Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2102.09325 · Physical review. B./Physical review. B

Plateau transitions of a spin pump and bulk-edge correspondence

Yoshihito Kuno, Yasuhiro Hatsugai

Published Jul 9, 2021• 9 citations
arXivHTMLPDF

Abstract

Sequential plateau transitions of quantum spin chains ($S=1$, 3/2, 2, and 3) are demonstrated by a spin pump using dimerization and a staggered magnetic field as synthetic dimensions. The bulk is characterized by the Chern number associated with the boundary twist and the pump protocol as the time. It counts the number of critical points in the loop that is specified by the ${Z}_{2}$ Berry phases. With an open boundary condition, the discontinuity of the spin weighted center of mass due to emergent effective edge spins also characterizes the pump as the bulk-edge correspondence. It requires extra level crossings in the pump as a superselection rule that is consistent with the valence bond solid picture.

DOI
10.1103/physrevb.104.045113

Related papers

Topological pump and its plateau transitions of $N$-leg spin ladder

Yamamoto, Kota, Yoshihito Kuno, Tomonari Mizoguchi +2 more

A topological pump on an $N\textrm{-}$leg spin ladder is discussed by introducing spatial clusterization whose adiabatic limit is a set of $2N\textrm{-}$site staircase clusters. We set a pump path in the parameter space that connects two different symmetry protected topological phases. By introducing a symmetry breaking staggered magnetic field, the system is always gapped during the pump. In the topological pump {thus obtained}, the bulk Chern number is given by the number of the critical points enclosed by the pump path. Plateau transitions characterized by the Chern number are demonstrated associated with deformation of the pump path. We find that there are $N$ critical points enclosed by the pump path for the $N\textrm{-}$leg ladder. The ground state phase diagram without symmetry breaking terms is numerically investigated by using the quantized Berry phase. We also discuss the physical picture of edge states in the diagonal boundary, and numerically demonstrate the bulk-edge correspondence for $N=2,3$ cases.

arXiv:2505.01153•May 2, 2025•0 citations

Topological pump and bulk-edge-correspondence in an extended Bose-Hubbard model

Yoshihito Kuno, Yasuhiro Hatsugai

An extended Bose-Hubbard model (EBHM) with three- and four-body constraints can be feasible in cold atoms in an optical lattice. A rich phase structure including various symmetry-protected topological (SPT) phases is obtained numerically with suitable parameter settings and particle filling. The SPT phase is characterized by the Berry phase as a local topological order parameter and the structure of the entanglement spectrum (ES). Based on the presence of various topological phases, separated by gapless phase boundaries, the EBHM exhibits various bosonic topological pumps, which are constructed by connecting the different SPT phases without gap closing. The bulk topological pumps exhibit the plateau transitions characterized by many-body Chern numbers. For the system with boundary, the center of mass (CoM) under grand canonical ensemble elucidates the contributions of multiple edge states and reveals the topology of the system. We demonstrate that the interacting bosonic pumps obey the bulk-edge correspondence.

arXiv:2107.09498•Physical review. B./Physical review. B•Sep 29, 2021•9 citations

Topological pump of SU(Q) quantum chain and Diophantine equation

Yasuhiro Hatsugai, Yoshihito Kuno

We propose a general construction scheme of topological pump for correlated systems with local gauge symmetry. The bulk-edge correspondence is one of its natural consequences. As a concrete example, an $SU(Q)$ quantum chain associated with a local ${[U(1)]}^{\ensuremath{\bigotimes}Q}$ gauge invariance of colored fermions is discussed in detail. The $SU(Q)$ invariant dimer phases are characterized by the ${Z}_{Q}$ Berry phases as a topological order parameter with a $d$-dimensional twist space ($d=Q\ensuremath{-}1$) as a synthetic Brillouin zone. By inclusion of the symmetry breaking perturbation specified by a rational parameter $\mathrm{\ensuremath{\Phi}}=P/Q$, the pump that encloses around the phase boundary, is characterized by the $Q$ Chern numbers associated with the currents due to uniform infinitesimal twists. The analysis of the systems under the open/periodic/twisted boundary conditions clarifies the bulk-edge correspondence of the pump where the large gauge transformation generated by the center-of-mass (CoM) plays a central role. An explicit formula for the Chern number is given by using the Diophantine equation. Numerical demonstrations by the exact diagonalization and the DMRG for finite systems ($Q=3,4,$ and 5) have been presented to confirm the general discussions for low-energy spectra, edge states, CoM's, Chern numbers, and the bulk-edge correspondence. A modified Lieb-Schultz-Mattis type argument for the general $SU(Q)$ quantum chain is also mentioned.

