Physics – Quantum Physics
Scientific paper
2006-08-07
Physics
Quantum Physics
14 pages, 5 figures
Scientific paper
10.1103/PhysRevB.75.014439
In this paper we analyze the ground state phase diagram of a class of fermionic Hamiltonians by looking at the fidelity of ground states corresponding to slightly different Hamiltonian parameters. The Hamiltonians under investigation can be considered as the variable range generalization of the fermionic Hamiltonian obtained by the Jordan-Wigner transformation of the XY spin-chain in a transverse magnetic field. Under periodic boundary conditions, the matrices of the problem become circulant and the models are exactly solvable. Their free-ends counterparts are instead analyzed numerically. In particular, we focus on the long range model corresponding to a fully connected directed graph, providing asymptotic results in the thermodynamic limit, as well as the finite-size scaling analysis of the second order quantum phase transitions of the system. A strict relation between fidelity and single particle spectrum is demonstrated, and a peculiar gapful transition due to the long range nature of the coupling is found. A comparison between fidelity and another transition marker borrowed from quantum information i.e., single site entanglement, is also considered.
Cozzini Marco
Giorda Paolo
Zanardi Paolo
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