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

Physica A Statistical Mechanics and its Applications

Exact ground states for a class of linear quantum spin systems

W.J. Caspers, Wim Magnus

Published Apr 1, 1983• 15 citations
Publisher
DOI
10.1016/0378-4371(83)90160-7

Related papers

Exact ground states for a class of linear antiferromagnetic spin systems

W.J. Caspers

Physica A Statistical Mechanics and its Applications•Sep 1, 1982•20 citations

Exact ground state of a class of quantum spin systems

Ido Kanter

We present some exact results for the ground-state wave function and the energy of disordered quantum-mechanical spin systems in any dimensions. The system contains all nearest- and some of the next-nearest-neighbor interactions. The solution is also available for some range of anisotropy. In all the cases the ground-state wave function is insensitive to the disorder.

Physical review. B, Condensed matter•Apr 1, 1989•17 citations

Ground states of quantum spin systems

Ola Bratteli, Akitaka Kishimoto, Derek W. Robinson

Communications in Mathematical Physics•Dec 1, 1978•16 citations

Exact ground states of one- and two-dimensional frustrated quantum spin systems

А. А. Овчинников, V. Ya. Krivnov, Д. В. Дмитриев

Theoretical and computational chemistry•Jan 1, 2002•1 citation

Exact ground states for coupled spin trimers

Heinz–Jürgen Schmidt, Johannes Richter

We consider a class of geometrically frustrated Heisenberg spin systems which admit exact ground states. The systems consist of suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers s and their ground state Φ will be the product state of the local singlet ground states of the trimers. We provide linear equations for the inter-trimer coupling constants which are equivalent to Φ being an eigenstate of the corresponding Heisenberg Hamiltonian and sufficient conditions for Φ being a ground state. The classical case s → ∞ can be completely analyzed. For the quantum case we consider a couple of examples, where the critical values of the inter-trimer couplings are numerically determined. These examples include chains of corner sharing tetrahedra as well as certain spin tubes. Φ is proven to be gapped in the case of trimer chains. This follows from a more general theorem on quantum chains with product ground states.

arXiv:1006.4299•Journal of Physics A Mathematical and Theoretical•Sep 16, 2010•12 citations

Vector Chiral States in Low-Dimensional Quantum-Spin Systems

Raoul Dillenschneider, Jung‐Hoon Kim, Jung Hoon Han

A class of exact spin ground states with nonzero averages of vector spin chirality, $$, is presented. It is obtained by applying non-uniform O(2) rotations of spin operators in the XY plane on the SU(2)-invariant Affleck-Kennedy-Lieb-Tasaki (AKLT) states and their parent Hamiltonians. Excitation energies of the new ground states are studied with the use of single-mode approximation in one dimension for S=1. The excitation gap remains robust. Construction of chiral AKLT states is shown to be possible in higher dimensions. We also present a general idea to produce vector chirality-condensed ground states as non-uniform O(2) rotations of the non-chiral parent states. Dzyaloshinskii-Moriya interaction is shown to imply non-zero spin chirality.

arXiv:0705.3993•Journal of the Korean Physical Society•Aug 14, 2008•1 citation
We consider a class of geometrically frustrated Heisenberg spin systems which admit exact ground states. The systems consist of suitably coupled antiferromagnetic spin trimers with integer spin quantum numbers s and their ground state Φ will be the product state of the local singlet ground states of the trimers. We provide linear equations for the inter-trimer coupling constants which are equivalent to Φ being an eigenstate of the corresponding Heisenberg Hamiltonian and sufficient conditions for Φ being a ground state. The classical case s → ∞ can be completely analyzed. For the quantum case we consider a couple of examples, where the critical values of the inter-trimer couplings are numerically determined. These examples include chains of corner sharing tetrahedra as well as certain spin tubes. Φ is proven to be gapped in the case of trimer chains. This follows from a more general theorem on quantum chains with product ground states.
A class of exact spin ground states with nonzero averages of vector spin chirality, $$, is presented. It is obtained by applying non-uniform O(2) rotations of spin operators in the XY plane on the SU(2)-invariant Affleck-Kennedy-Lieb-Tasaki (AKLT) states and their parent Hamiltonians. Excitation energies of the new ground states are studied with the use of single-mode approximation in one dimension for S=1. The excitation gap remains robust. Construction of chiral AKLT states is shown to be possible in higher dimensions. We also present a general idea to produce vector chirality-condensed ground states as non-uniform O(2) rotations of the non-chiral parent states. Dzyaloshinskii-Moriya interaction is shown to imply non-zero spin chirality.