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APS March Meeting Abstracts

Monte Carlo Study of the Magnetic Properties of the 3D Hubbard Model

Isabel Campos, J. W. Davenport

Published Mar 1, 2002• 0 citations
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Abstract

We investigate numerically the magnetic properties of the 3D Isotropic and Anisotropic Hubbard model at half-filling. The behavior of the transition temperature as a function of the anisotropic hopping parameter is qualitatively described. In the Isotropic model we measure the scaling properties of the susceptibility finding agreement with the magnetic critical exponents of the 3D Heisenberg model. We also describe several particularities concerning the implementation of our simulation in a cluster of personal computers. 1 1

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Monte Carlo study of the magnetic properties of the 3D Hubbard model

Isabel Campos, J. W. Davenport

We investigate numerically the magnetic properties of the 3D Isotropic and Anisotropic Hubbard model at half-filling. The behavior of the transition temperature as a function of the anisotropic hopping parameter is qualitatively described. In the Isotropic model we measure the scaling properties of the susceptibility finding agreement with the magnetic critical exponents of the 3D Heisenberg model. We also describe several particularities concerning the implementation of our simulation in a cluster of personal computers.

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Using quantum Monte Carlo techniques we study the magnetic susceptibility of the Hubbard model on a two-dimensional square lattice for values of the coupling U/t ranging from 4 to 20, and as a function of temperature and doping. For U/t=4 the magnetic susceptibility has a maximum at half filling and decreases with doping, in qualitative agreement with recent random-phase-approximation calculations. However, for U/t=10 the susceptibility increases with hole doping near half filling resembling the experimental results obtained for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$. At low electronic density the temperature dependence of the susceptibility is compatible with that of a Fermi liquid.

Physical review. B, Condensed matter•Aug 1, 1993•39 citations
We investigate numerically the magnetic properties of the 3D Isotropic and Anisotropic Hubbard model at half-filling. The behavior of the transition temperature as a function of the anisotropic hopping parameter is qualitatively described. In the Isotropic model we measure the scaling properties of the susceptibility finding agreement with the magnetic critical exponents of the 3D Heisenberg model. We also describe several particularities concerning the implementation of our simulation in a cluster of personal computers. 1 1
We investigate numerically the magnetic properties of the 3D Isotropic and Anisotropic Hubbard model at half-filling. The behavior of the transition temperature as a function of the anisotropic hopping parameter is qualitatively described. In the Isotropic model we measure the scaling properties of the susceptibility finding agreement with the magnetic critical exponents of the 3D Heisenberg model. We also describe several particularities concerning the implementation of our simulation in a cluster of personal computers.
We study the magnetic properties of the three-dimensional (3D) Hubbard model at half filling in the two particle self-consistent formalism, previously developed for the 2D model. We focus on the N\'eel transition approached from the disordered side and on the paramagnetic phase. We find a very good quantitative agreement with dynamical mean-field (DMF) results for the isotropic 3D model. Calculations on finite size lattices also provide satisfactory comparisons with Monte Carlo results up to the intermediate coupling regime. We point out a qualitative difference between the isotropic 3D case, and the 2D or anisotropic 3D cases for the double occupation factor. Even for this local correlation function, 2D or anisotropic 3D cases are out of reach of DMF: this comes from the inability of DMF to account for antiferromagnetic fluctuations, which are crucial.
Magnetic properties of the half-filled Hubbard model on three-dimensional bipartite lattices have been studied by using the linked-cluster series expansion method. The series for the free energy and the staggered susceptibility have been calculated as a function of \ensuremath{\mathrm{B}}t for three-dimensional bipartite lattices for an arbitrary value of the Coulomb interaction U. We obtain a transition from a paramagnetic to an antiferromagnetic U/t-TN{\mathrm{T}}_{\mathrm{N}}TN​ /t phase diagram from the divergence of the staggered susceptibility series. Comparisons with Monte Carlo simulation, Onsager reaction field result of an effective spin Hamiltonian, and large-U Heisenberg high-temperature solutions are made.
We present results of Monte Carlo simulations of the three-dimensional half-filled Hubbard model on simple-cubic 43{4}^{3}43 lattices and some 63{6}^{3}63 lattices with periodic boundary conditions, as well as of small clusters embedded in an effective medium. Magnetic properties were studied for values of the Hubbard repulsion U ranging from 0 to the bandwidth W=12t (t is the hopping matrix element). Our results show that antiferromagnetism is enhanced up to U\ensuremath{\sim}(5/6)W and then suppressed. The q=0 magnetic susceptibility is enhanced by U, although much less than predicted by the random-phase approximation. The transition temperature to an antiferromagnetic state is found to have a broad maximum around U\ensuremath{\sim}(5/6)W, with a maximum value of approximately W/18. The implications of our results for superconductivity in the attractive Hubbard model are also discussed.
We develop series expansions for the ground state properties of the Hubbard model by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility, and spin stiffness are calculated as a function of U/t, where U is the Coulomb constant and t is the hopping parameter. Magnetic susceptibility data indicate a crossover around U\ensuremath{\approxeq}4 between spin density wave antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte Carlo simulations, random phase approximation result, and mean-field solutions are also made.
Using quantum Monte Carlo techniques we study the magnetic susceptibility of the Hubbard model on a two-dimensional square lattice for values of the coupling U/t ranging from 4 to 20, and as a function of temperature and doping. For U/t=4 the magnetic susceptibility has a maximum at half filling and decreases with doping, in qualitative agreement with recent random-phase-approximation calculations. However, for U/t=10 the susceptibility increases with hole doping near half filling resembling the experimental results obtained for ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4{\mathrm{CuO}}_{4}CuO4​. At low electronic density the temperature dependence of the susceptibility is compatible with that of a Fermi liquid.