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

Physical review. B, Condensed matter

Linked-tetrahedra spin chain: Exact ground state and excitations

Martin P. Gelfand

Published Apr 1, 1991• 82 citations
Publisher

Abstract

A particular quasi-one-dimensional Heisenberg antiferromagnet, which falls into a large and well-known class of models with simple dimerized ground states, is shown to have some especially appealing properties. For S=1/2 spins, all excited states are strictly localized, and may be identified with the states of collections of finite, open, S=1 chains.

DOI
10.1103/physrevb.43.8644

Related papers

Exact ground state and kink-like excitations of a two-dimensional Heisenberg antiferromagnet

Rahul Siddharthan

A rare example of a two-dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagom\'e lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it exhibits domain-wall-like ``kink'' excitations normally associated only with one-dimensional systems. In some limits it decouples into noninteracting chains; unusually, this happens in the limit of strong, rather than weak, interchain coupling.

arXiv:cond-mat/9904376•Physical review. B, Condensed matter•Oct 1, 1999•2 citations

Ground-state properties of axially anisotropic quantum Heisenberg chains

Jenő Sólyom, Timothy A. L. Ziman

The ground state and low-lying excited states of a one-dimensional Heisenberg model with axial anisotropy are studied by extrapolation from finite lattices. The ground-state properties and the phase diagram are determined for quantum spins, especially for $S=\frac{1}{2}, 1, \mathrm{and} \frac{3}{2}$. Higher spin values do not give new features in the phase diagram. the limitations of finite-lattice extrapolation are discussed in connection with the possibility of a singlet phase for the $S=1$ isotropic Heisenberg antiferromagnet.

Physical review. B, Condensed matter•Oct 1, 1984•103 citations

Nature of Spinons in 1D Spin Chains

Teresa Kulka, Miłosz Panfil, Mona Berciu +1 more

We provide an intuitive understanding of the collective low-energy spin excitation of the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain, known as the spinon. To this end, we demonstrate how a single spinon can be excited by adding one extra spin to the ground state. This procedure accurately reproduces all key features of the spinon's dispersion. These follow from the vanishing norm of the excited state which is triggered by the ground state entanglement. Next, we show that the spinon dispersion can be approximately reproduced if we replace the true ground state with the simplest valence-bond solid. This proves that the spinon of the one-dimensional Heisenberg model can be understood as a single spin flowing through a valence-bond solid.

arXiv:2303.02276•Physical Review Letters•May 29, 2025•6 citations

Exact ground and excited states of an antiferromagnetic quantum spin model

Indrani Bose

A quasi-one-dimensional spin model that consists of a chain of octahedra of spins has been suggested, for which in a certain parameter regime of the Hamiltonian the ground state can be written down exactly. The ground state is highly degenerate and can be other than a singlet. Also, several excited states can be constructed exactly. The ground state is a local resonating valence bond state for which resonance is confined to rings of spins. Some exact numerical results for an octahedron of spins have also been reported.

Journal of Physics Condensed Matter•Nov 20, 1989•13 citations

Renormalization group and other calculations for the one-dimensional spin-1/2 dimerized Heisenberg antiferromagnet

J. N. Fields, Henk W. J. Blöte, J. C. Bonner

A zero-temperature renormalization group (RG) approach is applied to the one-dimensional, spin-1/2 antiferromagnetic Heisenberg dimerized (alternating) chain. Specifically, the ground state energy and lowest-lying spectral excitations are examined. The calculation indicates the existence of a gap in the spectrum of the dimerized chain which vanishes only in the limit of a uniform spin chain, in contrast to a recent Green’s function approach. The RG results are in reasonable agreement with numerical extrapolations on the exact eigenvalue spectrum of finite chains of up to 12 spins. Both methods are compared with several other approximate treatments of the Heisenberg system, and tested by comparison with exact results for the spin-1/2 XY dimerized chain.

