Finite temperature crossovers and the quantum Widom line near the Mott transition

TL;DR

This paper investigates the finite-temperature phase diagram of the half-filled Hubbard model, focusing on crossovers, quantum critical scaling, and the concept of quantum Widom lines near the Mott transition, using dynamical mean-field theory.

Contribution

It introduces the quantum Widom line concept in the context of quantum phase transitions and provides a detailed analysis of crossover phenomena near the Mott transition.

Findings

Identification of crossover lines in the phase diagram.

Observation of quantum critical scaling behavior.

Proposal of experimental methods to observe these phenomena.

Abstract

The experimentally established phase diagram of the half-filled Hubbard model features the existence of three distinct finite-temperature regimes, separated by extended crossover regions. A number of crossover lines can be defined to span those regions, which we explore in quantitative detail within the framework of dynamical mean-field theory. Most significantly, the high temperature crossover between the bad metal and Mott-insulator regimes displays a number of phenomena marking the gradual development of the Mott insulating state. We discuss the quantum critical scaling behavior found in this regime, and propose methods to facilitate its possible experimental observation. We also introduce the concept of {\em quantum Widom lines} and present a detailed discussion that highlights its physical meaning when used in the context of quantum phase transitions.