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Combinatorial Solution of One-Dimensional Quantum Systems

Domingos H. U. Marchetti·Claudio F. S. Rodrigues
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Abstract

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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Domingos H. U. Marchetti, Claudio F. S. Rodrigues. 2003-09-25. Combinatorial Solution of One-Dimensional Quantum Systems. https://arxiv.org/abs/cond-mat/0309593

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