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

Journal of Physics A Mathematical and General

Hidden symmetry breaking in a generalized valence-bond solid model

Kiyohito Totsuka, Masuo Suzuki

Published Oct 7, 1994• 20 citations
Publisher

Abstract

A 'boson' representation for the ground state of the generalized valence-bond solid model is derived. The relation between this expression and the matrix-product representation of Klumper et al. (1991,1992) is discussed. It is shown that the hidden Z 2 *Z 2 -symmetry is partially broken in this model. Elementary excitations of this system have a topological nature similar to that in the Affleck, Kennedy, Lieb and Tasaki (1988) model.

DOI
10.1088/0305-4470/27/19/017

Related papers

Matrix product representations for all valence bond states

Vahid Karimipour, Laleh Memarzadeh

We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the variety of valence bond states proposed in the Affleck--Kennedy--Lieb--Tasaki (AKLT) construction. These include the fully dimerized states of arbitrary spins, with uniform or alternating patterns of spins, which are ground states of Hamiltonians with nearest and next-nearest-neighbor interactions, and the partially dimerized or AKLT/valence bond solid states, which are constructed from them by projection. The latter states are translation-invariant ground states of Hamiltonians with nearest-neighbor interactions.

arXiv:0712.2018•Physical Review B•Mar 17, 2008•31 citations

Valence-bond-solid order in antiferromagnets with spin-lattice coupling

Chenglong Jia, Jung Hoon Han

We propose that a valence-bond-solid (VBS) order can be stabilized in certain two-dimensional antiferromagnets due to spin-lattice coupling. In contrast to the VBS state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) type, the spin-lattice coupling-induced VBS state can occur when $2S$ is not an integer multiple of the coordination number $z$. $S=2$ spins on the triangular lattice with $z=6$ is discussed as an example. Within the Schwinger boson mean-field theory the ground state is derived as the direct product of states, one of which represents the conventional long-range ordered spins, and the other given by the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ modulation of the valence bond amplitudes. Excitation spectrum for the modulated valence bond state is worked out within the single-mode approximation. The spectrum offers a new collective mode, distinct from the spin wave excitations of the magnetically ordered ground state, and observable in neutron scattering.

arXiv:cond-mat/0505573•Physical Review B•May 18, 2006•3 citations

Field theory of symmetry-protected valence bond solid states in (2+1) dimensions

Shintaro Takayoshi, Pierre Pujol, Akihiro Tanaka

This paper describes a semiclassical field-theory approach to the topological properties of spatially featureless Affleck-Kennedy-Lieb-Tasaki type valence bond solid ground states of antiferromagnets in spatial dimensions one to three. Using nonlinear sigma models set in the appropriate target manifold and augmented with topological terms, we argue that the path integral representation of the ground-state wave functional can correctly distinguish symmetry-protected topological ground states from topologically trivial ones. The symmetry-protection feature is demonstrated explicitly in terms of a dual field theory, where we take into account the nontrivial spatial structure of topological excitations, which are caused by competition among the relevant ordering tendencies. A temporal surface contribution to the action originating from the bulk topological term plays a central role in our study. We discuss how the same term governs the behavior of the so-called strange correlator. In particular, we find that the path integral expression for the strange correlator in two dimensions reduces to the well-known Haldane expression for the two point spin correlator of antiferromagnetic spin chains.

arXiv:1609.01316•Physical review. B./Physical review. B•Dec 29, 2016•12 citations

Spin-spin correlation functions of the q-valence-bond-solid state of an integer spin model

Chikashi Arita, Kohei Motegi

We consider the valence-bond-solid ground state of the q-deformed higher-spin Affleck, Kennedy, Lieb, and Tasaki model (q-VBS state) with q real. We investigate the eigenvalues and eigenvectors of a matrix (G matrix), which is constructed from the matrix product representation of the q-VBS state. We compute the longitudinal and transverse spin-spin correlation functions, and determine the correlation amplitudes and correlation lengths.

