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

Communications in Theoretical Physics

A Simple Calculation of the Central Charge for XXZ Heisenberg Chain

Xu Bo-wei

Published Apr 1, 1991• 2 citations
Publisher

Abstract

The XXZ Heisenberg chain is equivalent to the Thirring model, from which we can calculate the central charge. The result coincides with that by other means.
DOI
10.1088/0253-6102/15/3/383

Related papers

Non-equivalence between Heisenberg XXZ spin chain and Thirring model

T. Fujita, Takuya Kobayashi, Makoto Hiramoto +1 more

arXiv:hep-th/0307133•The European Physical Journal C•Jan 20, 2005•1 citation

The thirring model from the XXZ Heisenberg chain Schwinger terms

Hector J. de Vega, T. J. M. Simões

Physics Letters B•Jan 1, 1989•8 citations

Critical entanglement of XXZ Heisenberg chains with defects

Jize Zhao, Ingo Peschel, Xiaoqun Wang

We study the entanglement properties of anisotropic open spin one-half Heisenberg chains with a modified central bond. The entanglement entropy between the two half-chains is calculated with the density-matrix renormalization method (DMRG). We find a logarithmic behavior with an effective central charge ${c}^{\ensuremath{'}}$ varying with the length of the system. It flows to one in the ferromagnetic region and to zero in the antiferromagnetic region of the model. In the $XX$ case it has a nonuniversal limit and we recover previous results.

arXiv:cond-mat/0509338•Physical Review B•Jan 24, 2006•56 citations

XXZ Heisenberg chain: Ground state in the presence of a magnetic field

Ladislav Šamaj, Zoltán Bajnok

Cambridge University Press eBooks•May 16, 2013•0 citations

Simple Approach to Thermal Bethe Ansatz

Hector J. de Vega

We report on a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisenberg chain we derive, for arbitrary values of the anysotropy, a single non-linear integral equation from which the free energy can be exactly calculated.These equations are shown to be equivalent to an infinite set of algebraic equations of Bethe type which provide alternatively the thermodinamics. The high-temperature expansion follows in a sistematic and relatively simple way from our non-linear integral equations. For low temperatures we obtain the correct central charge and predict the analytic structure of the full expansion around T=0. Furthermore, we derive a single non-linear integral equation describing the finite-size ground-state energy of the Sine-Gordon quantum field theory.

arXiv:hep-th/9210056•Oct 9, 1992•0 citations

Test of modular invariance for finite XXZ chains

B -D Dorfel, Burkhard Militzer

The central charge c of the Virasoro algebra is determined using its relation to the set of anomalous dimensions of the scaling fields for the critical anisotropic Heisenberg chain. The results obtained by exactly solving the Bethe ansatz for N<or=4 are compared with the standard procedure for calculating c in the whole region of anisotropy. For odd N the system is no longer modular invariant and the analogous averaging leads to an anisotropy-dependent function which has been calculated.

Journal of Physics A Mathematical and General•Oct 7, 1993•1 citation
We study the entanglement properties of anisotropic open spin one-half Heisenberg chains with a modified central bond. The entanglement entropy between the two half-chains is calculated with the density-matrix renormalization method (DMRG). We find a logarithmic behavior with an effective central charge ${c}^{\ensuremath{'}}$ varying with the length of the system. It flows to one in the ferromagnetic region and to zero in the antiferromagnetic region of the model. In the XXXXXX case it has a nonuniversal limit and we recover previous results.
We report on a new approach to the calculation of thermodynamic functions for crossing-invariant models solvable by Bethe Ansatz. In the case of the XXZ Heisenberg chain we derive, for arbitrary values of the anysotropy, a single non-linear integral equation from which the free energy can be exactly calculated.These equations are shown to be equivalent to an infinite set of algebraic equations of Bethe type which provide alternatively the thermodinamics. The high-temperature expansion follows in a sistematic and relatively simple way from our non-linear integral equations. For low temperatures we obtain the correct central charge and predict the analytic structure of the full expansion around T=0. Furthermore, we derive a single non-linear integral equation describing the finite-size ground-state energy of the Sine-Gordon quantum field theory.