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arXiv:cond-mat/0105334 · Physical review. B, Condensed matter

Mott transition in the two-dimensional flux phase

Yuichi Otsuka, Yasuhiro Hatsugai

Published Jan 14, 2002• 18 citations
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Abstract

Effects of the electron-electron interaction in the two-dimensional flux phase are investigated. We treat the half-filled Hubbard model with a magnetic flux $\ensuremath{\pi}$ per plaquette by the quantum Monte Carlo method. When the interaction is small, an antiferromagnetic long-range order does not exist. It suggests that the Mott transition occurs at finite strength of the interaction in the flux phase, which is in contrast to the standard Hubbard model.

DOI
10.1103/physrevb.65.073101

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Effects of the electron-electron interaction in the two-dimensional flux phase are investigated. We treat the half-filled Hubbard model with a magnetic flux \ensuremathπ\ensuremath{\pi}\ensuremathπ per plaquette by the quantum Monte Carlo method. When the interaction is small, an antiferromagnetic long-range order does not exist. It suggests that the Mott transition occurs at finite strength of the interaction in the flux phase, which is in contrast to the standard Hubbard model.
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.
The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.
We investigate the phases of the ionic Hubbard model in a two-dimensional square lattice using determinant quantum Monte Carlo. At half-filling, when the interaction strength or the staggered potential dominates, we find Mott and band insulators, respectively. When these two energies are of the same order, we find a metallic region. Charge and magnetic structure factors demonstrate the presence of antiferromagnetism only in the Mott region, although the externally imposed density modulation is present everywhere in the phase diagram. Away from half-filling, other insulating phases are found. Kinetic energy correlations do not give clear signals for the existence of a bond-ordered phase.
For doped two-dimensional Mott insulators in their normal state, the challenge is to understand the evolution from a conventional metal at high doping to a strongly correlated metal near the Mott insulator at zero doping. To this end, we solve the cellular dynamical mean-field equations for the two-dimensional Hubbard model using a plaquette as the reference quantum impurity model and continuous-time quantum Monte Carlo method as impurity solver. The normal-state phase diagram as a function of interaction strength UUU, temperature TTT, and filling nnn shows that, upon increasing nnn toward the Mott insulator, there is a surface of first-order transition between two metals at nonzero doping. That surface ends at a finite temperature critical line originating at the half-filled Mott critical point. Associated with this transition, there is a maximum in scattering rate as well as thermodynamic signatures. These findings suggest a new scenario for the normal-state phase diagram of the high temperature superconductors. The criticality surmised in these systems can originate not from a T === 0 quantum critical point, nor from the proximity of a long-range ordered phase, but from a low temperature transition between two types of metals at finite doping. The influence of Mott physics therefore extends well beyond half-filling.
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.
A two-dimensional model of interacting electrons on a lattice, the Hubbard model, has been studied by means of a numerical simulation technique. Results for the half-filled-band sector are presented for lattices of up to 6\ifmmode\times\else\texttimes\fi{}6 spatial sites, as a function of temperature and electron-electron repulsion UUU. In the ground state, the system is found to exhibit antiferromagnetic long-range order for all values of UUU, although greatly reduced from the mean-field-theory predictions.