arXiv:1009.4018•Journal of Mathematical Physics•Jun 1, 2011•13 citations

A brief note on the G$_2$ Affleck-Kennedy-Lieb-Tasaki chain

Hosho Katsura, Dirk Schuricht

We consider the valence bond solid (VBS) state built of singlet pairs of fundamental representations and projected onto adjoint representations of the exceptional Lie group G _2 2 . The two-point correlation function in the VBS state is non-vanishing only for nearest neighbours, but possesses finite string order. We construct a parent Hamiltonian for the VBS state, which constitutes the G _2 2 analog of the famous AKLT chain.

arXiv:2503.18885•SciPost Physics Core•Aug 15, 2025•0 citations

EXACT GROUND STATES OF ONE-DIMENSIONAL VALENCE-BOND-SOLID HAMILTONIANS

Paul Louis Iske, W.J. Caspers

The ground state(s) of a Hamiltonian, introduced by Affleck, Kennedy, Lieb and Tasaki, in connection with the Valence-Bond-Solid (VBS) states, are explicitly given for the spin-1 chains. The structure of these ground states is a rather simple one. For a closed chain we find a unique ground state; for the open chain we find a fourfold-degenerate ground state. The ground state correlation function for the ring is calculated.

Modern Physics Letters B•Aug 1, 1987•2 citations
A 'boson' representation for the ground state of the generalized valence-bond solid model is derived. The relation between this expression and the matrix-product representation of Klumper et al. (1991,1992) is discussed. It is shown that the hidden Z 2 *Z 2 -symmetry is partially broken in this model. Elementary excitations of this system have a topological nature similar to that in the Affleck, Kennedy, Lieb and Tasaki (1988) model.
We introduce a simple representation for irreducible spherical tensor operators of the rotation group of arbitrary integer or half integer rank and use these tensor operators to construct matrix product states corresponding to all the variety of valence bond states proposed in the Affleck--Kennedy--Lieb--Tasaki (AKLT) construction. These include the fully dimerized states of arbitrary spins, with uniform or alternating patterns of spins, which are ground states of Hamiltonians with nearest and next-nearest-neighbor interactions, and the partially dimerized or AKLT/valence bond solid states, which are constructed from them by projection. The latter states are translation-invariant ground states of Hamiltonians with nearest-neighbor interactions.
We propose that a valence-bond-solid (VBS) order can be stabilized in certain two-dimensional antiferromagnets due to spin-lattice coupling. In contrast to the VBS state of the Affleck-Kennedy-Lieb-Tasaki (AKLT) type, the spin-lattice coupling-induced VBS state can occur when 2S2S2S is not an integer multiple of the coordination number zzz. S=2S=2S=2 spins on the triangular lattice with z=6z=6z=6 is discussed as an example. Within the Schwinger boson mean-field theory the ground state is derived as the direct product of states, one of which represents the conventional long-range ordered spins, and the other given by the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ modulation of the valence bond amplitudes. Excitation spectrum for the modulated valence bond state is worked out within the single-mode approximation. The spectrum offers a new collective mode, distinct from the spin wave excitations of the magnetically ordered ground state, and observable in neutron scattering.
This paper describes a semiclassical field-theory approach to the topological properties of spatially featureless Affleck-Kennedy-Lieb-Tasaki type valence bond solid ground states of antiferromagnets in spatial dimensions one to three. Using nonlinear sigma models set in the appropriate target manifold and augmented with topological terms, we argue that the path integral representation of the ground-state wave functional can correctly distinguish symmetry-protected topological ground states from topologically trivial ones. The symmetry-protection feature is demonstrated explicitly in terms of a dual field theory, where we take into account the nontrivial spatial structure of topological excitations, which are caused by competition among the relevant ordering tendencies. A temporal surface contribution to the action originating from the bulk topological term plays a central role in our study. We discuss how the same term governs the behavior of the so-called strange correlator. In particular, we find that the path integral expression for the strange correlator in two dimensions reduces to the well-known Haldane expression for the two point spin correlator of antiferromagnetic spin chains.
A brief note on the G2_22​ Affleck-Kennedy-Lieb-Tasaki chain