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arXiv:1310.0127 · International Conference on Strongly Correlated Electron Systems (SCES)

Cluster Mean-Field Approach with Density Matrix Renormalization Group: Application to the Hard-Core Bosonic Hubbard Model on a Triangular Lattice

Ryota Suzuki, Akihisa Koga

Published Jun 16, 2014• 3 citations
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Abstract

We introduce a new numerical method for the solution of self-consistent equations in the cluster mean-field theory. The method uses the density matrix renormalization group method to solve the associated cluster problem. We obtain an accurate critical value of the supersolid-superfluid transitions in the hard-core bosonic Hubbard model on a triangular lattice, which is comparable with the recent quantum Monte Carlo results. This algorithm is applicable to more general classes of models with a larger number of degrees of freedom.

DOI
10.7566/jpscp.3.016005

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We introduce a new numerical method for the solution of self-consistent equations in the cluster mean-field theory. The method uses the density matrix renormalization group method to solve the associated cluster problem. We obtain an accurate critical value of the supersolid-superfluid transitions in the hard-core bosonic Hubbard model on a triangular lattice, which is comparable with the recent quantum Monte Carlo results. This algorithm is applicable to more general classes of models with a larger number of degrees of freedom.
A new numerical method for the solution of the dynamical mean field theory's self-consistent equations is introduced. The method uses the density matrix renormalization group technique to solve the associated impurity problem. The new algorithm makes no a priori approximations and is only limited by the number of sites that can be considered. We obtain accurate estimates of the critical values of the metal-insulator transitions and provide evidence of substructure in the Hubbard bands of the correlated metal. With this algorithm, more complex models having a larger number of degrees of freedom can be considered and finite-size effects can be minimized.
We study ground-state properties in a hard-core Bose-Hubbard model on a layered triangular lattice. Combining cluster mean-field theory with the density matrix renormalization group method, we discuss the effect of the interlayer coupling on the supersolid states realized in a single layered model. By examining the distributions for the particle density and superfluid order parameter, the rich phase diagram of the system is obtained. We find that the supersolid states are widely stabilized at a commensurate filling, in contrast to the case of the single layered model. The nature of the supersolid states is also addressed.
We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using the density-matrix renormalization group method. A rich ground-state phase diagram is determined. In this phase diagram there is a supersolid phase and a pair superfluid phase due to the interplay between the ordinary frustrated boson hopping and an unusual correlated hopping. In particular, we find that the quantum phase transition between the supersolid phase and the pair superfluid phase is continuous.
We study the phase diagram of the boson Hubbard model at T=0T=0T=0 without disorder in a one-site and a two-site mean-field approximations. The two-site mean-field significantly improves the results compared to ordinary mean-field solutions and allows to use a simple scheme of mean-field renormalization group (MFRG). Some results obtained with MFRG are even better including the critical exponents for the density-driven transition between the Mott insulator and superfluid phases. However, when we evaluate critical exponents for transitions through the tip of the insulating lobes (special transitions without density change), we get similar exponents indicating that the MFRG apparently does not distinguish between both type of transitions and places them in the same universality class. The results for the first insulating lobe in d=1d=1d=1 and d=2d=2d=2 are in good agreement with a perturbative method and with the more reliable quantum Monte Carlo results. Our MFRG method provides analytical results for any lobe in any dimension and can be systematically improved if we consider larger clusters.
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We explore the use of exact diagonalization methods for solving the self-consistent equations of the cellular dynamical mean field theory for the one-dimensional regular and extended Hubbard models. We investigate the nature of the Mott transition and convergence of the method as a function of cluster size as well as the optimal allocation of computational resources between bath and ``cluster-impurity'' sites, with a view to develop a renormalization group method in higher dimensions. We assess the performance of the method by comparing results for the Green's functions in both the spin density wave and charge density wave phases with accurate density matrix renormalization group (DMRG) calculations.