General theory for discrete symmetry-breaking equilibrium states

• URL: http://arxiv.org/abs/2303.18020v1
• Date: Fri, 31 Mar 2023 12:52:36 GMT
• Title: General theory for discrete symmetry-breaking equilibrium states
• Authors: \'Angel L. Corps, Armando Rela\~no
• Abstract summary: Spontaneous symmetry-breaking in phase transitions occurs when the system Hamiltonian is symmetric under a certain transformation. We show that when a discrete symmetry is spontaneously broken in a quantum system, the time evolution necessarily conserves two additional and non-commuting quantities.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Spontaneous symmetry-breaking in phase transitions occurs when the system Hamiltonian is symmetric under a certain transformation, but the equilibrium states observed in nature are not. Here, we prove that when a discrete symmetry is spontaneously broken in a quantum system, then the time evolution necessarily conserves two additional and non-commuting quantities, besides the one linked to the symmetry. This implies the existence of equilibrium states consisting in superpositions of macroscopic configurations. Then, we propose an experimental realization of such equilibrium states with the current state-of-the art in quantum technologies. Through numerical calculations, we show that they survive as very long-lived pre-thermal states, even very far away from the thermodynamic limit. Finally, we also show that a small symmetry-breaking perturbation in the Hamiltonian stabilizes the conservation of one of the two former quantities, implying that symmetry-breaking equilibrium states become stable even in small quantum systems.

Related papers

• Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect [0.0]
  We study the non-equilibrium dynamics of bosons in a two-dimensional optical lattice after a sudden quench from the superfluid phase to the free-boson regime.
  arXiv  Detail & Related papers  (2024-10-18T09:00:01Z)
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking [14.693424479293737]
  We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. We find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. We construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.
  arXiv  Detail & Related papers  (2024-10-16T18:00:00Z)
• Diagnosing Strong-to-Weak Symmetry Breaking via Wightman Correlators [20.572965801171225]
  Recent developments have extended the discussion of symmetry and its breaking to mixed states. We propose the Wightman correlator as an alternative diagnostic tool.
  arXiv  Detail & Related papers  (2024-10-12T02:04:40Z)
• Non-equilibrium dynamics of charged dual-unitary circuits [44.99833362998488]
  interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the centre of an intense multidisciplinary research effort. We show that one can introduce a class of solvable states, which extends that of generic dual unitary circuits. In contrast to the known class of solvable states, which relax to the infinite temperature state, these states relax to a family of non-trivial generalised Gibbs ensembles.
  arXiv  Detail & Related papers  (2024-07-31T17:57:14Z)
• Unraveling the emergence of quantum state designs in systems with symmetry [15.699822139827916]
  We study the emergence of state designs from the random generator states exhibiting symmetries. We find faster convergence of the trace distance during the early time evolution in comparison to the cases when the symmetry is broken. We expect our findings to pave the way for further exploration of deep thermalization and equilibration of closed and open quantum many-body systems.
  arXiv  Detail & Related papers  (2024-02-14T05:35:03Z)
• Asymmetry activation and its relation to coherence under permutation operation [53.64687146666141]
  A Dicke state and its decohered state are invariant for permutation. When another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation.
  arXiv  Detail & Related papers  (2023-11-17T03:33:40Z)
• Entanglement asymmetry and quantum Mpemba effect in the XY spin chain [0.0]
  Entanglement asymmetry is a quantity introduced to measure how much a symmetry is broken in a part of an extended quantum system. We study the entanglement asymmetry at equilibrium taking the ground state of the XY spin chain. We find that the power law governing symmetry restoration depends discontinuously on whether the initial state is critical or not.
  arXiv  Detail & Related papers  (2023-10-11T14:10:53Z)
• Non-Abelian symmetry can increase entanglement entropy [62.997667081978825]
  We quantify the effects of charges' noncommutation on Page curves. We show analytically and numerically that the noncommuting-charge case has more entanglement.
  arXiv  Detail & Related papers  (2022-09-28T18:00:00Z)
• Phase transitions as a manifestation of spontaneous unitarity violation [0.0]
  We argue that singling out a global choice for the ordered state is in fact forbidden under unitary time evolution. We argue that the observation of phase transitions in our everyday world presents a manifestation of the unitarity of quantum dynamics itself being spontaneously broken.
  arXiv  Detail & Related papers  (2022-09-09T12:32:13Z)
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles [0.0]
  We consider nonequilibrium time evolution in quantum spin chains after a global quench. Because of them, the stationary state emerging at infinite time can exhibit exceptional features. Among the exceptional properties, we find that, at late times, the excess of entropy of a spin block triggered by a local perturbation in the initial state grows logarithmically with the subsystem's length.
  arXiv  Detail & Related papers  (2022-05-04T17:55:10Z)
• Breaking strong symmetries in dissipative quantum systems: Bosonic atoms coupled to a cavity [0.0]
  In dissipative quantum systems, strong symmetries can lead to the existence of conservation laws and multiple steady states. We show that for ideal bosons coupled to the cavity multiple steady states exist and in each symmetry sector a dissipative phase transition occurs at a different critical point. We point out the phenomenon of dissipative freezing, the breaking of the conservation law at the level of individual realizations in the presence of the strong symmetry.
  arXiv  Detail & Related papers  (2021-02-04T10:54:31Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.