Fidelity approach to the Hubbard model

Year: 2008

Authors: Campos Venuti L., Cozzini M., Buonsante P., Massel F., Bray-Ali N., Zanardi P.

Autors Affiliation: ISI Foundation for Scientific Interchange, Villa Gualino, Viale Settimio Severo 65, I-10133 Torino, Italy; Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy; CNISM, Unità di Ricerca Torino Politecnico, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy; Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-0484, USA

Abstract: We use the fidelity approach to quantum critical points to study the zero-temperature phase diagram of the one-dimensional Hubbard model. Using a variety of analytical and numerical techniques, we analyze the fidelity metric in various regions of the phase diagram with particular care to the critical points. Specifically we show that close to the Mott transition, taking place at on-site repulsion U=0 and electron density n=1, the fidelity metric satisfies an hyperscaling form which we calculate. This implies that in general, as one approaches the critical point U=0, n=1, the fidelity metric tends to a limit which depends on the path of approach. At half-filling, the fidelity metric is expected to diverge as U(-4) when U is sent to zero.

Journal/Review: PHYSICAL REVIEW B

Volume: 78 (11)      Pages from: 115410  to: 115410

More Information: L. C. V. would like to thank Cristian Degli Esposti Boschi for a critical reading of the manuscript. P. B. acknowledges financial support from the PRIN project Microscopic description of fermionic quantum devices as well as from the CNISM project Quantum Phase Transitions, Nonlocal Quantum Correlations, and Nonlinear Dynamics in Ultracold Lattice Boson Systems.
DOI: 10.1103/PhysRevB.78.115410

Citations: 44
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