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International Conference on Strongly Correlated Electron Systems (SCES)

Spectral Weights of the Square-Lattice Hubbard Model with Frustration in the Magnetic and Mott Insulator Phases

Atsushi Yamada, Kazuhiro Seki, R. Eder, Y. Ohta

Published Jun 16, 2014• 0 citations
Publisher

Abstract

Spectral weights of the square-lattice Hubbard model with frustration are studied at half-filling and zero temperature by the variational cluster approximation.We study in detail the finite size effects on the spectral weight functions for magnetically ordered and paramagnetic insulator states using 12-site clusters of three different shapes.We find that when the on-site Coulomb repulsion is larger than the band width, the finite size effects on the spectral functions are very small.

DOI
10.7566/jpscp.3.013008

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Spectral weights of the square-lattice Hubbard model with frustration are studied at half-filling and zero temperature by the variational cluster approximation.We study in detail the finite size effects on the spectral weight functions for magnetically ordered and paramagnetic insulator states using 12-site clusters of three different shapes.We find that when the on-site Coulomb repulsion is larger than the band width, the finite size effects on the spectral functions are very small.
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The Mott transition is observed experimentally in materials that are magnetically frustrated so that long-range order does not hide the Mott transition at finite temperature. The Hubbard model on the triangular lattice at half filling is a paradigmatic model to study the interplay of interactions and frustration on the normal-state phase diagram. We use the dynamical cluster approximation with continuous-time auxiliary-field quantum Monte Carlo to solve this model for 1-, 4-, 6-, 12-, and 16-site clusters with detailed analysis performed for the 6-site cluster. We show that (a) for every cluster there is an inflection point in the double occupancy as a function of interaction, defining a Widom line that extends above the critical point of the first-order Mott transition; (b) the presence of this line and the cluster size dependence argue for the observability of the Mott transition at finite temperature in the thermodynamic limit; and (c) the loss of spectral weight in the metal-to-Mott-insulator transition as a function of temperature and for strong interactions is momentum dependent, the hallmark of a pseudogap. That pseudogap spans a large region of the phase diagram near the Mott transition.
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 metal-insulator transition in the half-filled Hubbard model on the two-dimensional triangular lattice using both the Kotliar-Ruckenstein slave-boson technique and an exact numerical diagonalization of finite clusters. Contrary to the case of a square lattice, where a perfect nesting of the Fermi surface leads to a metal-insulator transition at arbitrarily small values of U, always accompanied by antiferromagnetic ordering, on a triangular lattice, due to the lack of perfect nesting, the transition takes place at a finite value of U, and frustration induces a nontrivial competition among different magnetic phases. Indeed, within the mean-field approximation in the slave-boson approach, as the interaction grows the paramagnetic metal turns into a metallic phase with incommensurate spiral ordering. Increasing the interaction further, a linear spin-density wave is stabilized, and finally for strong coupling the latter phase undergoes a first-order transition toward an antiferromagnetic insulator. No trace of the intermediate phases is seen in the exact diagonalization results, indicating a transition between a paramagnetic metal and an antiferromagnetic insulator.
We study the extended Hubbard model on a two-dimensional half-filled square lattice using the dynamical cluster approximation. We present results on the phase boundaries between the paramagnetic metallic (normal) state and the insulating antiferromagnetic state, as well as between the antiferromagnetic and charge-order states. We find hysteresis along the antiferromagnet/charge order and normal/charge-order phase boundaries (at larger values of the on-site interaction), indicating first-order phase transitions. We show that nearest-neighbor interactions lower the critical temperature for the antiferromagnetic phase. We also present results for the effect of nearest-neighbor interactions on the antiferromagnetic phase boundary and for the evolution of spectral functions and energetics across the phase transitions.
We study the ground-state properties of the Hubbard model on the honeycomb lattice at half filling. Using the variational cluster approximation, We study the semimetal-insulator transition and antiferromagnetism as functions of the on-site Coulomb interaction U . When U is switched on, a small, but finite, single-particle gap appears; thus, we conclude that a tiny gap appears with arbitrary small U > 0. With further increases in U , the system goes into the antiferromagnetic state. We find that the staggered magnetization increases continuously with increasing U and that the antiferromagnetic phase transition is of the second order.