arXiv:2210.11646•Physical review. B./Physical review. B•Jun 2, 2023•5 citations

Mapping Chern numbers in quasi-periodic interacting spin chains

Yifei Liu, Emil V. Prodan

Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary dimension that are characterized by first and higher order Chern numbers. In the present work, we use those findings to generate topological phases at finite magnetization densities that carry first Chern numbers. Given the reduced dimensionality of the spin chains, this provides a unique opportunity to investigate the bulk-boundary correspondence as well as the stability and quantization of the Chern number in the presence of interactions. The later is reformulated using a torus action on the algebra of observables and its quantization and stability is confirmed by numerical simulations. The relations between Chern values and the observed edge spectrum are also discussed.

arXiv:2010.06171•Oct 12, 2020•1 citation

Topological Domain-Wall Pump with Z 2 Spontaneous Symmetry Breaking

Yoshihito Kuno, Yasuhiro Hatsugai

A domain-wall pump by an extended cluster model of S=1/2 spins is proposed with local U(1) gauge invariance. In contrast to the conventional pump, the current and the gauge field are defined on sites instead of links. Its snapshot ground state is gapped and doubly degenerated due to Z_{2} invariance, which is broken by an infinitesimal boundary magnetic field. The ground state associated with the spontaneous symmetry breaking is, at the same time, symmetry-protected with additional spatial inversion that is characterized by the Z_{2} Berry phase defined by the twist on the boundary site. We investigate the topological domain-wall pump with and without boundaries. The topological pump associated with the inversion symmetry-breaking path induces a nontrivial Chern number of bulk and a singular behavior of edge states of the domain wall. Generalization to the multispin interaction is also explicitly given. These extended quantum degrees of freedom are prominent qubits that are topologically protected.

Physical Review Letters•Jun 5, 2025•1 citation

Berry phase investigation of spin- S ladders

Natalia Chepiga, Frédéric Michaud, Frédéric Mila

We investigate the properties of antiferromagnetic spin-$S$ ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time-reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of nonfrustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains, with the surprising conclusion that, at least far enough from dimerized chains, they define different domains in parameter space. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated with a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated with a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes $2S$ times. By analogy with the fully frustrated ladder, these changes are interpreted as crossovers between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to $2S$ in the weak rung limit. This interpretation is further supported by the observation that these crossovers turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin $2S$ impurity.

