Combinatorial Solution of One-Dimensional Quantum Systems
统计力学
2007-05-23 v1
摘要
We give a self-contained exposition of the combinatorial solution of quantum mechanical systems of coupled spins on a one-dimensional lattice. Using Trotter formula, we write the partition function as a generating function of a spanning subgraph of a two-dimensional lattice and solve the combinatorial problem by the method of Pfaffians provided the weights satisfy the so-called free fermion condition. The free energy and the ground state energy as a function of the inverse temperature, couplings J and magnetic fields h, for the XY model in a transverse field with period p=1 and 2, is then obtained.
引用
@article{arxiv.cond-mat/0309593,
title = {Combinatorial Solution of One-Dimensional Quantum Systems},
author = {Domingos H. U. Marchetti and Claudio F. S. Rodrigues},
journal= {arXiv preprint arXiv:cond-mat/0309593},
year = {2007}
}
备注
Number of figures: 9 (eps)