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Journal of Physics Condensed Matter

New variational method for quasi-one-dimensional spin problems

V. Ya. Krivnov, А. А. Овчинников

Published Aug 15, 1994• 0 citations
Publisher

Abstract

A new variational method for determining the ground-state energy of quasi-1D systems is proposed. The method consists of decomposition of a lattice into non-interacting blocks. A trial wavefunction is the product of exact ground-state block functions multiplied by operator correlation factors. The ground-state energy of a spin-1/2 and fermionic particle ladder is evaluated. The calculation is very simple and gives energies with an accuracy of about 2% or even less.

DOI
10.1088/0953-8984/6/33/012

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A variational method with nonlocal trial function is developed for quantum one-dimensional systems. It is applied to the XXZ spin-1/2 chain with an alternating magnetic field. A four-node trial wave function for the fermionic representation of the model is constructed. The results obtained in the model with an extended trial wave function demonstrate a significant increase in the accuracy of the ground state energy in the region of critical behavior compared with the solutions obtained previously. A method for calculation of the spin correlation function are discussed.
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.