A universal formula for the entanglement asymmetry of matrix product states

Abstract

Symmetry breaking is a fundamental concept in understanding quantum phases of matter, studied so far mostly through the lens of local order parameters. Recently, a new entanglement-based probe of symmetry breaking has been introduced under the name of \textit{entanglement asymmetry}, which has been employed to investigate the mechanism of dynamical symmetry restoration. Here, we provide a universal formula for the entanglement asymmetry of matrix product states with finite bond dimension, valid in the large volume limit. We show that the entanglement asymmetry of any compact -- discrete or continuous -- group depends only on the symmetry breaking pattern, and is not related to any other microscopic features.

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• Quantum Mpemba Effects from Symmetry Perspectives
• Symmetry restoration and quantum Mpemba effect in many-body localization systems
• Non-equilibrium dynamics of symmetry-resolved entanglement and entanglement asymmetry: Exact asymptotics in Rule 54
• Entanglement asymmetry in the critical XXZ spin chain
• Entanglement asymmetry and symmetry defects in boundary conformal field theory
• Entanglement asymmetry in conformal field theory and holography
• A simpler probe of the quantum Mpemba effect in closed systems
• Symmetry Breaking Dynamics in Quantum Many-Body Systems
• Entanglement asymmetry dynamics in random quantum circuits
• Symmetry breaking in chaotic many-body quantum systems at finite temperature
• Translation symmetry restoration in integrable systems: the noninteracting case
• Non-Abelian entanglement asymmetry in random states
• Disorder-Order Interface Propagating over the Ferromagnetic Ground State in the Transverse Field Ising Chain
• Breaking global symmetries with locality-preserving operations
• Quench dynamics of entanglement entropy under projective charge measurements: the free fermion case
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Quantum Pontus-Mpemba Effects in Real and Imaginary-time Dynamics
• Revisiting the symmetry-resolved entanglement for non-invertible symmetries in $1+1$d conformal field theories
• Extracting the symmetries of nonequilibrium quantum many-body systems
• Quantum geometric tensor determines the pure-state i.i.d. conversion rate in the resource theory of asymmetry for any compact Lie group
• Higher-form entanglement asymmetry and topological order
• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices