Duality and Symmetry Breaking (Analytical Study of Quantum Information and Related Fields)

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

Symmetry breaking and its applications to quantum information processing

彰忠櫻井, アキタダサクライ, SAKURAI Akitada

Mar 24, 20220 citations

Interplay of symmetry breaking and deconfinement in three-dimensional quantum vertex models

Shankar Balasubramanian, Daniel Bulmash, Victor M. Galitski +1 more

We construct a broad class of frustration-free quantum vertex models in $3+1$ dimensions ( $3+1\mathrm{D}$ ) whose ground states are weighted superpositions of classical 3D vertex model configurations. Our results are illustrated for diamond, cubic, and BCC lattices, but hold in general for 3D lattices with even coordination number. The corresponding classical vertex models have a ${\mathbb{Z}}_{2}$ gauge constraint enriched with a ${\mathbb{Z}}_{2}$ global symmetry. We study the interplay between these symmetries by exploiting exact wave function dualities and effective field theories. We find an exact gapless point which by duality is related to the Rokhsar-Kivelson (RK) point of $U(1)$ spin liquids. At this point, both the symmetry breaking and deconfinement order parameters exhibit long range order. The gapless point is additionally a self-dual point of a second duality that maps the ${\mathbb{Z}}_{2}$ deconfined and ${\mathbb{Z}}_{2}$ symmetry-broken phases to one another. For the BCC lattice vertex model, we find that gapless point is proximate to an unusual intermediate phase where symmetry breaking and deconfinement coexist.We construct a broad class of frustration-free quantum vertex models in $3+1$ dimensions ($3+1\mathrm{D}$) whose ground states are weighted superpositions of classical 3D vertex model configurations. Our results are illustrated for diamond, cubic, and BCC lattices, but hold in general for 3D lattices with even coordination number. The corresponding classical vertex models have a ${\mathbb{Z}}_{2}$ gauge constraint enriched with a ${\mathbb{Z}}_{2}$ global symmetry. We study the interplay between these symmetries by exploiting exact wave function dualities and effective field theories. We find an exact gapless point which by duality is related to the Rokhsar-Kivelson (RK) point of $U(1)$ spin liquids. At this point, both the symmetry breaking and deconfinement order parameters exhibit long range order. The gapless point is additionally a self-dual point of a second duality that maps the ${\mathbb{Z}}_{2}$ deconfined and ${\mathbb{Z}}_{2}$ symmetry-broken phases to one another. For the BCC lattice vertex model, we find that gapless point is proximate to an unusual intermediate phase where symmetry breaking and deconfinement coexist.

arXiv:2201.08856Physical review. B./Physical review. BNov 6, 20244 citations

Entanglement asymmetry and quantum Mpemba effect for Kramers-Wannier duality

Milo Vescovo, Pasquale Calabrese, Filiberto Ares

The Kramers-Wannier duality is the prototypical example of a non-invertible symmetry, yet little is known about its fate away from criticality and out of equilibrium. We introduce the Kramers-Wannier entanglement asymmetry, a quantum-information measure that quantifies the breaking of this non-invertible symmetry in the transverse-field Ising chain. We first investigate its equilibrium properties, showing that it exhibits a striking crossover between the ordered and disordered phases together with a pronounced dip at the critical point that becomes increasingly sharp with subsystem size. We then study quantum quenches from both gapped phases to criticality and show that the Kramers-Wannier entanglement asymmetry decays to zero, signaling the dynamical restoration of the non-invertible symmetry. Remarkably, we uncover the emergence of a quantum Mpemba effect: under suitable conditions, states initially farther from equilibrium restore the Kramers-Wannier symmetry faster than states prepared closer to it. We provide both analytical and numerical evidence for this phenomenon and identify the mechanism responsible for its occurrence. Our work establishes entanglement asymmetry as a powerful probe of non-invertible symmetries beyond equilibrium and opens new perspectives on the dynamics of dualities in quantum many-body systems.The Kramers-Wannier duality is the prototypical example of a non-invertible symmetry, yet little is known about its fate away from criticality and out of equilibrium. We introduce the Kramers-Wannier entanglement asymmetry, a quantum-information measure that quantifies the breaking of this non-invertible symmetry in the transverse-field Ising chain. We first investigate its equilibrium properties, showing that it exhibits a striking crossover between the ordered and disordered phases together with a pronounced dip at the critical point that becomes increasingly sharp with subsystem size. We then study quantum quenches from both gapped phases to criticality and show that the Kramers-Wannier entanglement asymmetry decays to zero, signaling the dynamical restoration of the non-invertible symmetry. Remarkably, we uncover the emergence of a quantum Mpemba effect: under suitable conditions, states initially farther from equilibrium restore the Kramers-Wannier symmetry faster than states prepared closer to it. We provide both analytical and numerical evidence for this phenomenon and identify the mechanism responsible for its occurrence. Our work establishes entanglement asymmetry as a powerful probe of non-invertible symmetries beyond equilibrium and opens new perspectives on the dynamics of dualities in quantum many-body systems.

cond-mat.stat-mechCross-listedarXiv:2607.21226Jul 24, 20260 citations

Quantum information and fields

Mohammad H. Ansari

Jan 1, 20170 citations

The Physics of Quantum Information

Dirk Bouwmeester, ARTUR K. EKERT, Anton Zeilinger

Springer eBooksJan 1, 20001,982 citations

We construct a broad class of frustration-free quantum vertex models in

3+1

dimensions (

3+1\mathrm{D}

) whose ground states are weighted superpositions of classical 3D vertex model configurations. Our results are illustrated for diamond, cubic, and BCC lattices, but hold in general for 3D lattices with even coordination number. The corresponding classical vertex models have a

{\mathbb{Z}}_{2}

gauge constraint enriched with a

{\mathbb{Z}}_{2}

global symmetry. We study the interplay between these symmetries by exploiting exact wave function dualities and effective field theories. We find an exact gapless point which by duality is related to the Rokhsar-Kivelson (RK) point of

U(1)

spin liquids. At this point, both the symmetry breaking and deconfinement order parameters exhibit long range order. The gapless point is additionally a self-dual point of a second duality that maps the

{\mathbb{Z}}_{2}

deconfined and

{\mathbb{Z}}_{2}

symmetry-broken phases to one another. For the BCC lattice vertex model, we find that gapless point is proximate to an unusual intermediate phase where symmetry breaking and deconfinement coexist.