Entanglement asymmetry in the critical XXZ spin chain

• URL: http://arxiv.org/abs/2407.06427v1
• Date: Mon, 8 Jul 2024 22:16:22 GMT
• Title: Entanglement asymmetry in the critical XXZ spin chain
• Authors: Marco Lastres, Sara Murciano, Filiberto Ares, Pasquale Calabrese,
• Abstract summary: We study the explicit breaking of a $SU(2)$ symmetry to a $U(1)$ subgroup employing the entanglement asymmetry. We consider as specific model the critical XXZ spin chain, which breaks the $SU(2)$ symmetry of spin rotations except at the isotropic point.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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