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arXiv:0808.2364 · Europhysics Letters (EPL)

First-order Mott transition at zero temperature in two dimensions: Variational plaquette study

M. Balzer, Bumsoo Kyung, David Sénéchal, A.–M. S. Tremblay, Michael Potthoff

Published Jan 1, 2009• 82 citations
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Abstract

The nature of the metal-insulator Mott transition at zero temperature has been discussed for a number of years. Whether it occurs through a quantum critical point or through a first-order transition is expected to profoundly influence the nature of the finite-temperature phase diagram. In this paper, we study the zero temperature Mott transition in the two-dimensional Hubbard model on the square lattice with the variational cluster approximation. This takes into account the influence of antiferromagnetic short-range correlations. By contrast to single-site dynamical mean-field theory, the transition turns out to be first order even at zero temperature.

DOI
10.1209/0295-5075/85/17002

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The nature of the metal-insulator Mott transition at zero temperature has been discussed for a number of years. Whether it occurs through a quantum critical point or through a first-order transition is expected to profoundly influence the nature of the finite-temperature phase diagram. In this paper, we study the zero temperature Mott transition in the two-dimensional Hubbard model on the square lattice with the variational cluster approximation. This takes into account the influence of antiferromagnetic short-range correlations. By contrast to single-site dynamical mean-field theory, the transition turns out to be first order even at zero temperature.
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.
We investigate the Mott transition in a two-dimensional two-orbital Hubbard model on a square lattice at half filling by using the variational Monte Carlo method. As a variational trial wave function, we consider Gutzwiller's on-site correlations and nearest-neighbor doublon-holon correlations. We calculate the ground-state energy and the other physical quantities, all of which clearly signal a first-order Mott transition. We thus obtain the phase diagram at zero temperature, where we find the coexistence region of the metal and the Mott insulator. We discuss how Hund's coupling affects the nature of the Mott transition in this system.
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.
Abstract. We investigate the phase diagram of the square lattice bilayer Hubbard model at half filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping t ⊥ and on-site Coulomb repulsion U. With this study we resolve some discrepancies in previous calculations based on the dynamical mean field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: An antiferromagnetic Mott insulator at small t ⊥ for any value of U and a band insulator at large t⊥. At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small t ⊥ a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing t ⊥ in the range of 5.5t < U < 7.5t. Finally, we discuss the obtained phase diagrams in relation to previous studies based on different many-body approaches. PACS numbers: 71.10.Fd, 71.27.+a, 71.30.+h 1.
We investigate the phase diagram of the square lattice bilayer Hubbard model at half-filling with the variational Monte Carlo method for both the magnetic and the paramagnetic case as a function of the interlayer hopping and on-site Coulomb repulsion U . With this study we resolve some discrepancies in previous calculations based on the dynamical mean-field theory, and we are able to determine the nature of the phase transitions between metal, Mott insulator and band insulator. In the magnetic case we find only two phases: an antiferromagnetic Mott insulator at small for any value of U and a band insulator at large . At large U values we approach the Heisenberg limit. The paramagnetic phase diagram shows at small a metal to Mott insulator transition at moderate U values and a Mott to band insulator transition at larger U values. We also observe a re-entrant Mott insulator to metal transition and metal to band insulator transition for increasing in the range of . Finally, we discuss the phase diagrams obtained in relation to findings from previous studies based on different many-body approaches.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.