Journal of Applied Physics•Mar 1, 1979•50 citations

Exact Antiferromagnetic Ground States of Quantum Spin Chains

M. Fannes, Bruno Nachtergaele, Reinhard F. Werner

We recall a simple class of translation invariant states for an infinite quantum spin chain, which was introduced by Accardi. Those states have exponential decay of correlation functions, and a subclass contains the groun states of a certain class of finite-range interactions. We consider, in particular, a family of states for integer spin chains, containing as its simplest member the ground state of a spin-1 Heisenberg antiferromagnet recently studied by Affleck, Kennedy, Lieb and Tasaki. For this family we compute explicitly the correlation functions and other properties.

Europhysics Letters (EPL)•Dec 1, 1989•135 citations
A particular quasi-one-dimensional Heisenberg antiferromagnet, which falls into a large and well-known class of models with simple dimerized ground states, is shown to have some especially appealing properties. For S=1/2 spins, all excited states are strictly localized, and may be identified with the states of collections of finite, open, S=1 chains.
A rare example of a two-dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagom\'e lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it exhibits domain-wall-like ``kink'' excitations normally associated only with one-dimensional systems. In some limits it decouples into noninteracting chains; unusually, this happens in the limit of strong, rather than weak, interchain coupling.
The ground state and low-lying excited states of a one-dimensional Heisenberg model with axial anisotropy are studied by extrapolation from finite lattices. The ground-state properties and the phase diagram are determined for quantum spins, especially for S=12,1,and32S=\frac{1}{2}, 1, \mathrm{and} \frac{3}{2}S=21​,1,and23​. Higher spin values do not give new features in the phase diagram. the limitations of finite-lattice extrapolation are discussed in connection with the possibility of a singlet phase for the S=1S=1S=1 isotropic Heisenberg antiferromagnet.
We provide an intuitive understanding of the collective low-energy spin excitation of the one-dimensional spin-1/2 antiferromagnetic Heisenberg chain, known as the spinon. To this end, we demonstrate how a single spinon can be excited by adding one extra spin to the ground state. This procedure accurately reproduces all key features of the spinon's dispersion. These follow from the vanishing norm of the excited state which is triggered by the ground state entanglement. Next, we show that the spinon dispersion can be approximately reproduced if we replace the true ground state with the simplest valence-bond solid. This proves that the spinon of the one-dimensional Heisenberg model can be understood as a single spin flowing through a valence-bond solid.
A quasi-one-dimensional spin model that consists of a chain of octahedra of spins has been suggested, for which in a certain parameter regime of the Hamiltonian the ground state can be written down exactly. The ground state is highly degenerate and can be other than a singlet. Also, several excited states can be constructed exactly. The ground state is a local resonating valence bond state for which resonance is confined to rings of spins. Some exact numerical results for an octahedron of spins have also been reported.
A zero-temperature renormalization group (RG) approach is applied to the one-dimensional, spin-1/2 antiferromagnetic Heisenberg dimerized (alternating) chain. Specifically, the ground state energy and lowest-lying spectral excitations are examined. The calculation indicates the existence of a gap in the spectrum of the dimerized chain which vanishes only in the limit of a uniform spin chain, in contrast to a recent Green’s function approach. The RG results are in reasonable agreement with numerical extrapolations on the exact eigenvalue spectrum of finite chains of up to 12 spins. Both methods are compared with several other approximate treatments of the Heisenberg system, and tested by comparison with exact results for the spin-1/2 XY dimerized chain.
We recall a simple class of translation invariant states for an infinite quantum spin chain, which was introduced by Accardi. Those states have exponential decay of correlation functions, and a subclass contains the groun states of a certain class of finite-range interactions. We consider, in particular, a family of states for integer spin chains, containing as its simplest member the ground state of a spin-1 Heisenberg antiferromagnet recently studied by Affleck, Kennedy, Lieb and Tasaki. For this family we compute explicitly the correlation functions and other properties.