Combinatorial Solution of One-Dimensional Quantum Systems

Details Combinatorial Solution of One-Dimensional Quantum Systems Combinatorial Solution of One-Dimensional Quantum Systems

2003-09-25

arxiv.org/abs/cond-mat/0309593v1

Physics

Condensed Matter

Statistical Mechanics

Number of figures: 9 (eps)

Scientific paper

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.

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