arXiv:1304.0392•Physical Review B•Nov 19, 2013•19 citations
Sequential plateau transitions of quantum spin chains (S=1S=1S=1, 3/2, 2, and 3) are demonstrated by a spin pump using dimerization and a staggered magnetic field as synthetic dimensions. The bulk is characterized by the Chern number associated with the boundary twist and the pump protocol as the time. It counts the number of critical points in the loop that is specified by the Z2{Z}_{2}Z2​ Berry phases. With an open boundary condition, the discontinuity of the spin weighted center of mass due to emergent effective edge spins also characterizes the pump as the bulk-edge correspondence. It requires extra level crossings in the pump as a superselection rule that is consistent with the valence bond solid picture.
Topological pump and its plateau transitions of NNN-leg spin ladder
A topological pump on an N-N\textrm{-}N-leg spin ladder is discussed by introducing spatial clusterization whose adiabatic limit is a set of 2N-2N\textrm{-}2N-site staircase clusters. We set a pump path in the parameter space that connects two different symmetry protected topological phases. By introducing a symmetry breaking staggered magnetic field, the system is always gapped during the pump. In the topological pump {thus obtained}, the bulk Chern number is given by the number of the critical points enclosed by the pump path. Plateau transitions characterized by the Chern number are demonstrated associated with deformation of the pump path. We find that there are NNN critical points enclosed by the pump path for the N-N\textrm{-}N-leg ladder. The ground state phase diagram without symmetry breaking terms is numerically investigated by using the quantized Berry phase. We also discuss the physical picture of edge states in the diagonal boundary, and numerically demonstrate the bulk-edge correspondence for N=2,3N=2,3N=2,3 cases.
An extended Bose-Hubbard model (EBHM) with three- and four-body constraints can be feasible in cold atoms in an optical lattice. A rich phase structure including various symmetry-protected topological (SPT) phases is obtained numerically with suitable parameter settings and particle filling. The SPT phase is characterized by the Berry phase as a local topological order parameter and the structure of the entanglement spectrum (ES). Based on the presence of various topological phases, separated by gapless phase boundaries, the EBHM exhibits various bosonic topological pumps, which are constructed by connecting the different SPT phases without gap closing. The bulk topological pumps exhibit the plateau transitions characterized by many-body Chern numbers. For the system with boundary, the center of mass (CoM) under grand canonical ensemble elucidates the contributions of multiple edge states and reveals the topology of the system. We demonstrate that the interacting bosonic pumps obey the bulk-edge correspondence.
We propose a general construction scheme of topological pump for correlated systems with local gauge symmetry. The bulk-edge correspondence is one of its natural consequences. As a concrete example, an SU(Q)SU(Q)SU(Q) quantum chain associated with a local ${[U(1)]}^{\ensuremath{\bigotimes}Q}$ gauge invariance of colored fermions is discussed in detail. The SU(Q)SU(Q)SU(Q) invariant dimer phases are characterized by the ZQ{Z}_{Q}ZQ​ Berry phases as a topological order parameter with a ddd-dimensional twist space ($d=Q\ensuremath{-}1$) as a synthetic Brillouin zone. By inclusion of the symmetry breaking perturbation specified by a rational parameter $\mathrm{\ensuremath{\Phi}}=P/Q$, the pump that encloses around the phase boundary, is characterized by the QQQ Chern numbers associated with the currents due to uniform infinitesimal twists. The analysis of the systems under the open/periodic/twisted boundary conditions clarifies the bulk-edge correspondence of the pump where the large gauge transformation generated by the center-of-mass (CoM) plays a central role. An explicit formula for the Chern number is given by using the Diophantine equation. Numerical demonstrations by the exact diagonalization and the DMRG for finite systems (Q=3,4,Q=3,4,Q=3,4, and 5) have been presented to confirm the general discussions for low-energy spectra, edge states, CoM's, Chern numbers, and the bulk-edge correspondence. A modified Lieb-Schultz-Mattis type argument for the general SU(Q)SU(Q)SU(Q) quantum chain is also mentioned.
Quasi-periodic quantum spin chains were recently found to support many topological phases in the finite magnetization sectors. They can simulate strong topological phases from class A in arbitrary dimension that are characterized by first and higher order Chern numbers. In the present work, we use those findings to generate topological phases at finite magnetization densities that carry first Chern numbers. Given the reduced dimensionality of the spin chains, this provides a unique opportunity to investigate the bulk-boundary correspondence as well as the stability and quantization of the Chern number in the presence of interactions. The later is reformulated using a torus action on the algebra of observables and its quantization and stability is confirmed by numerical simulations. The relations between Chern values and the observed edge spectrum are also discussed.
A domain-wall pump by an extended cluster model of S=1/2 spins is proposed with local U(1) gauge invariance. In contrast to the conventional pump, the current and the gauge field are defined on sites instead of links. Its snapshot ground state is gapped and doubly degenerated due to Z_{2} invariance, which is broken by an infinitesimal boundary magnetic field. The ground state associated with the spontaneous symmetry breaking is, at the same time, symmetry-protected with additional spatial inversion that is characterized by the Z_{2} Berry phase defined by the twist on the boundary site. We investigate the topological domain-wall pump with and without boundaries. The topological pump associated with the inversion symmetry-breaking path induces a nontrivial Chern number of bulk and a singular behavior of edge states of the domain wall. Generalization to the multispin interaction is also explicitly given. These extended quantum degrees of freedom are prominent qubits that are topologically protected.
We investigate the properties of antiferromagnetic spin-SSS ladders with the help of local Berry phases defined by imposing a twist on one or a few local bonds. In gapped systems with time-reversal symmetry, these Berry phases are quantized, hence able in principle to characterize different phases. In the case of a fully frustrated ladder where the total spin on a rung is a conserved quantity that changes abruptly upon increasing the rung coupling, we show that two Berry phases are relevant to detect such phase transitions: the rung Berry phase defined by imposing a twist on one rung coupling, and the twist Berry phase defined by twisting the boundary conditions along the legs. In the case of nonfrustrated ladders, we have followed the fate of both Berry phases when interpolating between standard ladders and dimerized spin chains, with the surprising conclusion that, at least far enough from dimerized chains, they define different domains in parameter space. A careful investigation of the spin gap and of edge states shows that a change of twist Berry phase is associated with a quantum phase transition at which the bulk gap closes, and at which, with appropriate boundary conditions, edge states appear or disappear, while a change of rung Berry phase is not necessarily associated with a quantum phase transition. The difference is particularly acute for regular ladders, in which the twist Berry phase does not change at all upon increasing the rung coupling from zero to infinity while the rung Berry phase changes 2S2S2S times. By analogy with the fully frustrated ladder, these changes are interpreted as crossovers between domains in which the rungs are in different states of total spin from 0 in the strong rung limit to 2S2S2S in the weak rung limit. This interpretation is further supported by the observation that these crossovers turn into real phase transitions as a function of rung coupling if one rung is strongly ferromagnetic, or equivalently if one rung is replaced by a spin 2S2S2S impurity.