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:cond-mat/0607024 · Journal of Physics Condensed Matter

Quantized Berry phases for a local characterization of spin liquids in frustrated spin systems

Yasuhiro Hatsugai

Published Mar 23, 2007• 41 citations
arXivHTMLPDF

Abstract

Recently, by using quantized Berry phases, a prescription for a local characterization of gapped topological insulators has been given (Hatsugai 2006 Preprint cond-mat/0603230). It requires that the ground state is gapped and is invariant under some anti-unitary operation. A spin liquid which is realized as a unique ground state of the Heisenberg spin system with frustrations is a typical target system, since pairwise exchange couplings are always time-reversal invariants even with frustrations. As for a generic Heisenberg model with a finite excitation gap, we locally modify the Hamiltonian by a continuous SU (2) twist only at a specific link and define the Berry connection by the derivative. Then the Berry phase evaluated by the entire many-spin wavefunction is used to define the local topological order parameter at the link. We numerically apply this scheme for several spin liquids and show its physical validity. For example, it implies that the Haldane phase of the S = 1 chains is characterized by uniform π quantized Berry phases.

DOI
10.1088/0953-8984/19/14/145209

Related papers

Quantized Berry Phases for a Local Characterization of Spin Liquids in Frustrated Spin Systems

Yasuhiro Hatsugai

Recently by using quantized Berry phases, a prescription for a local characterization of gapped topological insulators is given [1].One requires the ground state is gapped and is invariant under some anti-unitary operation.A spin liquid which is realized as a unique ground state of the Heisenberg spin system with frustrations is a typical target system, since pairwise exchange couplings are always time-reversal invariants even with frustrations.As for a generic Heisenberg model with a finite excitation gap, we locally modify the Hamiltonian by a continuous SU (2) twist only at a specific link and define the Berry connection by the derivative.Then the Berry phase evaluated by the entire many-spin wavefunction is used to define the local topological order parameter at the link.We numerically apply this scheme for several spin liquids and show its physical validity.

•Apr 1, 2007•19 citations

Quantized Berry Phases as a Local Order Parameter of a Quantum Liquid

Yasuhiro Hatsugai

We propose to use quantized Berry phases as local order parameters of gapped quantum liquids, which are invariant under some anti-unitary operation. After presenting a general prescription, the scheme is applied for Heisenberg models with frustrations and two dimensional extended Su-Schrieffer-Heeger models associated with a random dimer covering. In each phases, the quantized Berry phases, as 0 or $π$, describe the ground state texture pattern of local singlet bonds and dimer bonds. Also possible applications to large classes of correlated electron systems are discussed.

arXiv:cond-mat/0603230•Journal of the Physical Society of Japan•Nov 27, 2006•143 citations

Topological classification of gapped spin chains: Quantized Berry phase as a local order parameter

Takaaki Hirano, Hosho Katsura, Yasuhiro Hatsugai

We characterize several phases of gapped spin systems by local order parameters defined by quantized Berry phases [Y. Hatsugai, J. Phys. Soc. Jpn. 75, 123601 (2006)]. This characterization is topologically stable against any small perturbation as long as the energy gap remains finite. The models we pick up are $S=1,2$ dimerized Heisenberg chains and $S=2$ Heisenberg chains with uniaxial single-ion-type anisotropy. Analytically, we also evaluate the topological local order parameters for the generalized Affleck-Kennedy-Lieb-Tasaki model. The relation between the present Berry phases and the fractionalization in the integer spin chains are discussed as well.

arXiv:0710.4198•Physical Review B•Mar 26, 2008•80 citations

Fractionally quantized Berry phase in spin-1/2 frustrated Heisenberg model

Shin Miyahara

Spin-1/2 frustrated Heisenberg model show novel ground states due to the quantum fluctulation. To classify the ground states with toprogical invariant, we introduce fractionally quantized Berry phase. The Berry phase for the Heisenberg model is defined by local spin twists in the spin xy plane. As typical examples, we consider plateau states in frustrated magnets, e.g., a multimer ( N -mer) chains. Fractional quantization of the Berry phase comes from rotational symmetry of the twisted cluster. The Z N Berry phases are obtained from the numerical integration with using the ground states calculated by the Lanczos method. As a result, we obtained fractional quantization of Z 2 and Z 4 Berry phases in dimer ( N =2) and tetramer ( N =4) chains respectively.

StatPhys 27 Main Conference•Apr 16, 2019•0 citations

Nontrivial Quantized Berry Phases for Itinerant Spin Liquids

Isao Maruyama, Yasuhiro Hatsugai

Quantized Berry phases as local order parameters in t-J models are studied. A texture pattern of the local order parameters is topologically stable due to the quantization of non-Abelian Berry phases defined by low-energy states below a spin gap, which exists in the large J/t case with a few electrons. We have confirmed that itinerant singlets in the wide class of t-J models carry the nontrivial Berry phase pi. In the large J/t case for the one-dimensional t-J model, Berry phases are uniformly pi when the number of electrons is N =4n +2, ($n=0,1,2,...$).

arXiv:0708.1530•Journal of the Physical Society of Japan•Oct 24, 2007•16 citations

Momentum space Z 2 number, quantized Berry phase and the quantum phase transitions in spin chain systems

Yu-Quan Ma, Zhaoxian Yu, Deng‐Shan Wang +2 more

We characterize the quantum phase transitions of gapped time-reversal invariant spin chain systems by nontrivial Z 2 numbers derived from a quantized Berry phase in a (1 + 1)-dimensional Bloch momentum space. We study this approach analytically in a general two-band model and give a concrete example in a transverse field XY spin chain system. In our scheme, an extra local gauge transformation is performed to the spin system by a time-dependent twist operator, which endows the Hamiltonian of the system with the topology of a torus without changing its energy spectrum. The Z 2 number is obtained by a loop integral of the Berry gauge potential along a quarter of the Brillouin zone. We show that the different phases of the XY spin chain system are distinguished by the Z 2 topological order in momentum space.

