Physical review. B, Condensed matter

Green’s-function Monte Carlo study of thet-Jmodel

Massimo Boninsegni, Efstratios Manousakis

Published Jul 1, 1992• 40 citations

Abstract

We show how the Green's function Monte Carlo method can be used to compute accurately the ground-state energy of two-dimensional t-J model for lattices of large size. This is demonstrated for the case of a single hole, with the aid of suitable initial and guidance functions. Our transient estimates for the ground-state energy of the 4\ifmmode\times\else\texttimes\fi{}4 lattice are in remarkable agreement with the exact values; we report results for lattices of significantly larger size than 4\ifmmode\times\else\texttimes\fi{}4.

DOI: 10.1103/physrevb.46.560

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Physical review. B, Condensed matter

Green’s-function Monte Carlo study of thet-Jmodel

Massimo Boninsegni, Efstratios Manousakis

Published Jul 1, 1992• 40 citations

Publisher

Abstract

DOI: 10.1103/physrevb.46.560

Related papers

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Massimo Boninsegni, Efstratios Manousakis

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Thierry Giamarchi, C. Lhuillier

Physical review. B, Condensed matterFeb 1, 199315 citations

Spectral function of a hole in thet-Jmodel

Zhiping Liu, Efstratios Manousakis

We give numerical solutions, on finite but large-size square lattices, of the equation for the single-hole Green's function obtained by the self-consistent approach of Schmitt-Rink et al. and Kane et al. The spectral function of the hole in a quantum antiferromagnet shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the ${4}^{2}$ lattice in the region of J/t\ensuremath{\le}0.2. Our results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function survive in the thermodynamic limit while others change due to finite-size effects. We find that the leading nonzero vertex correction is given by a two-loop diagram, which has a small contribution.We give numerical solutions, on finite but large-size square lattices, of the equation for the single-hole Green's function obtained by the self-consistent approach of Schmitt-Rink et al. and Kane et al. The spectral function of the hole in a quantum antiferromagnet shows that most features describing the hole motion are in close agreement with the results of the exact diagonalization on the ${4}^{2}$ lattice in the region of J/t\ensuremath{\le}0.2. Our results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function survive in the thermodynamic limit while others change due to finite-size effects. We find that the leading nonzero vertex correction is given by a two-loop diagram, which has a small contribution.

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We investigate numerically the ground state of two holes with

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

symmetry in the two-dimensional t-J model, on lattices of significantly larger sizes than the ones studied so far. The Green's-function Monte Carlo method, in conjunction with suitable initial states and guidance functions, is used to estimate the ground-state energy of one and two holes, as well as to compute the two-hole distribution function. Our results show a significant decrease of the two-hole binding energy as the size of the lattice is increased from 4\ifmmode\times\else\texttimes\fi{}4. A critical value

{\mathit{J}}_{\mathit{c}}

\ensuremath{\sim}0.27t is found such that d-wave hole binding no longer occurs for J

{\mathit{J}}_{\mathit{c}}

J/t

. In particular, it is unstable at the hole dopings and interaction strengths at which the model was thought to describe the cuprate superconductors.

We present Monte Carlo results for the band structure of the lowest-lying

{\mathit{S}}_{\mathrm{tot}}

=1/2 one-hole band in the t-J model on 4\ifmmode\times\else\texttimes\fi{}4 and 6\ifmmode\times\else\texttimes\fi{}6 lattices. In this paper we report measurements for all k states in the small t/J regime 0\ensuremath{\le}t/J\ensuremath{\le}0.2, and extrapolate to 0\ensuremath{\le}t/J\ensuremath{\le}0.5. Our results support the conjecture that the linear-t component of the bandwidth at small t/J vanishes as \ensuremath{\kappa}/

{\mathit{L}}^{2}

in the bulk limit, as was anticipated on theoretical grounds; this implies that the propagation of isolated holes is strongly hindered by the staggered magnetization of the ground state. For this initial study we used a very simple trial wave function for importance sampling; it should be possible to obtain comparably accurate Monte Carlo results for band structure at appreciably larger t/J with improved importance sampling.

{4}^{2}

lattice in the region of J/t\ensuremath{\le}0.2. Our results obtained on sufficiently large-size lattices suggest that certain important features of the spectral function survive in the thermodynamic limit while others change due to finite-size effects. We find that the leading nonzero vertex correction is given by a two-loop diagram, which has a small contribution.