The fidelity approach to the Hubbard model

TL;DR

This paper employs the fidelity approach to analyze quantum critical points in the one-dimensional Hubbard model, revealing how the fidelity metric behaves near the Mott transition at U=0 and n=1, with divergence predictions at half filling.

Contribution

It introduces a detailed analysis of the fidelity metric in the Hubbard model, including hyper-scaling behavior near critical points and divergence predictions at half filling.

Findings

Fidelity metric follows a hyper-scaling form near the Mott transition.

Fidelity metric tends to a path-dependent limit approaching the critical point.

At half filling, the fidelity metric diverges as U^{-4} when U approaches zero.

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 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.