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:1105.3529 · Physical Review B

Hidden order and dynamics in supersymmetric valence-bond solid states: Super-matrix product state formalism

Kazuki Hasebe, Keisuke Totsuka

Published Sep 15, 2011• 12 citations
arXivHTMLPDF

Abstract

Supersymmetric valence-bond solid models are extensions of the VBS model, a paradigmatic model of ``solvable'' gapped quantum antiferromagnets, to the case with doped fermionic holes. In this paper, we present a detailed analysis of physical properties of the models. For systematic studies, a supersymmetric version of the matrix-product formalism is developed. On 1D chains, we exactly evaluate the hole-doping behavior of various physical quantities, such as the spin or the charge excitation spectrum, the superconducting order parameter. A generalized hidden order is proposed, and the corresponding string nonlocal order parameter is also calculated. The behavior of the string-order parameter is discussed in the light of the entanglement spectrum.

DOI
10.1103/physrevb.84.104426

Related papers

Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry

Kazuki Hasebe, Keisuke Totsuka

Recent vigorous investigations of topological order have not only discovered new topological states of matter, but also shed new light on “already known” topological states. One established example with topological order is the valence bond solid (VBS) states in quantum antiferromagnets. The VBS states are disordered spin liquids with no spontaneous symmetry breaking, but most typically manifest a topological order known as a hidden string order on the 1D chain. Interestingly, the VBS models are based on mathematics analogous to fuzzy geometry. We review applications of the mathematics of fuzzy supergeometry in the construction of supersymmetric versions of VBS (SVBS) states and give a pedagogical introduction of SVBS models and their properties. As concrete examples, we present detailed analysis of supersymmetric versions of SU(2) and SO(5) VBS states, i.e., UOSp(N|2) and UOSp(N|4) SVBS states, whose mathematics are closely related to fuzzy two- and four-superspheres. The SVBS states are physically interpreted as hole-doped VBS states with a superconducting property that interpolates various VBS states, depending on the value of a hole-doping parameter. The parent Hamiltonians for SVBS states are explicitly constructed, and their gapped excitations are derived within the single-mode approximation on 1D SVBS chains. Prominent features of the SVBS chains are discussed in detail, such as a generalized string order parameter and entanglement spectra. It is realized that the entanglement spectra are at least doubly degenerate, regardless of the parity of bulk (super)spins. The stability of the topological phase with supersymmetry is discussed, with emphasis on its relation to particular edge (super)spin states.

arXiv:1303.2287•Symmetry•Apr 26, 2013•6 citations

Quantum entanglement and topological order in hole-doped valence-bond solid states

Kazuki Hasebe, Keisuke Totsuka

We present a detailed analysis of topological properties of the valence-bond solid (VBS) states doped with fermionic holes. As concrete examples, we consider the supersymmetric extension of the SU(2) and the SO(5) VBS states, dubbed UOSp(1$|$2) and UOSp(1$|$4) supersymmetric VBS states, respectively. Specifically, we investigate the string-order parameters and the entanglement spectra of these states to find that, even when the parent states (bosonic VBS states) do not support the string order, they recover it when holes are doped and the fermionic sector appears in the entanglement spectrum. These peculiar properties are discussed in light of the symmetry-protected topological order. To this end, we characterize a few typical classes of symmetry-protected topological orders in terms of supermatrix product states (SMPS). From this, we see that the topological order in the bulk manifests itself in the transformation properties of the SMPS in question and thereby affects the structure of the entanglement spectrum. Then, we explicitly relate the existence of the string order and the structure of the entanglement spectrum to explain the recovery and the stabilization of the string order in the supersymmetric systems.

arXiv:1210.0299•Physical Review B•Jan 17, 2013•18 citations

Matrix formalism for the VBS-type models and hidden order

Kiyohito Totsuka, Masuo Suzuki

We give a simple method to reduce the VBS-type states, usually expressed by the valence bonds, to the matrix-product representation. In this representation, peculiar properties of the VBS-type states are quite manifest. Using it, we investigate hidden order in the spin-S VBS model. The possibility that the Haldane phase for higher spin S is characterized by string order parameters is discussed. A picture of an approximate excitation is also presented.

