central claim rests on the validity of bosonisation for the dissipative system and on the assumption that the bath spectrum is characterized by a single exponent s that controls all low-energy behavior.

free parameters (1)
  • bath exponent s
    Single parameter that defines the regimes s<3/2, 1<s<3/2 and s<1 and sets the critical exponents.
assumptions (1)
  • domain assumption Bosonisation plus exact integration of bath degrees of freedom accurately describes the low-energy effective theory for local density coupling.
    Invoked to derive the phase diagram and the effective field theory for the second transition.

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Cite this review

Pith. "Pith review of Dissipation splits the Mott transition in one dimension." pith.science (2026). https://pith.science/paper/OYUQHMKB

@misc{pith2026260700086,
  author       = {Pith},
  title        = {Pith review of: Dissipation splits the Mott transition in one dimension},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OYUQHMKB}},
  note         = {Machine review of arXiv:2607.00086}
}
abstract

Understanding how dissipation modifies quantum phase transitions is a central challenge in many-body physics. A paradigmatic example is the one-dimensional Mott transition, which in isolated systems separates a conducting Luttinger liquid (LL) from a Mott insulator (MI). Here, we study the fate of this transition in the presence of dissipative baths locally coupled to the density. Using bosonisation and an exact integration of the bath degrees of freedom, we show that dissipation fundamentally reshapes the phase diagram for bath exponents $s<3/2$, where $s$ characterises the low-energy bath spectrum. Rather than undergoing a direct LL-MI transition, the system develops an intermediate dissipative phase (DP) that is compressible and gapless, yet has zero superfluid stiffness. As a result, the conventional Mott transition splits into two distinct critical phenomena: a Berezinskii-Kosterlitz-Thouless transition from the LL to the DP, followed by a new commensurate-incommensurate transition from the DP to the MI. We derive an effective field theory for the latter transition and characterize its universality. For $1<s<3/2$, the critical exponents vary continuously with the bath exponent as $\beta=\nu=1/z=s-1$, while for $s<1$ the transition is governed by $\beta=\nu=1/z=0$ and the doping vanishes sharper than any power law. State-of-the-art Monte Carlo simulations quantitatively support our predictions. These results demonstrate that dissipation can qualitatively alter the nature of the Mott transition and generate novel critical behaviour in strongly correlated one-dimensional systems.

Figures

Figures reproduced from arXiv: 2607.00086 by the authors.

Figure 1
Figure 1. Schematic representation of the dissipative sys [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Bosonized representation of density excita [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Phase diagrams for s < 1 (top), 1 < s < 3/2 (middle) and s > 3/2 (bottom). The blue transition lines and the tip of the lobe belong to the BKT universality class. The magenta lines are second order commensurate￾incommensurate transitions with exponents depending on the bath exponent s. the bath exponent is larger or smaller than the threshold value sc = 3 2 . (15) For s > sc ( [PITH_FULL_IMAGE:figures/full_fig_p005… view at source ↗
Figures from the paper (8 more)
Figure 4
Figure 4. Figure 4: Typical field configurations ϕ(x, τ ) on a lattice of size 256 × 256. The colourmap encodes the value of the field ϕ with darker blue signifying higher values of ϕ. Each kink has an amplitude π/2. We have highlighted one kink for each of the three rightmost plots. From…
Figure 5
Figure 5. Figure 5: C/IC transitions at s = 1.25 (top) and s = 1.75 (bottom) for increasing L = β. Top: MI to DP transition. The MI is at µ < µc ≃ 0.8, while the DP is at µ > µc. Bottom: MI to LL transition. The MI is at µ < µc ≃ 0.5, while the LL is at µ > µc. From left to right: doping …
Figure 6
Figure 6. Figure 6: At infinitesimal densities, the kinks become [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Typical configurations X(τ ) obtained from Monte Carlo simulations of Eq. (56) with α = 1. The offsets are arbitrary. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]
Figure 8
Figure 8. Figure 8: Left: inverse propagator G −1 (ωn) = 1/⟨|X(ωn)| 2 ⟩ for the frequencies ωn = 2πn/β from Monte Carlo simulations of Eq. (56) with β = 217 , α = 1 and varying s. The dashed lines capture the low￾frequency power-law behaviours. Right: roughness expo￾nent ζ. The blue point…
Figure 9
Figure 9. Figure 9: Finite-size scaling collapse for the compressibility [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: BKT finite-size scaling collapse for KR = π √ρsκ at the DP to LL transition with s = 1. Only α is varied while K, u, g, s, µ = 0.6, 1, 0, 1, 1. The optimal fitting parameters L0 = 1.33(3) and αc = 0.0605(5) were determined through the deviation from a local linear fit…
Figure 11
Figure 11. Figure 11: Integrated autocorrelation times tint as a function of system size β for s = 1 and α = 1. The three scalings correspond to the Metropolis–Hastings al￾gorithm (Met), the naive event-chain Monte Carlo algo￾rithm (ECMC), and the ECMC adapted to long-range interactions (E…

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