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arXiv:cond-mat/9306019 · The European Physical Journal B

Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains

Andreas Kl�mper

Published Dec 1, 1993• 296 citations
arXivHTMLPDF
DOI
10.1007/bf01316831

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Using the density-matrix renormalization group, we investigate the critical behavior of the anisotropic Heisenberg chains with spins up to s=9/2s=9/2s=9/2. We show that through the relations arising from the conformal invariance and the DMRG technique it is possible to obtain accurate finite-size estimates of the conformal anomaly ccc, the sound velocity vs{v}_{s}vs​, the anomalous dimension xbulk{x}_{bulk}xbulk​, and the surface exponent xs{x}_{s}xs​ of the anisotropic spin-sss Heisenberg chains with relatively good accuracy without fitting parameters. Our results indicate that the entanglement entropy S(L,lA,s)S(L,{l}_{A},s)S(L,lA​,s) of the spin-sss Heisenberg chains satisfies the relation $S(L,{l}_{A},s)\ensuremath{-}S(L,{l}_{A},s\ensuremath{-}1)=1/(2s+1)$ for s>3/2s>3/2s>3/2 in the thermodynamic limit.
The ground state and the thermodynamics of a spin-1/2 asymmetric diamond Ising--Heisenberg chain are considered. For the XYZXYZXYZ anisotropic Heisenberg interaction, the exact calculations of the free energy, entropy, heat capacity, magnetization, and magnetic susceptibility are performed using the method of decoration-iteration transformation. In the case of antiferromagnetic interactions (Ising and XXZXXZXXZ anisotropic Heisenberg ones), the ground state, magnetization process, temperature dependence of the magnetization, magnetic susceptibility, and heat capacity are investigated. The influence of geometric frustration and quantum fluctuations on these characteristics is studied.