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Springer series in solid-state sciences

Variational Wave Functions in the One-Dimensional t-J Model for Strongly Correlated Regimes

Masao Ogata

Published Jan 1, 1994• 0 citations
Publisher
DOI
10.1007/978-3-642-85129-2_12

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The ground state of the Hubbard model on one-dimensional and two-dimensional square lattices is studied with the effective Hamiltonian derived for the strong correlation regime and Gutzwiller-type wave function. The non-half-filled band as well as the half-filled band is discussed. The variational Monte-Carlo method enables us to evaluate the energy for the singlet liquid (resonating-valence-bond state) and for Néel state. The result shows that the stability of the singlet liquid depends on the dimensionality of the system.
We study a class of variational wave functions for strongly interacting one-dimensional lattice fermions in which correlations among the particles are specified by a single variational parameter. We find that the wave functions describe the ground-state properties of the one-dimensional t-J model remarkably well over the entire phase diagram in which interaction strength and density are varied. Specifically the wave function describes a Tomonaga-Luttinger liquid at low J/t, a phase-separated state at large J/t, and a stable state with infinite compressibility between these phases at low densities.
A scheme of optimization of a trial wave function in the variational Monte Carlo calculation is developed. It provides a more precise description of the ground state for strongly correlated electronic systems with highly improved trial wave function. A general type of variational wave function constructed from a linear combination of Slater determinants multiplied by Jastrow correlation factors is proposed. They can explicitly contain low-energy fluctuations and long-range correlations. Using this optimization method, we examine the properties of these wave functions by applying them to a one-dimensional Hubbard model for which the exact solution is available for comparison. It is found that these wave functions prove to be substantial improvements compared to the conventional Jastrow-type wave functions.