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Physical Review Letters

Variational Monte Carlo calculations for thet’-Jmodel with Fermi holes and boson spins

N. E. Bonesteel, John W. Wilkins

Published Mar 4, 1991• 7 citations
Publisher

Abstract

We have performed variational Monte Carlo calculations for the two-dimensional t'-J model (t' is an effective, describe fermionic holes hopping in a background liquid of singlet bonds represented by products of bosonic spin operators. The variational energies we obtain from these wave functions can be directly compared with those of other proposed wave functions. We find that our energies are lowest in the t'/J\ensuremath{\ll}1 limit.

DOI
10.1103/physrevlett.66.1232

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We have performed variational Monte Carlo calculations for the two-dimensional t'-J model (t' is an effective, describe fermionic holes hopping in a background liquid of singlet bonds represented by products of bosonic spin operators. The variational energies we obtain from these wave functions can be directly compared with those of other proposed wave functions. We find that our energies are lowest in the t'/J\ensuremath{\ll}1 limit.
We have numerically evaluated the energy of several kinds of wave functions considered to be candidate ground states of the two-dimensional t-J model at various hole densities. We searched a parameter space which includes d-wave and s-wave superconductivity and spin-density-wave ordering as well as the projected Fermi-liquid state. Coexistence of different orderings, such as the s+id state and d-wave spin-density-wave state, were found to be stable states. We find a phase diagram in the density-t/J plane which has coexistence of antiferromagnetism and superconductivity at very low hole concentrations and superconductivity up to rather high values of density---about 40%. At intermediate concentrations, the time-reversal symmetry-breaking s+id state is found.
Excitations of the two-dimensional electron gas, including many-body effects, are calculated with a variational Monte Carlo method. Correlated sampling is introduced to calculate small energy differences between different excitations. The usual pair-product (Slater-Jastrow) trial wave function is found to lack certain correlations entirely so that backflow correlation is crucial. From the excitation energies calculated here, we determine Fermi-liquid parameters and related physical quantities such as the effective mass and the Land\'e g factor of the system. Our results for the effective mass are compared with previous analytic calculations.
We study wave functions for generalized flux phases by the variational Monte Carlo method. Flux tubes are attached to the holes, which produce additional phase factors besides those due to the motion of electrons. The phase factors cancel each other when the electrons and holes interchange position at some special electron densities and, as a result, there are no orbital currents in these states. We investigate especially the one-third filled case and find a slightly lower kinetic energy than the original commensurate flux phase. We also calculate the chirality to confirm that time-reversal symmetry is also broken in these states. The analogy to the quantum-Hall-effect wave functions leads us to study modified forms of off-diagonal long-range order in the pair-correlation function. The existence of this long-range order is shown explicitly by variational Monte Carlo calculations and renormalized mean-field approximations. The flux phases do not have the usual off-diagonal long-range order but do have a modified form similar to that in the quantum Hall effect. The relationships to the slave-boson mean-field theories and anyon systems are also discussed.
The conventional tensor-network states employ real-space product states as reference wave functions. Here, we propose a many-variable variational Monte Carlo (mVMC) method combined with tensor networks by taking advantages of both to study fermionic models. The variational wave function is composed of a pair product wave function operated by real-space correlation factors and tensor networks. Moreover, we can apply quantum number projections, such as spin, momentum, and lattice symmetry projections, to recover the symmetry of the wave function to further improve the accuracy. We benchmark our method for one- and two-dimensional Hubbard models, which show significant improvement over the results obtained individually either by mVMC or by tensor network. We have applied the present method to a hole-doped Hubbard model on the square lattice, which indicates the stripe charge/spin order coexisting with a weak ddd-wave superconducting order in the ground state for the doping concentration of less than 0.3, where the stripe oscillation period gets longer with increasing hole concentration. The charge homogeneous and highly superconducting state also exists as a metastable excited state for the doping concentration less than 0.25.
We propose a correlated spin-singlet-pair wave function to describe the spin-gap phase of the one-dimensional t-J model at low density and large J/t. In addition to having singlet pairs, this wave function has a Jastrow factor with a variational parameter \ensuremath{\nu}. Several correlation functions are calculated by using the variational Monte Carlo method. The result shows the expected long-range behavior of the Luther-Emery phase with the Luttinger exponent ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$ related to \ensuremath{\nu}, ${\mathit{K}}_{\mathrm{\ensuremath{\rho}}}$=1/2\ensuremath{\nu}. \textcopyright{} 1996 The American Physical Society.