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arXiv:0811.3718

Comment on arXiv:0811.1575 entitled "Quantum phase transitions in the Hubbard model on triangular lattice" by T. Yoshioka, A. Koga and N. Kawakami

Shinji Watanabe, T. Mizusaki, Masatoshi Imada

Published Nov 22, 2008• 1 citation
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Abstract

We show that the phase boundary between the paramagnetic metal and the nonmagnetic Mott insulator for the Hubbard model on a triangular lattice obtained by Yoshioka et al. in arXiv:0811.1575 does not correctly represent that of the thermodynamic limit but is an artifact of the 6 by 6 lattice they rely on. After the system size extrapolation, the phase boundary is located at U/t=5.2 as proposed by Morita et al., J. Phys. Soc. Jpn. 71 (2008) 2109 and in contrast to Yoshioka et al. Here, U is the onsite Coulomb repulsion and t is the nearest-neighbor transfer.

DOI
10.48550/arxiv.0811.3718

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We show that the phase boundary between the paramagnetic metal and the nonmagnetic Mott insulator for the Hubbard model on a triangular lattice obtained by Yoshioka et al. in arXiv:0811.1575 does not correctly represent that of the thermodynamic limit but is an artifact of the 6 by 6 lattice they rely on. After the system size extrapolation, the phase boundary is located at U/t=5.2 as proposed by Morita et al., J. Phys. Soc. Jpn. 71 (2008) 2109 and in contrast to Yoshioka et al. Here, U is the onsite Coulomb repulsion and t is the nearest-neighbor transfer.
We investigate the quantum phase transitions in the half-filled Hubbard model on the triangular lattice by means of the path-integral renormalization group (PIRG) method with a new iteration scheme proposed recently. It is found that as the Hubbard interaction UUU increases, the paramagnetic metallic state undergoes a first-order phase transition to a nonmagnetic insulating (NMI) state at Uc1∼7.7tU_{c1}\sim 7.7tUc1​∼7.7t, which is followed by another first-order transition to a 120∘120^\circ120∘ Néel ordered state at Uc2∼10tU_{c2}\sim 10tUc2​∼10t, where ttt is the transfer integral. Our results ensure the existence of the intermediate NMI phase, and resolve some controversial arguments on the nature of the previously proposed quantum phase transitions. We find that κκκ-(BEDT-TTF)2_22​Cu2_22​(CN)3_33​ is located in the NMI phase close to the metal-insulator transition point.
We investigate the quantum phase transitions in the half-filled Hubbard model on the triangular lattice by means of the path-integral renormalization group method with a new iteration and truncation scheme proposed recently. It is found for a cluster of 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic state undergoes a first-order phase transition to a nonmagnetic insulating (NMI) state at Uc1 approximately 7.4t, which is followed by another first-order transition to a 120 degrees Néel ordered state at Uc2 approximately 9.2t, where t is the transfer integral. The size dependence of the results is also addressed. Our results suggest the existence of the intermediate NMI phase and resolve some controversial arguments on the nature of the previously proposed quantum phase transitions.
We investigate the half-filled Hubbard model on an isotropic triangular lattice with the variational cluster approximation. By decreasing the on-site repulsion U (or equivalently increasing pressure) we go from a phase with long-range, three-sublattice, spiral magnetic order, to a nonmagnetic Mott insulating phase--a spin liquid--and then, for U less or similar to 6.7t, to a metallic phase. Clusters of sizes 3, 6, and 15 with open boundary conditions are used in these calculations, and an extrapolation to infinite size is argued to lead to a disordered phase at U = 8t, but to a spiral order at U greater or similar to 12.
Abstract We investigate a metal–insulator Mott transition in the half‐filled Hubbard model on the triangular lattice. In this study, we make use of the path‐integral renormalization group method with an iteration and truncation scheme proposed recently, which allows us to access the competing ground states around the transition point. We find for a cluster with 36 sites that as the Hubbard interaction U increases, the paramagnetic metallic (PM) state undergoes a metal–insulator phase transition to a nonmagnetic insulating (NMI) state at Uc∼7.4tU_{\rm c} \sim 7.4tUc​∼7.4t , where t is the transfer integral. A detailed analysis around the transition point shows that the Mott transition is of first order.
We study Mott transition in the two-dimensional Hubbard model on an anisotropic triangular lattice. We use the Lanczos exact diagonalization of finite-size clusters up to eighteen sites, and calculate Drude weight, charge gap, double occupancy and spin structure factor. We average these physical quantities over twisted boundary conditions in order to reduce finite-size effects. We find a signature of the Mott transition in the dependence of the Drude weight and/or charge gap on the system size. We also examine the possibility of antiferromagnetic order from the spin structure factor. Combining these information, we propose a ground-state phase diagram which has a nonmagnetic insulating phase between a metallic phase and an insulating phase with antiferromagnetic order. Finally, we compare our results with those reported in the previous theoretical studies, and discuss the possibility of an unconventional insulating state.
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.