Recent work has shown that the entanglement of finite-temperature eigenstates in chaotic quantum many-body local Hamiltonians can be accurately described by an ensemble of random states with an internal U(1) symmetry. We build upon this result to investigate the universal symmetry-breaking properties of such eigenstates. As a probe of symmetry breaking, we employ the entanglement asymmetry, a quantum information observable that quantifies the extent to which symmetry is broken in a subsystem. This measure enables us to explore the finer structure of finite-temperature eigenstates in terms of the U(1)-symmetric random state ensemble; in particular, the relation between the Hamiltonian and the effective conserved charge in the ensemble. Our analysis is supported by analytical calculations for the symmetric random states, as well as exact numerical results for the Mixed-Field Ising spin-1/2 chain, a paradigmatic model of quantum chaoticity.Recent work has shown that the entanglement of finite-temperature eigenstates in chaotic quantum many-body local Hamiltonians can be accurately described by an ensemble of random states with an internal U(1) symmetry. We build upon this result to investigate the universal symmetry-breaking properties of such eigenstates. As a probe of symmetry breaking, we employ the entanglement asymmetry, a quantum information observable that quantifies the extent to which symmetry is broken in a subsystem. This measure enables us to explore the finer structure of finite-temperature eigenstates in terms of the U(1)-symmetric random state ensemble; in particular, the relation between the Hamiltonian and the effective conserved charge in the ensemble. Our analysis is supported by analytical calculations for the symmetric random states, as well as exact numerical results for the Mixed-Field Ising spin-1/2 chain, a paradigmatic model of quantum chaoticity.

arXiv:2504.06146Physical review. EAug 13, 20259 citations

Spontaneous symmetry breaking in quantum systems

Franco Strocchi

ScholarpediaJan 1, 201211 citations

Non-Markovian equilibration controlled by symmetry breaking

Nicholas Chancellor, C. Petri, Stephan Haas

We study the effects of symmetry breaking on non-Markovian dynamics in various system-bath arrangements. It is shown that by breaking certain symmetries, features signaling non-Markovian time evolution disappear within a finite time ${t}_{g}$ . We demonstrate numerically that the scaling of ${t}_{g}$ with the symmetry breaking strength is different for various types of symmetry. We provide a mathematical explanation for these differences related to the spectrum of the total system-bath Hamiltonian and provide arguments that the scaling properties of ${t}_{g}$ should be universal.We study the effects of symmetry breaking on non-Markovian dynamics in various system-bath arrangements. It is shown that by breaking certain symmetries, features signaling non-Markovian time evolution disappear within a finite time ${t}_{g}$. We demonstrate numerically that the scaling of ${t}_{g}$ with the symmetry breaking strength is different for various types of symmetry. We provide a mathematical explanation for these differences related to the spectrum of the total system-bath Hamiltonian and provide arguments that the scaling properties of ${t}_{g}$ should be universal.

arXiv:1301.5624Physical Review BMay 24, 20135 citations

Symmetry and quantum systems

Anthony Brinton Wolbarst

Jan 1, 19776 citations

{t}_{g}

. We demonstrate numerically that the scaling of

{t}_{g}

with the symmetry breaking strength is different for various types of symmetry. We provide a mathematical explanation for these differences related to the spectrum of the total system-bath Hamiltonian and provide arguments that the scaling properties of

{t}_{g}

should be universal.