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Physical review. B, Condensed matter

Magnetic moment of a spinon and thermodynamic properties of the one-dimensional Heisenberg model

Wayne M. McRae, Oleg P. Sushkov

Published Jul 1, 1998• 11 citations
Publisher

Abstract

The one-dimensional spin-$\frac{1}{2}$ Heisenberg antiferromagnet is considered using a simple quasiparticle picture: a weakly interacting Fermi gas of kinks. Using this picture, the low-temperature heat capacity, and the magnetic susceptibility with logarithmic field and temperature corrections are derived. The results obtained are in agreement with previous Bethe ansatz and conformal field-theory calculations. We demonstrate from comparison with previous calculations that the magnetic moment of the kink ${g}_{\mathrm{kink}}=\sqrt{2}{g}_{\mathrm{electron}}.$

DOI
10.1103/physrevb.58.62

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We investigate the low-temperature behavior of the integrable one-dimensional two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find that for strong coupling the characteristics of the thermodynamics at low temperatures are quantitatively affected by the spin ferromagnetic states, which are described by an effective ferromagnetic Heisenberg chain. The free energy, specific heat, susceptibility, and local pair correlation function are calculated for various physical regimes in terms of temperature and interaction strength. These thermodynamic properties reveal spin effects which are significantly different than those of the spinless Bose gas. The zero-field susceptibility for finite strong repulsion exceeds that of a free spin paramagnet. The critical exponents of the specific heat ${c}_{v}\ensuremath{\sim}{T}^{1∕2}$ and the susceptibility $\ensuremath{\chi}\ensuremath{\sim}{T}^{\ensuremath{-}2}$ are indicative of the ferromagnetic signature of the two-component spinor Bose gas. Our analytic results are consistent with general arguments by Eisenberg and Lieb for polarized spinor bosons.
We use the Quantum Monte Carlo Stochastic Series Expansion (SSE) algorithm to investigate the properties of the one-dimensional Heisenberg ferromagnet.We consider the model for two spin values s = 1 2 and s = 1 and study the dependence of the specific heat, magnetisation, magnetic susceptibility and correlation functions on temperature and magnetic field.Obtained results are compared to those derived by analytical methods (Bethe ansatz, Green's function, Random Phase Approximation).In particular, the surprising prediction of a double-peak structure in the specific heat at low temperatures and small magnetic fields can be confirmed.