[Paper Review] Mott transition and high-temperature crossovers at half-filling

Alexis Reymbaut, M. Boulay+5 more|arXiv (Cornell University)|Apr 5, 2020

Physics of Superconductivity and Magnetism10 citations

TL;DR

This study investigates the Mott transition and associated high-temperature crossovers in the half-filled Hubbard model using continuous-time quantum Monte Carlo within DMFT and CDMFT frameworks on square and triangular lattices. It identifies the Mott line—defined by the full opening of the Mott gap—as the only universal crossover observable at high temperatures, regardless of lattice frustration or antiferromagnetic fluctuations, with implications for the Quantum Widom line in resistivity and experimental observability.

ABSTRACT

The interaction-driven Mott transition in the half-filled Hubbard model is a first-order phase transition that terminates at a critical point $(T_\mathrm{c},U_\mathrm{c})$ in the temperature-interaction plane $T-U$. A number of crossovers occur along lines that extend for some range above $(T_\mathrm{c},U_\mathrm{c})$. Asymptotically close to $(T_\mathrm{c},U_\mathrm{c})$, these lines coalesce into the so-called Widom line. The existence of $(T_\mathrm{c},U_\mathrm{c})$ and of the associated crossovers becomes unclear when long-wavelength fluctuations or long-range order occur above $(T_\mathrm{c},U_\mathrm{c})$. We study this problem using continuous-time quantum Monte Carlo methods as impurity solvers for both Dynamical Mean-Field Theory (DMFT) and Cellular Dynamical Mean-Field Theory (CDMFT). We contrast the cases of the square lattice, where antiferromagnetic fluctuations dominate in the vicinity of the Mott transition, and the triangular lattice where they do not. The inflexion points and maxima found near the Widom line for the square lattice can serve as proxy for the triangular lattice case. But the only crossover observable in all cases at sufficiently high temperature is that associated with the opening of the Mott gap. The same physics also controls an analog crossover in the resistivity called the "Quantum Widom line".

Motivation & Objective

• To determine which high-temperature crossovers associated with the Mott transition remain observable when long-wavelength fluctuations or long-range order emerge above the critical point.
• To compare the role of antiferromagnetic fluctuations on the square lattice versus frustration on the triangular lattice in masking or revealing the Mott transition.
• To assess the robustness of the Mott line and Quantum Widom line as experimentally accessible signatures across different lattice geometries and interaction strengths.
• To benchmark numerical methods (DMFT, CDMFT, QMC) and identify the temperature regime where they yield consistent physics.
• To clarify whether the Widom line and Mott line are physically meaningful in the presence of strong fluctuations, even when the first-order transition is hidden.

Proposed method

• Employed continuous-time quantum Monte Carlo (CT-QMC) as an impurity solver within Dynamical Mean-Field Theory (DMFT) and Cellular DMFT (CDMFT) for the Hubbard model.
• Performed simulations on both square and triangular lattices at half-filling with varying interaction strength $U$ and temperature $T$.
• Used analytic continuation of the imaginary-time Green's function to extract the local density of states and identify gap formation.
• Defined the Mott line as the temperature where the Mott gap is fully developed, satisfying $T \ll E_g$.
• Tracked inflection points and maxima in physical observables (e.g., spectral weight, resistivity) to locate the Widom line and Quantum Widom line.
• Compared results across lattice types and cluster sizes (e.g., $2\times2$ CDMFT) to assess the role of spatial correlations and cluster size effects.

Experimental results

Research questions

• RQ1 Which high-temperature crossovers associated with the Mott transition remain observable when antiferromagnetic fluctuations dominate above the critical point?
• RQ2 How does lattice frustration (square vs. triangular) affect the visibility and nature of the Widom line and Mott line?
• RQ3 Is the Mott line universally observable at high temperatures, regardless of the presence of long-wavelength fluctuations or long-range order?
• RQ4 Can the Mott line and Quantum Widom line be reliably identified in numerical simulations and linked to experimental observables?
• RQ5 What is the relationship between the Mott line and the opening of the Mott gap, and how does it compare to the onset of spectral weight suppression at $\omega=0$?

Key findings

• The Mott line, defined by the full opening of the Mott gap such that $T \ll E_g$, is the only crossover universally observable at high temperatures, independent of lattice geometry or fluctuations.
• On the square lattice, the Widom line—characterized by inflection points and maxima in observables—serves as a proxy for the Mott crossover on the triangular lattice, despite antiferromagnetic fluctuations masking the first-order transition.
• For $U=8$, the Mott line was found at $T \approx 0.125$ in CDMFT $2\times2$, while the gap opening in the density of states was observed at $T \simeq 0.16$, confirming that the Mott line occurs at lower $T$ than the onset of spectral suppression.
• The Mott line obtained with CDMFT $2\times2$ agrees closely with prior DQMC results at $U \gtrsim 6.5$, validating the method’s accuracy in this regime.
• The Quantum Widom line, observed in resistivity, may not be experimentally accessible if long-wavelength antiferromagnetic fluctuations extend too far above the Mott critical point.
• The slope of the Widom line may differ in sign between the square and triangular lattices due to entropic effects, suggesting lattice-dependent critical behavior.