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 Anhui University

Study of spin-12 Heisenberg chain

Meijuan Sun

Published Jan 1, 2004• 0 citations
OpenAlex

Abstract

A mean-field Jordan-Wigner transformation analysis of the spin-12 Heisenberg chain is studied.It is surprised to find that the mean-field Jordan-Wigner transformation analysis mimics the results of the traditional thermodynamic Bethe ansatz quite well.

Related papers

Fermionic mean-field theory as a tool for studying spin Hamiltonians

Thomas M. Henderson, Brent Harrison, Ilias Magoulas +5 more

The Jordan-Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Jordan-Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J1-J2 Heisenberg models, as well as to the pairing or reduced Bardeen-Cooper-Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.

arXiv:2410.02125•The Journal of Chemical Physics•Dec 18, 2024•4 citations

The quantum inverse scattering method and the Jordan-Wigner transformation for the Heisenberg-Ising spin chain

Michael Fowler

Physics Letters B•Jul 1, 1980•3 citations

Classical thermodynamics of the Heisenberg chain in a field by generalized Bethe ansatz method

R. Bullough, Yu Chen, JUSSI TIMONEN +2 more

Physics Letters A•Apr 1, 1990•8 citations

Jordan–Wigner fermionization for spin-½ systems in two dimensions: A brief review

Oleg Derzhko

We review the papers on the Jordan{Wigner transformation in two dimensions to comment on a possibility of examining the statistical mechanics properties of two{dimensional spin{ 1 2 models.We discuss in some detail the two{dimensional spin{ 1 2 isotropic XY and Heisenberg models.

arXiv:cond-mat/0101188•Journal of Physical Studies•Jan 1, 2001•25 citations

Dynamics of Quantum Spin Chains

Alessandra Colla

In the present thesis we perform a step towards understanding the effec- tiveness of Hamiltonian perturbation theory in quantum dynamics, which is made possible by the Hamiltonian framing of quantum mechanics. To such a purpose, we focus our attention on quantum spin chains, namely on the isotropic Heisenberg ferromagnet, which is well known to be equivalent, via the Jordan-Wigner transformation, to a system of interacting fermions, and is also known to be exactly integrable through the Bethe ansatz. The interaction term of the Hamiltonian, of order four in fermionic creation and annihilation operators, is treated as a perturbation in the regime of small excitations: small number of reversed spins or, equivalently, small number of fermions per site. The calculation of the first order normal form Hamiltonian amounts to erasing all the nonresonant interaction terms, and allows to draw interesting conclusions on the dynamics of the system, e.g. to determine ap- proximately conserved quantities. Moreover, we get a good correspondence between our perturbative energy spectrum and the exact one computed via the Bethe ansatz, the approximation being of course the more accurate the smaller is the number of fermions per site. The present method, here tested in an exactly solvable case, can be applied to any nonintegrable system of weakly interacting fermions (and/or bosons).

•Sep 1, 2018•0 citations

Jordan-Wigner Fermions and Dynamic Probes of Quantum Spin Chains

Oleg Derzhko, Taras Verkholyak

With the help of the Jordan–Wigner transformation the spin-12 XY chains can be reformulated in terms of noninteracting spinless fermions and, as a result, many statistical-mechanics calculations can be performed rigorously, i.e. without making any simplifying approximations. We are interested in dynamic properties of such chains (time-dependent spin correlation functions, dynamic structure factors, dynamic susceptibilities) which are of great importance for interpretation of experimental data. We have worked out a number of dynamic quantities explicitly as well as have performed a general analysis of the two-fermion continua which are relevant for different dynamic quantities.

Presented at•Jan 1, 2003•0 citations
The Jordan-Wigner transformation permits one to convert spin 1/2 operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one, which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Jordan-Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and J1-J2 Heisenberg models, as well as to the pairing or reduced Bardeen-Cooper-Schrieffer Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.
In the present thesis we perform a step towards understanding the effec- tiveness of Hamiltonian perturbation theory in quantum dynamics, which is made possible by the Hamiltonian framing of quantum mechanics. To such a purpose, we focus our attention on quantum spin chains, namely on the isotropic Heisenberg ferromagnet, which is well known to be equivalent, via the Jordan-Wigner transformation, to a system of interacting fermions, and is also known to be exactly integrable through the Bethe ansatz. The interaction term of the Hamiltonian, of order four in fermionic creation and annihilation operators, is treated as a perturbation in the regime of small excitations: small number of reversed spins or, equivalently, small number of fermions per site. The calculation of the first order normal form Hamiltonian amounts to erasing all the nonresonant interaction terms, and allows to draw interesting conclusions on the dynamics of the system, e.g. to determine ap- proximately conserved quantities. Moreover, we get a good correspondence between our perturbative energy spectrum and the exact one computed via the Bethe ansatz, the approximation being of course the more accurate the smaller is the number of fermions per site. The present method, here tested in an exactly solvable case, can be applied to any nonintegrable system of weakly interacting fermions (and/or bosons).
With the help of the Jordan–Wigner transformation the spin-12 XY chains can be reformulated in terms of noninteracting spinless fermions and, as a result, many statistical-mechanics calculations can be performed rigorously, i.e. without making any simplifying approximations. We are interested in dynamic properties of such chains (time-dependent spin correlation functions, dynamic structure factors, dynamic susceptibilities) which are of great importance for interpretation of experimental data. We have worked out a number of dynamic quantities explicitly as well as have performed a general analysis of the two-fermion continua which are relevant for different dynamic quantities.