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

Fidelity approach to the Hubbard model

Cozzini, Marco;
2008

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
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11582/19613
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