Journal of Physics Condensed Matter•Feb 20, 1995•72 citations

Valence bond solid states with symplectic symmetry

Dirk Schuricht, Stephan Rachel

We introduce a one-dimensional valence bond solid (VBS) state with symplectic symmetry $\text{SP}(n)$ and construct the corresponding parent Hamiltonian. We argue that there is a gap in the spectrum. We calculate exactly the static correlation functions, which fall off exponentially. Hence the model introduced here shares all properties of the Haldane scenario for integer-spin quantum antiferromagnets. We further show that the VBS state possesses string order and discuss its generalization to higher dimensions.

arXiv:0805.3918•Physical Review B•Jul 30, 2008•37 citations

Supersymmetric valence bond solid states

Daniel P. Arovas, Kazuki Hasebe, Xiao-Liang Qi +1 more

In this work we investigate the supersymmetric version of the valence bond solid (SVBS) state. In one dimension, the SVBS states continuously interpolate between the valence bond states for integer and half-integer spin chains, and they generally describe superconducting valence bond liquid states. Spin and superconducting correlation functions can be computed exactly for these states and their correlation lengths are equal at the supersymmetric point. In higher dimensions, the wave function for the SVBS states can describe resonating valence bond states. The SVBS states for the spin models are shown to be precisely analogous to the bosonic Pfaffian states of the quantum Hall effect. We also give microscopic Hamiltonians for which the SVBS state is the exact ground state.

arXiv:0901.1498•Physical Review B•Jun 2, 2009•34 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
Supersymmetric valence-bond solid models are extensions of the VBS model, a paradigmatic model of ``solvable'' gapped quantum antiferromagnets, to the case with doped fermionic holes. In this paper, we present a detailed analysis of physical properties of the models. For systematic studies, a supersymmetric version of the matrix-product formalism is developed. On 1D chains, we exactly evaluate the hole-doping behavior of various physical quantities, such as the spin or the charge excitation spectrum, the superconducting order parameter. A generalized hidden order is proposed, and the corresponding string nonlocal order parameter is also calculated. The behavior of the string-order parameter is discussed in the light of the entanglement spectrum.
Recent vigorous investigations of topological order have not only discovered new topological states of matter, but also shed new light on “already known” topological states. One established example with topological order is the valence bond solid (VBS) states in quantum antiferromagnets. The VBS states are disordered spin liquids with no spontaneous symmetry breaking, but most typically manifest a topological order known as a hidden string order on the 1D chain. Interestingly, the VBS models are based on mathematics analogous to fuzzy geometry. We review applications of the mathematics of fuzzy supergeometry in the construction of supersymmetric versions of VBS (SVBS) states and give a pedagogical introduction of SVBS models and their properties. As concrete examples, we present detailed analysis of supersymmetric versions of SU(2) and SO(5) VBS states, i.e., UOSp(N|2) and UOSp(N|4) SVBS states, whose mathematics are closely related to fuzzy two- and four-superspheres. The SVBS states are physically interpreted as hole-doped VBS states with a superconducting property that interpolates various VBS states, depending on the value of a hole-doping parameter. The parent Hamiltonians for SVBS states are explicitly constructed, and their gapped excitations are derived within the single-mode approximation on 1D SVBS chains. Prominent features of the SVBS chains are discussed in detail, such as a generalized string order parameter and entanglement spectra. It is realized that the entanglement spectra are at least doubly degenerate, regardless of the parity of bulk (super)spins. The stability of the topological phase with supersymmetry is discussed, with emphasis on its relation to particular edge (super)spin states.
We present a detailed analysis of topological properties of the valence-bond solid (VBS) states doped with fermionic holes. As concrete examples, we consider the supersymmetric extension of the SU(2) and the SO(5) VBS states, dubbed UOSp(1$|2)andUOSp(12) and UOSp(12)andUOSp(1|$4) supersymmetric VBS states, respectively. Specifically, we investigate the string-order parameters and the entanglement spectra of these states to find that, even when the parent states (bosonic VBS states) do not support the string order, they recover it when holes are doped and the fermionic sector appears in the entanglement spectrum. These peculiar properties are discussed in light of the symmetry-protected topological order. To this end, we characterize a few typical classes of symmetry-protected topological orders in terms of supermatrix product states (SMPS). From this, we see that the topological order in the bulk manifests itself in the transformation properties of the SMPS in question and thereby affects the structure of the entanglement spectrum. Then, we explicitly relate the existence of the string order and the structure of the entanglement spectrum to explain the recovery and the stabilization of the string order in the supersymmetric systems.
We introduce a one-dimensional valence bond solid (VBS) state with symplectic symmetry SP(n)\text{SP}(n)SP(n) and construct the corresponding parent Hamiltonian. We argue that there is a gap in the spectrum. We calculate exactly the static correlation functions, which fall off exponentially. Hence the model introduced here shares all properties of the Haldane scenario for integer-spin quantum antiferromagnets. We further show that the VBS state possesses string order and discuss its generalization to higher dimensions.
In this work we investigate the supersymmetric version of the valence bond solid (SVBS) state. In one dimension, the SVBS states continuously interpolate between the valence bond states for integer and half-integer spin chains, and they generally describe superconducting valence bond liquid states. Spin and superconducting correlation functions can be computed exactly for these states and their correlation lengths are equal at the supersymmetric point. In higher dimensions, the wave function for the SVBS states can describe resonating valence bond states. The SVBS states for the spin models are shown to be precisely analogous to the bosonic Pfaffian states of the quantum Hall effect. We also give microscopic Hamiltonians for which the SVBS state is the exact ground state.
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.