Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-01-16
Phys. Rev. B 78, 115410 (2008)
Physics
Condensed Matter
Statistical Mechanics
8 pages, 4 figures, added results on the hyper-scaling form of the fidelity metric
Scientific paper
10.1103/PhysRevB.78.115410
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 hyper-scaling 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.
Bray-Ali Noah
Buonsante Pierfrancesco
Cozzini Marco
Massel Francesco
Venuti Lorenzo Campos
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