Translation symmetry restoration in integrable systems: the noninteracting case

Abstract

The study of symmetry restoration has recently emerged as a fruitful means to extract high-level information on the relaxation of quantum many-body systems. However, while the restoration of internal symmetries has been investigated intensively, that of spatial symmetries has hitherto only been considered in the context of random unitary circuits. Here we present a complementary study of translation symmetry restoration in integrable systems. In particular, we consider a one-dimensional chain of spinless, non-interacting fermions quenched from a $\nu >1$ shift invariant state, and follow the local restoration of one-site shift invariance using the Frobenius distance $\Delta F_A$ between the state on a subsystem and its symmetrised counterpart. Distinct from the case of random unitary circuits, where symmetry restoration occurs abruptly for times proportional to the subsystem size, we find that symmetry here is restored smoothly and over timescales of the order of the subsystem size squared. We also find that the so-called `quantum Mpemba effect' is readily observed. Most importantly, we show that - in contrast to the case of continuous internal symmetries - this discrete symmetry restoration is not qualitatively described by a quasiparticle picture for $\Delta F_A$, and therefore goes beyond the hydrodynamic description. Our results can be directly extended to higher dimensions.

10 pages, 5 figures

References in corpus (21)

• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Entanglement asymmetry as a probe of symmetry breaking
• Microscopic origin of the quantum Mpemba effect in integrable systems
• Symmetry restoration and quantum Mpemba effect in symmetric random circuits
• Entanglement asymmetry and quantum Mpemba effect in the XY spin chain
• Entanglement asymmetry and quantum Mpemba effect in two-dimensional free-fermion systems
• Lack of symmetry restoration after a quantum quench: an entanglement asymmetry study
• The quantum Mpemba effects
• Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
• Dynamics of charge fluctuations from asymmetric initial states
• Multiple crossing during dynamical symmetry restoration and implications for the quantum Mpemba effect
• Entangled multiplets, asymmetry, and quantum Mpemba effect in dissipative systems
• The quantum Mpemba effect in free-fermionic mixed states
• A universal formula for the entanglement asymmetry of matrix product states
• Translation symmetry restoration under random unitary dynamics
• An entanglement asymmetry study of black hole radiation
• Entanglement asymmetry in CFT and its relation to non-topological defects
• Non-equilibrium dynamics of charged dual-unitary circuits
• Confinement and Kink Entanglement Asymmetry on a Quantum Ising Chain
• Prethermalisation and Thermalisation in the Entanglement Dynamics
• Quench dynamics in lattices above one dimension: the free fermionic case

Cited by in corpus (3)

• Quantum Mpemba effect in long-range spin systems
• Dynamics of entanglement fluctuations and quantum Mpemba effect in the $\nu =1$ QSSEP model
• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices