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arXiv:cond-mat/0004092 · Physical review. B, Condensed matter

Ground-state properties of the two-dimensional disordered Hubbard model

Gaëtan Caldara, Bhargavi Srinivasan, Dima L. Shepelyansky

Published Oct 15, 2000• 7 citations
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Abstract

We study the ground state of the two-dimensional disordered Hubbard model by means of the projector quantum Monte Carlo method. This approach allows us to investigate the ground-state properties of this model for lattice sizes up to 10\ifmmode\times\else\texttimes\fi{}10, at quarter filling, for a broad range of interaction and disorder strengths. Our results show that the ground state of this system of spin-$\frac{1}{2}$ fermions remains localized in the presence of the short-ranged Hubbard interaction.

DOI
10.1103/physrevb.62.10680

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We study the ground state of the two-dimensional disordered Hubbard model by means of the projector quantum Monte Carlo method. This approach allows us to investigate the ground-state properties of this model for lattice sizes up to 10\ifmmode\times\else\texttimes\fi{}10, at quarter filling, for a broad range of interaction and disorder strengths. Our results show that the ground state of this system of spin-12\frac{1}{2}21​ fermions remains localized in the presence of the short-ranged Hubbard interaction.
We study the ground state of the two-dimensional (2D) disordered Hubbard model by means of the projector quantum Monte Carlo (PQMC) method. This approach allows us to investigate the ground state properties of this model for lattice sizes up to 10×1010 \times 1010×10, at quarter filling, for a broad range of interaction and disorder strengths. Our results show that the ground state of this system of spin-1/2 fermions remains localised in the presence of the short-ranged Hubbard interaction.
We study numerically the ground-state properties of the repulsive Hubbard model for spin-1/2 electrons on two-dimensional lattices with disordered on-site energies. The projector quantum Monte Carlo method is used to obtain very accurate values of the ground-state charge density distributions with Np{N}_{p}Np​ and Np+1{N}_{p}+1Np​+1 particles. The difference in these charge densities allows us to study the localization properties of an added particle. The results obtained at quarter filling on finite clusters show that the Hubbard repulsion has a strong delocalizing effect on the electrons in disordered two-dimensional lattices. However, numerical restrictions do not allow us to reach a definite conclusion about the existence of a metal-insulator transition in the thermodynamic limit in two dimensions.
We study the effects of disorder on long range antiferromagnetic correlations and the Mott gap in the half-filled, two dimensional, repulsive Hubbard model. We employ Hartree-Fock (HF) and Quantum Monte Carlo (QMC) techniques in our study of the bond and site disordered models. Results from mean field (HF) calculations are used to develop a qualitative picture of the physics and to guide our choice for input to the QMC methods. The basic properties of two QMC methods for correlated fermions are discussed, and the results from these different approaches are presented.
Ground-state properties of the Hubbard model on a two-dimensional square lattice are studied by the auxiliary-field quantum Monte Carlo method. Accurate results for energy, double occupancy, effective hopping, magnetization, and momentum distribution are calculated for interaction strengths of U/tU/tU/t from 2 to 8, for a range of densities including half-filling and n=0.3,0.5,0.6,0.75n=0.3,0.5,0.6,\phantom{\rule{0.16em}{0ex}}0.75n=0.3,0.5,0.6,0.75, and 0.8750.8750.875. At half-filling, the results are numerically exact. Away from half-filling, the constrained path Monte Carlo method is employed to control the sign problem. Our results are obtained with several advances in the computational algorithm, which are described in detail. We discuss the advantages of generalized Hartree-Fock trial wave functions and its connection to pairing wave functions, as well as the interplay with different forms of Hubbard-Stratonovich decompositions. We study the use of different twist angle sets when applying the twist averaged boundary conditions. We propose the use of quasirandom sequences, which improves the convergence to the thermodynamic limit over pseudorandom and other sequences. With it and a careful finite size scaling analysis, we are able to obtain accurate values of ground-state properties in the thermodynamic limit. Detailed results for finite-sized systems up to $16\ifmmode\times\else\texttimes\fi{}16$ are also provided for benchmark purposes.
The Hubbard model has been widely used to describe magnetism due to itinerant electrons. However, except for the one-dimensional case, no exact solution of the model exists. We have studied the two-dimensional Hubbard model on a square lattice using a Monte Carlo simulation technique. Simulations were performed on lattices of up to 8×8 in spatial size. We will discuss results for thermodynamic properties and correlation functions as a function of temperature and interaction strength. For the half-filled band case, our results indicate that the system exhibits long-range antiferromagnetic order in the ground state for any nonzero interaction, although substantially reduced from the classical Néel state due to both charge and spin fluctuations. For the non-half-filled band case, our results suggest that no long-range magnetic order exists. We also don’t find any indication of short-ranged ferromagnetic correlations in the parameter range studied. We have also studied the predictions of various approximate treatments for this model, particularly the static approximation and the coherent potential approximation (CPA). By comparison with the Monte Carlo results, we discuss the validity of these schemes. Finally, we discuss the effect of changing the band structure on the magnetic properties of the system.
We employ the determinant projector quantum Monte Carlo method to investigate the ground-state magnetic properties in the Mott insulating states of the half-filled SU(4)SU(4)SU(4) and SU(6)SU(6)SU(6) Fermi-Hubbard model in the two-dimensional square lattice, which is free of the sign problem. The long-range antiferromagnetic Neel order is found for the SU(4)SU(4)SU(4) case with a small residual Neel moment. Quantum fluctuations are even stronger in the SU(6)SU(6)SU(6) case. Numeric results are consistent with either a vanishing or even weaker Neel ordering than that of SU(4)SU(4)SU(4).