Europhysics Letters (EPL)•Dec 1, 2012•7 citations
Recently, by using quantized Berry phases, a prescription for a local characterization of gapped topological insulators has been given (Hatsugai 2006 Preprint cond-mat/0603230). It requires that the ground state is gapped and is invariant under some anti-unitary operation. A spin liquid which is realized as a unique ground state of the Heisenberg spin system with frustrations is a typical target system, since pairwise exchange couplings are always time-reversal invariants even with frustrations. As for a generic Heisenberg model with a finite excitation gap, we locally modify the Hamiltonian by a continuous SU (2) twist only at a specific link and define the Berry connection by the derivative. Then the Berry phase evaluated by the entire many-spin wavefunction is used to define the local topological order parameter at the link. We numerically apply this scheme for several spin liquids and show its physical validity. For example, it implies that the Haldane phase of the S = 1 chains is characterized by uniform π quantized Berry phases.
Recently by using quantized Berry phases, a prescription for a local characterization of gapped topological insulators is given [1].One requires the ground state is gapped and is invariant under some anti-unitary operation.A spin liquid which is realized as a unique ground state of the Heisenberg spin system with frustrations is a typical target system, since pairwise exchange couplings are always time-reversal invariants even with frustrations.As for a generic Heisenberg model with a finite excitation gap, we locally modify the Hamiltonian by a continuous SU (2) twist only at a specific link and define the Berry connection by the derivative.Then the Berry phase evaluated by the entire many-spin wavefunction is used to define the local topological order parameter at the link.We numerically apply this scheme for several spin liquids and show its physical validity.
We propose to use quantized Berry phases as local order parameters of gapped quantum liquids, which are invariant under some anti-unitary operation. After presenting a general prescription, the scheme is applied for Heisenberg models with frustrations and two dimensional extended Su-Schrieffer-Heeger models associated with a random dimer covering. In each phases, the quantized Berry phases, as 0 or πππ, describe the ground state texture pattern of local singlet bonds and dimer bonds. Also possible applications to large classes of correlated electron systems are discussed.
We characterize several phases of gapped spin systems by local order parameters defined by quantized Berry phases [Y. Hatsugai, J. Phys. Soc. Jpn. 75, 123601 (2006)]. This characterization is topologically stable against any small perturbation as long as the energy gap remains finite. The models we pick up are S=1,2S=1,2S=1,2 dimerized Heisenberg chains and S=2S=2S=2 Heisenberg chains with uniaxial single-ion-type anisotropy. Analytically, we also evaluate the topological local order parameters for the generalized Affleck-Kennedy-Lieb-Tasaki model. The relation between the present Berry phases and the fractionalization in the integer spin chains are discussed as well.
Spin-1/2 frustrated Heisenberg model show novel ground states due to the quantum fluctulation. To classify the ground states with toprogical invariant, we introduce fractionally quantized Berry phase. The Berry phase for the Heisenberg model is defined by local spin twists in the spin xy plane. As typical examples, we consider plateau states in frustrated magnets, e.g., a multimer ( N -mer) chains. Fractional quantization of the Berry phase comes from rotational symmetry of the twisted cluster. The Z N Berry phases are obtained from the numerical integration with using the ground states calculated by the Lanczos method. As a result, we obtained fractional quantization of Z 2 and Z 4 Berry phases in dimer ( N =2) and tetramer ( N =4) chains respectively.
Quantized Berry phases as local order parameters in t-J models are studied. A texture pattern of the local order parameters is topologically stable due to the quantization of non-Abelian Berry phases defined by low-energy states below a spin gap, which exists in the large J/t case with a few electrons. We have confirmed that itinerant singlets in the wide class of t-J models carry the nontrivial Berry phase pi. In the large J/t case for the one-dimensional t-J model, Berry phases are uniformly pi when the number of electrons is N =4n +2, (n=0,1,2,...n=0,1,2,...n=0,1,2,...).
We characterize the quantum phase transitions of gapped time-reversal invariant spin chain systems by nontrivial Z 2 numbers derived from a quantized Berry phase in a (1 + 1)-dimensional Bloch momentum space. We study this approach analytically in a general two-band model and give a concrete example in a transverse field XY spin chain system. In our scheme, an extra local gauge transformation is performed to the spin system by a time-dependent twist operator, which endows the Hamiltonian of the system with the topology of a torus without changing its energy spectrum. The Z 2 number is obtained by a loop integral of the Berry gauge potential along a quarter of the Brillouin zone. We show that the different phases of the XY spin chain system are distinguished by the Z 2 topological order in momentum space.