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arXiv:cond-mat/0210497 · The European Physical Journal B

Numerical and Monte Carlo Bethe ansatz method: 1D Heisenberg model

S.-J. Gu, Nuno M. R. Peres, You‐Quan Li

Published Nov 1, 2005• 10 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2005-00390-1

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Abstract. In this paper we present two new numerical methods for studying thermodynamic quantities of integrable models. As an example of the effectiveness of these two approaches, results from numerical solutions of all sets of Bethe ansatz equations, for small Heisenberg chains, and Monte Carlo simulations in quasi-momentum space, for a relatively larger chains, are presented. Our results agree with those obtained by the thermodynamic Bethe ansatz (TBA). As an application of these ideas, the pairwise entanglement between two nearest neighbors at finite temperatures is studied. PACS. 75.10.Jm Quantized spin models – 75.40.-s Critical-point effects, specific heats, short-range order 1
This chapter reviews various theoretical methods that can be applied to investigate Bose–Hubbard models. In particular, it discusses the Bogolyubov method, strong coupling expansion, the perturbative mean field approach and the Gutzwiller method, exact diagonalization, quantum Monte Carlo methods, semi-classical phase space methods, and methods specifics for 1D (Wigner-Jordan transformation, Bethe ansatz, bosonization). The chapter end with a discussion about numerical renormalization approaches in 1D (DMRG, MPS) and 2D (PEPS; MERA).