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arXiv:cond-mat/0507494 · Physical Review B

One-band Hubbard model with hopping asymmetry and the effective theory at finite U : Phase diagram and metal-insulator transition

Yu-Chuan Wen, Yue Yu

Published Jul 19, 2005• 1 citation
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Abstract

We study the one-band Hubbard model at half filling with hopping asymmetry and its effective model at finite but large $U$ up to the second order of ${t}_{\text{mix}}∕U$. Two variational wave functions, the resonating valence bond (RVB) wave function and antiferromagnetic (AF) RVB coexisted wave function, are studied by variational Monte Carlo method on $L\ifmmode\times\else\texttimes\fi{}L$ square lattices up to $L=12$. Based on these two wave functions, the phase diagrams for both models are presented. For the Hubbard model, we find that there is a metal-insulator transition when the hopping parameter ${t}_{\text{mix}}$ which changes the local double occupant vanishes while only a metal-insulator crossover is explored for any finite ${t}_{\text{mix}}$. For the effective model in which the perturbation expansion is up to the second order of ${t}_{\text{mix}}∕U$, a clear metal-insulator transition can be identified for both variational wave functions and the phase diagram can be drawn accordingly. In both models, we find that the systems are dominated by AF-RVB wave function when $U$ is large while the RVB wave function is favored when $U$ is small.

DOI
10.1103/physrevb.72.045130

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We study the one-band Hubbard model at half filling with hopping asymmetry and its effective model at finite but large UUU up to the second order of tmix∕U{t}_{\text{mix}}∕Utmix​∕U. Two variational wave functions, the resonating valence bond (RVB) wave function and antiferromagnetic (AF) RVB coexisted wave function, are studied by variational Monte Carlo method on L\ifmmode×\else\texttimes\fiLL\ifmmode\times\else\texttimes\fi{}LL\ifmmode×\else\texttimes\fiL square lattices up to L=12L=12L=12. Based on these two wave functions, the phase diagrams for both models are presented. For the Hubbard model, we find that there is a metal-insulator transition when the hopping parameter tmix{t}_{\text{mix}}tmix​ which changes the local double occupant vanishes while only a metal-insulator crossover is explored for any finite tmix{t}_{\text{mix}}tmix​. For the effective model in which the perturbation expansion is up to the second order of tmix∕U{t}_{\text{mix}}∕Utmix​∕U, a clear metal-insulator transition can be identified for both variational wave functions and the phase diagram can be drawn accordingly. In both models, we find that the systems are dominated by AF-RVB wave function when UUU is large while the RVB wave function is favored when UUU is small.
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.
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.
Employing a combination of functional renormalization group calculations and projective determinantal quantum Monte Carlo simulations, we examine the Hubbard model on the square lattice bilayer at half filling. From this combined analysis, we obtain a comprehensive account of the ground-state phase diagram with respect to the extent of the system's metallic and (antiferromagnetically ordered) Mott-insulating as well as band-insulating regions. By means of an unbiased functional renormalization group approach, we exhibit the antiferromagnetic Mott-insulating state as the relevant instability of the free metallic state, induced by any weak finite on-site repulsion. Upon performing a careful analysis of the quantum Monte Carlo data, we resolve the difficulty of identifying this antiferromagnetic ground state for finite interlayer hopping in the weak-coupling regime, where nonmonotonic finite-size corrections are shown to relate to the two-sheeted Fermi surface structure of the metallic phase. On the other hand, quantum Monte Carlo simulations are well suited to identify the transition between the Mott-insulating phase and the band insulator in the intermediate-to-strong coupling regime. Here, we compare our numerical findings to indications for the transition region obtained from the functional renormalization group procedure.
We study the Mott metal-insulator transition in the two-band Hubbard model with different hopping amplitudes t1 and t2 for the two orbitals on the two-dimensional square lattice by using non-magnetic variational wave functions, similarly to what has been considered in the limit of infinite dimensions by dynamical mean-field theory. We work out the phase diagram at half filling (i.e. two electrons per site) as a function of R = t2/t1 and the on-site Coulomb repulsion U, for two values of the Hund's coupling J = 0 and J/U = 0.1. Our results are in good agreement with previous dynamical mean-field theory calculations, demonstrating that the non-magnetic phase diagram is only slightly modified from infinite to two spatial dimensions. Three phases are present: a metallic one, for small values of U, where both orbitals are itinerant; a Mott insulator, for large values of U, where both orbitals are localized because of the Coulomb repulsion; and the so-called orbital-selective Mott insulator (OSMI), for small values of R and intermediate Us, where one orbital is localized while the other one is still itinerant. The effect of the Hund's coupling is two-fold: on one side, it favors the full Mott phase over the OSMI; on the other side, it stabilizes the OSMI at larger values of R.
We investigate the ionic Hubbard model (IHM) at half-filling in the limit of strong correlations and large ionic potential. The low-energy effective Hamiltonian in this limit, obtained by a similarity transformation, is a modified $t\ensuremath{-}J$ model with effective second-neighbor hopping terms. We explore the possibilities of ddd-wave pairing and extended sss-wave pairing superconducting (SC) phases on a two-dimensional square lattice at zero temperature within a Gutzwiller projected renormalized mean-field theory. In the sector of solutions that forbid spin-ordering, the system shows a finite nonzero ddd-wave as well as extended sss-wave pairing amplitude for $\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}U\ensuremath{\gg}t$. The width of the superconducting phase in $U\ensuremath{-}\mathrm{\ensuremath{\Delta}}$ regime shrinks with increase in UUU and $\mathrm{\ensuremath{\Delta}}$, though the extended sss-wave pairing phase is higher in energy than the ddd-wave pairing superconducting phase. But in a spin-resolved renormalized mean-field calculation, which allows for an antiferromagnetic (AF) order along with the ddd-wave or extended sss-wave pairing, the SC phase is no longer viable and the system shows a direct transition from an AF ordered phase to a paramagnetic band insulator. Except for a thin sliver of a half-metallic AF phase close to the AF transition point, most of the AF ordered phase is a Mott insulator. We benchmarked the AF Mott insulator to band insulator transition within the Gutzwiller projected renormalized mean-field theory against the dynamical mean-field theory solved using continuous time quantum Monte Carlo. Our work suggests that the ground-state phase diagram of the IHM at half-filling in the limit of extreme correlations does not have any SC phase. The SC phase seen in the paramagnetic sector is a metastable phase, being higher in energy than the AF Mott insulator phase.
The Quantum Monte Carlo simulations of the ionic Hubbard model on a two-dimensional square lattice at half filling were performed. The method based on the direct-space, proposed by Suzuki and al., Hirsch and al., was used. Cycles of increasing and decreasing values of the Coulomb interaction $ U $ were performed for fixed temperature ($ kT=0.01 $). Results indicate that, at low temperature, the two insulator phases are separated by a metallic phase for weak to intermediate values of the staggered potential $ Δ$. For large Coulomb repulsion the system is in a Mott insulator with an antiferromagnetism order. On increasing and decreasing the Coulomb interaction $ U $ the metal-Mott insulator transition shows an hysteresis phenomenon while the metal-band insulator transition is continue. For large $ Δ$ it seems that the metallic region shrinks to a single metallic point. However, the band insulator to the Mott insulator transition is not direct for the studied model. A phase diagram is drawn for the temperature $ kT=0.01 $. For $ Δ=0.5 $ cycles of increasing and decreasing temperature were programmed for different values of the Coulomb interaction $ U $ . A behaviour change appears for $ U\simeq 1.75 $. This suggests that a crossover line divides the metallic region of the phase diagram.