Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2007/02/L02002
Keywords
other numerical approaches; quantum phase transitions (theory)
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We compute the fidelity of the ground states of general quadratic fermionic Hamiltonians and analyse its connections with quantum phase transitions. Each of these systems is characterized by an L x L real matrix whose polar decomposition, into a non-negative Lambda(Phi) and a unitary T, contains all the relevant ground state (GS) information. The boundaries between different regions in the GS phase diagram are given by the points of, possibly asymptotic, singularity of Delta(Phi). This latter in turn implies a critical drop of the fidelity function. We present general results as well as their exempli. cation by a model of fermions on a totally connected graph.
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