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arXiv:1702.01821 · Physical review. B./Physical review. B

Signatures of the Mott transition in the antiferromagnetic state of the two-dimensional Hubbard model

Lorenzo Fratino, P. Sémon, M. Charlebois, G. Sordi, A.–M. S. Tremblay

Published Jun 6, 2017• 70 citations
arXivHTMLPDF

Abstract

The properties of a phase with large correlation length can be strongly influenced by the underlying normal phase. We illustrate this by studying the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo. Sharp crossovers in the mechanism that favors antiferromagnetic correlations and in the corresponding local density of states are observed. These crossovers occur at values of the interaction strength $U$ and temperature $T$ that are controlled by the underlying normal-state Mott transition.

DOI
10.1103/physrevb.95.235109

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The properties of a phase with large correlation length can be strongly influenced by the underlying normal phase. We illustrate this by studying the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo. Sharp crossovers in the mechanism that favors antiferromagnetic correlations and in the corresponding local density of states are observed. These crossovers occur at values of the interaction strength UUU and temperature TTT that are controlled by the underlying normal-state Mott transition.
Experiments on layered materials call for a study of the influence of short-range spin correlations on the Mott transition. To this end, we solve the cellular dynamical mean-field equations for the Hubbard model on a plaquette with continuous-time quantum Monte Carlo calculations. The normal-state phase diagram as a function of temperature T, interaction strength U, and filling n reveals that upon increasing n towards the insulator, there is a surface of first-order transition between two metals at nonzero doping. For T above the critical end line there is a maximum in scattering rate.
The interaction-driven Mott transition in the half-filled Hubbard model is a first-order phase transition that terminates at a critical point (Tc,Uc)(T_\mathrm{c},U_\mathrm{c})(Tc​,Uc​) in the temperature-interaction plane T−UT-UT−U. A number of crossovers occur along lines that extend for some range above (Tc,Uc)(T_\mathrm{c},U_\mathrm{c})(Tc​,Uc​). Asymptotically close to (Tc,Uc)(T_\mathrm{c},U_\mathrm{c})(Tc​,Uc​), these lines coalesce into the so-called Widom line. The existence of (Tc,Uc)(T_\mathrm{c},U_\mathrm{c})(Tc​,Uc​) and of the associated crossovers becomes unclear when long-wavelength fluctuations or long-range order occur above (Tc,Uc)(T_\mathrm{c},U_\mathrm{c})(Tc​,Uc​). 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".
Entanglement and information are powerful lenses to probe phases transitions in many-body systems. Motivated by recent cold atom experiments, which are now able to measure the corresponding information-theoretic quantities, we study the Mott transition in the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory, and focus on two key measures of quantum correlations: entanglement entropy and a measure of total mutual information. We show that they detect the first-order nature of the transition, the universality class of the end point, and the crossover emanating from the end point.
The two-dimensional half-filled Hubbard model is studied by a nonperturbative analytic theory of correlator projection. The dynamical mean-field approximation (DMFA) is reproduced at the first-order projection and then improved by systematic inclusion of spatial correlations at higher orders. A geometrical frustration induces a first-order Mott transition surface with a finite-temperature critical end curve and related crossovers. Growth of antiferromagnetic correlations gives single-particle spectra strongly modified from DMFA with shadow bands and flat dispersions observed in high-Tc{T}_{\mathrm{c}}Tc​ cuprates.
At the Mott transition, electron-electron interaction changes a metal, in which electrons are itinerant, to an insulator, in which electrons are localized. This phenomenon is central to quantum materials. Here we contribute to its understanding by studying the two-dimensional Hubbard model at finite temperature with plaquette cellular dynamical mean-field theory. We provide an exhaustive thermodynamic description of the correlation-driven Mott transition of the half-filled model by calculating pressure, charge compressibility, entropy, kinetic energy, potential energy, and free energy across the first-order Mott transition and its high-temperature crossover (Widom line). The entropy is extracted from the Gibbs-Duhem relation and shows complex behavior near the transition, marked by discontinuous jumps at the first-order boundary, singular behavior at the Mott endpoint, and inflections marking sharp variations in the supercritical region. The free energy allows us to identify the thermodynamic phase boundary, to discuss phases stability and metastability, and to touch upon nucleation and spinodal decomposition mechanisms for the transition. We complement this thermodynamic description of the Mott transition by an information-theoretic description. We achieve this by calculating the local entropy, which is a measure of entanglement, and the single-site total mutual information, which quantifies quantum and classical correlations. These information-theoretic measures exhibit characteristic behaviors that allow us to identify the first-order coexistence regions, the Mott critical endpoint and the crossovers along the Widom line in the supercritical region.
We investigate a nonmagnetic metal-insulator transition in the 1/5-depleted square lattice Hubbard model at half filling within the eight-site cellular dynamical mean field theory. We find that a metal-insulator transition without any signatures of a first-order transition, a continuous Mott transition, takes place in a certain range of parameters. The nature of the continuous Mott transition is merely a Lifshitz transition driven by the on-site Coulomb interaction. The renormalized matrix elements of hoppings and the spin-spin correlation functions reveal that the physics of this transition is a strong enhancement of the dimerization due to the nonlocal effects of the electron-electron interaction.