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Entanglement asymmetry in the critical XXZ spin chain

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arxiv 2407.06427 v1 pith:73XHWTZV submitted 2024-07-08 cond-mat.stat-mech hep-thquant-ph

Marco Lastres , Sara Murciano , Filiberto Ares , Pasquale Calabrese This is my paper · ORCID
classification cond-mat.stat-mechhep-thquant-ph
keywords asymmetryentanglementspinbrokenchaincriticalisotropicpoint
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abstract

We study the explicit breaking of a $SU(2)$ symmetry to a $U(1)$ subgroup employing the entanglement asymmetry, a recently introduced observable that measures how much symmetries are broken in a part of extended quantum systems. We consider as specific model the critical XXZ spin chain, which breaks the $SU(2)$ symmetry of spin rotations except at the isotropic point, and is described by the massless compact boson in the continuum limit. We examine the $U(1)$ subgroup of $SU(2)$ that is broken outside the isotropic point by applying conformal perturbation theory, which we complement with numerical simulations on the lattice. We also analyse the entanglement asymmetry of the full $SU(2)$ group. By relying on very generic scaling arguments, we derive an asymptotic expression for it.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Entanglement asymmetry in the gapped XYZ spin-$\frac12$ chain

    cond-mat.stat-mech 2026-07 conditional novelty 8.0 of 10

    In the gapped XYZ chain, the Rényi entanglement asymmetry of a large interval is ½ log(πℓχzz) + log n/(2(n−1)), with χzz/M computed from sine-Gordon form factors.

  2. Entanglement asymmetry dynamics in random quantum circuits

    cond-mat.stat-mech 2025-01 conditional novelty 6.0 of 10

    Subsystem entanglement asymmetry in random unitary circuits relaxes on the scrambling time for subsystems smaller than half the system, growing linearly with size in local circuits and logarithmically in non-local cir...

  3. Entanglement asymmetry in CFT with boundary symmetry breaking

    hep-th 2024-11 conditional novelty 6.0 of 10

    For a (1+1)-dimensional CFT with a symmetry-breaking boundary, the entanglement asymmetry of an interval anchored at the boundary tends to log|G| with an algebraic correction whose exponent is twice the smallest bound...

  4. Entanglement asymmetry and symmetry defects in boundary conformal field theory

    hep-th 2024-11 conditional novelty 6.0 of 10

    For 2D CFTs with boundary-only symmetry breaking, the entanglement asymmetry is log|G| with power-law corrections for finite groups, (dim G/2) log log(ℓ/ε) for compact Lie groups, and it drops from log|G| to 0 at t=ℓ/...

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