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arXiv:cond-mat/9404095 · Physical review. B, Condensed matter

t-Jmodel studied by the power Lanczos method

Y.-C. Chen, Ting-Kuo Lee

Published Mar 1, 1995• 21 citations
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Abstract

The initial trial wave function used in a simple ground-state projection method, the power method, is systematically improved by using Lanczos algorithm. Much faster convergence to the ground state achieved by using these wave functions significantly reduces the effect of the fermion sign problem. The results for the ground state of the two-dimensional t-J model are presented. The density correlation function for the t-J model at small J shows a surprisingly good agreement with that of a system of noninteracting hard-core bosons.

DOI
10.1103/physrevb.51.6723

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The initial trial wave function used in a simple ground-state projection method, the power method, is systematically improved by using Lanczos algorithm. Much faster convergence to the ground state achieved by using these wave functions significantly reduces the effect of the fermion sign problem. The results for the ground state of the two-dimensional t-J model are presented. The density correlation function for the t-J model at small J shows a surprisingly good agreement with that of a system of noninteracting hard-core bosons.
The spin, charge and pairing correlation functions for the ground state of two-dimensional t−Jt-Jt−J model are calculated by using the power method which projects out the ground state from a variational wave function. ``Exact'' results are obtained for 10×1010\times1010×10 and 8×88\times88×8 lattices with low particle densities. The results are surprisingly similar to that of one-dimensional t−Jt-Jt−J model. The phenomenology is almost perfectly correlated with the concept of Tomonaga-Luttinger liquid and it is incompatible with traditional Fermi liquid theory.
The purpose of this paper is to present some simple variants of a recently developed iterative algorithm for improvement of any given trial wave function. These modifications improve the convergence rate of the iterative process and allow us to obtain a good variational state for larger lattices. We apply the method to the one-dimensional Gross-Neveu model with one flavor in a finite-size lattice. The ground-state energy, the density-density correlation function, and the single-particle Green's function are calculated. They are in good agreement with existing results.
Ground-state properties of the one-dimensional t-J model are studied by using exact diagonalization of small systems and compared with those found with Gutzwiller-Jastrow--type variational functions. Near the supersymmetric case (J/t=2), the Gutzwiller wave function is an extremely good trial function for all electron densities. It reproduces momentum distribution and correlation functions of the exact ground state except for critical behaviors. For J/t2 (>2), the ground-state properties are well described by Jastrow functions with repulsive (attractive) intersite correlations.
A new phase of a gas of pairs of electrons bounded in a singlet state is found in the one-dimensional t-J model for J>2t and the density of electrons less than 0.2. This phase was conjectured in the study of the diagonalization of small lattices [Phys. Rev. Lett. 66, 2388 (1991)]. The existence of this new phase for much larger lattice sizes is demonstrated by a combination of two numerical methods, the variational Monte Carlo and the power method. A trial wave function for this phase is proposed and shown to be in good agreement with the ground state obtained by the power method.
We describe and discuss a recently proposed quantum Monte Carlo algorithm to compute the ground-state properties of various systems of interacting fermions. In this method, the ground state is projected from an initial wave function by a branching random walk in an overcomplete basis of Slater determinants. By constraining the determinants according to a trial wave function |${\mathrm{\ensuremath{\psi}}}_{\mathrm{T}}$〉, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if |${\mathrm{\ensuremath{\psi}}}_{\mathrm{T}}$〉 is exact. We illustrate the method by describing in detail its implementation for the two-dimensional one-band Hubbard model. We show results for lattice sizes up to 16\ifmmode\times\else\texttimes\fi{}16 and for various electron fillings and interaction strengths. With simple single-determinant wave functions as |${\mathrm{\ensuremath{\psi}}}_{\mathrm{T}}$〉, the method yields accurate (often to within a few percent) estimates of the ground-state energy as well as correlation functions, such as those for electron pairing. We conclude by discussing possible extensions of the algorithm.
We propose a new quantum Monte Carlo algorithm to compute fermion ground-state properties. The ground state is projected from an initial wave function by a branching random walk in an over-complete basis space of Slater determinants. By constraining the determinants according to a trial wave function $|{\ensuremath{\Psi}}_{T}〉$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|{\ensuremath{\Psi}}_{T}〉$ is exact. We report results on the two-dimensional Hubbard model up to size $16\ifmmode\times\else\texttimes\fi{}16$, for various electron fillings and interaction strengths.