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Journal of Zhongyuan University of Technology

Effect of Disorder and Hole-doped on the Antiferromagnetism in The 2D Hubbard Model

Wensheng Liu

Published Jan 1, 2008• 0 citations
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Abstract

In this paper,we investigate the two-dimensional Hubbard model with different disorder strength.Using the exact diagonal method,we self-consistently calculate the effects of disorder on the spatial distribution of the order parameters and density of states at half-filling.We also discuss the effect of disorder on antiferromagnetic phase.Furthermore,we consider the case for adding a hole at half-filling.

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In this paper,we investigate the two-dimensional Hubbard model with different disorder strength.Using the exact diagonal method,we self-consistently calculate the effects of disorder on the spatial distribution of the order parameters and density of states at half-filling.We also discuss the effect of disorder on antiferromagnetic phase.Furthermore,we consider the case for adding a hole at half-filling.
We study the dimensional dependence of the interplay between correlation and disorder in two dimension at half filling using 2D t−t′t-t't−t′ disordered Hubbard model with deterministic disorder both at zero and finite temperatures. Inclusion of t′t't′ without disorder leads to a metallic phase at half filling below a certain critical value of UUU. Above this critical value UcU_cUc​ correlation favours antiferromagnetic phase. Since disorder leads to double occupancy over the lower energy site, the competition between Hubbard UUU and disorder leads to the emergence of a metallic phase, which can be quantified by the calculation of Kubo conductivity, gap at half-filling, density of states, spin order parameter, Inverse participation ratio (IPR) and bandwidth. We have studied the effect of disorder on the system in a very novel way through a deterministic disorder which follows a Fibonacci sequence. Behaviour of different parameters show interesting features on going from a two to quasi one dimensional system.
We study the dimensional dependence of the interplay between correlation and disorder in two dimensions at half-filling using the 2D t- t ' disordered Hubbard model with deterministic disorder both at zero and finite temperatures. Inclusion of t ' without disorder leads to a metallic phase at half-filling below a certain critical value of U . Above this critical value U c correlation favours an antiferromagnetic phase. Since disorder leads to double occupancy over the lower-energy site, the competition between Hubbard U and disorder leads to the emergence of a metallic phase, which can be quantified by the calculation of Kubo conductivity, gap at half-filling, density of states, spin order parameter, inverse participation ratio (IPR) and bandwidth. We have studied the effect of disorder on the system in a very novel way through a deterministic disorder which follows a Fibonacci sequence. The behaviour of different quantities shows interesting features on going from a two- to quasi–one-dimensional system.
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.
We determine the spin and charge orders in the ground state of the doped two-dimensional (2D) Hubbard model in its simplest form, namely with only nearest-neighbor hopping and on-site repulsion. At half-filling, the ground state is known to be an antiferromagnetic Mott insulator. Doping Mott insulators is believed to be relevant to the superconductivity observed in cuprates. A variety of candidates have been proposed for the ground state of the doped 2D Hubbard model. A recent work employing a combination of several state-of-the-art numerical many-body methods established the stripe order as the ground state near 1/81/81/8 doping at strong interactions. In this paper, we apply one of these methods, the cutting-edge constrained-path auxiliary field quantum Monte Carlo (AFQMC) method with self-consistently optimized gauge constraints, to systematically study the model as a function of doping and interaction strength. With careful finite size scaling based on large-scale computations, we map out the ground state phase diagram in terms of its spin and charge order. We find that modulated antiferromagnetic order persists from near half-filling to about 1/51/51/5 doping. At lower interaction strengths or larger doping, these ordered states are best described as spin-density waves, with essentially delocalized holes and modest oscillations in charge correlations. When the charge correlations are stronger (large interaction or small doping), they are best described as stripe states, with the holes more localized near the node in the antiferromagnetic spin order. In both cases, we find that the wavelength in the charge correlations is consistent with so-called filled stripes.
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The two-dimensional Hubbard model in the presence of diagonal and off-diagonal disorder is studied at half-filling with a finite-temperature quantum Monte Carlo method. Magnetic correlations as well as the electronic compressibility are calculated to determine the behavior of local magnetic moments, the stability of antiferromagnetic long-range order (AFLRO), and properties of the disordered phase. The existence of random potentials (diagonal or ``site'' disorder) leads to a suppression of local magnetic moments which eventually destroys AFLRO. Randomness in the hopping elements (off-diagonal disorder), on the other hand, does not significantly reduce the density of local magnetic moments. For this type of disorder, at half-filling, there is no ``sign problem'' in the simulations as long as the hopping is restricted between neighbor sites on a bipartite lattice. This allows the study of sufficiently large lattices and low temperatures to perform a finite-size scaling analysis. For off-diagonal disorder, AFLRO is eventually destroyed when the fluctuations of antiferromagnetic exchange couplings exceed a critical value. The disordered phase close to the transition appears to be incompressible, and shows an increase of the uniform susceptibility at low temperatures.