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arXiv:cond-mat/0608248 · Physical Review B

Mott transition in the Hubbard model away from particle-hole symmetry

Daniel J. García, E. Miranda, K. Hallberg, Marcelo J. Rozenberg

Published Mar 26, 2007• 22 citations
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Abstract

We solve the dynamical mean-field theory equations for the Hubbard model away from the particle-hole-symmetric case using the density matrix renormalization group method. We focus our study on the region of strong interactions and finite doping where two solutions coexist. We obtain precise predictions for the boundaries of the coexistence region. In addition, we demonstrate the capabilities of this precise method by obtaining the frequency-dependent optical conductivity spectra.

DOI
10.1103/physrevb.75.121102

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We solve the dynamical mean-field theory equations for the Hubbard model away from the particle-hole-symmetric case using the density matrix renormalization group method. We focus our study on the region of strong interactions and finite doping where two solutions coexist. We obtain precise predictions for the boundaries of the coexistence region. In addition, we demonstrate the capabilities of this precise method by obtaining the frequency-dependent optical conductivity spectra.
The single-particle spectral properties near the Mott transition in the one-dimensional Hubbard model are investigated by using the dynamical density-matrix renormalization group method and the Bethe ansatz. The pseudogap, hole-pocket behavior, spectral-weight transfer, and upper Hubbard band are explained in terms of spinons, holons, antiholons, and doublons. The Mott transition is characterized by the emergence of a gapless mode whose dispersion relation extends up to the order of hopping t (spin exchange J) in the weak (strong) interaction regime caused by infinitesimal doping.
In this paper, I discuss the finite-temperature metal-insulator transition of the paramagnetic Hubbard model within dynamical mean-field theory. I show that coexisting solutions, the hallmark of such a transition, can be obtained in a consistent way both from quantum Monte Carlo (QMC) simulations and from the exact diagonalization method. I pay special attention to discretization errors within the QMC method. These errors explain why it is difficult to obtain the solutions from the QMC method close to the boundaries of the coexistence region.
We use the density-matrix renormalization group method to investigate ground-state and dynamic properties of the one-dimensional Bose-Hubbard model, the effective model of ultracold bosonic atoms in an optical lattice. For fixed maximum site occupancy n b = 5, we calculate the phase boundaries between the Mott insulator and the "superfluid" phase for the lowest two Mott lobes. We extract the Tomonaga-Luttinger parameter from the density-density correlation function and determine accurately the critical interaction strength for the Mott transition. For both phases, we study the momentum distribution function in the homogeneous system, and the particle distribution and quasi-momentum distribution functions in a parabolic trap. With our zero-temperature method we determine the photoemission spectra in the Mott insulator and in the "superfluid" phase of the one-dimensional Bose-Hubbard model. In the insulator, the Mott gap separates the quasi-particle and quasi-hole dispersions. In the "superfluid" phase the spectral weight is concentrated around zero momentum.
We present clear numerical evidence for the coexistence of metallic and insulating dynamical mean-field theory (DMFT) solutions in a half-filled single-band Hubbard model at finite temperature. The quantum Monte Carlo (QMC) method is used to solve the DMFT equation. We discuss important technical aspects of the DMFT-QMC method, which should be properly dealt with in order to obtain reliable DMFT solutions at low temperatures. Among these technical aspects are the critical slowing down near the boundaries of the coexistence region, the convergence criteria for the DMFT iterations, and the correct interpolation of the discretized Green's functions.
We consider the optical conductivity ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ in the metallic phase of the one-dimensional Hubbard model. Our results focus on the vicinity of half filling and the frequency regime around the optical gap in the Mott insulating phase. By means of a density-matrix renormalization group implementation of the correction-vector approach, ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ is computed for a range of interaction strengths and dopings. We identify an energy scale Eopt{E}_{\mathrm{opt}}Eopt​ above which the optical conductivity shows a rapid increase. We then use a mobile impurity model in combination with exact results to determine the behavior of ${\ensuremath{\sigma}}_{1}(\ensuremath{\omega})$ for frequencies just above Eopt{E}_{\mathrm{opt}}Eopt​ which is in agreement with our numerical data. As a main result, we find that this onset behavior is not described by a power law.
The optical conductivity of the weakly doped two-dimensional repulsive Hubbard model on the square lattice with the nearest and next-nearest hoppings is calculated within the generalized dynamical mean-field $(\mathrm{DMFT}+{\ensuremath{\sum}}_{\mathbf{p}})$ approach, which includes correlation length scale $\ensuremath{\xi}$ into the standard DMFT equations via the momentum dependent self-energy ${\ensuremath{\sum}}_{\mathbf{p}}$, with a full account of appropriate vertex corrections. This approach takes into consideration the nonlocal dynamical correlations induced, e.g., by short-ranged collective spin-density-wavelike antiferromagnetic spin fluctuations, which (at high enough temperatures) can be viewed as a quenched Gaussian random field with finite correlation length $\ensuremath{\xi}$. The DMFT effective single-impurity problem is solved by numerical renormalization group. We consider both the case of correlated metal with the bandwidth $W\ensuremath{\lesssim}U$ and that of doped Mott insulator with U⪢WU⪢WU⪢W (UUU---the value of local Hubbard interaction). The optical conductivity calculated within $\mathrm{DMFT}+{\ensuremath{\sum}}_{\mathbf{p}}$ demonstrates typical pseudogap behavior within the quasiparticle band, in qualitative agreement with experiments in copper oxide superconductors. For large values of UUU, pseudogap anomalies are effectively suppressed.