Correlated Wave-Functions and the Absence of Long Range Order in Numerical Studies of the Hubbard Model

TL;DR

This paper introduces a generalized Constrained Path Monte Carlo method for fermions, demonstrating that superconducting correlations in the Hubbard model are unaffected by the choice of trial wave-function, confirming the suppression of long-range order.

Contribution

It develops a new formulation of the CPMC method using many-body trial wave-functions and shows that correlation results are independent of the trial state used.

Findings

Correlation functions are independent of the trial wave-function used.

Long-range pairing correlations are suppressed as system size increases.

The results reaffirm previous findings about the absence of long-range order.

Abstract

We present a formulation of the Constrained Path Monte Carlo (CPMC) method for fermions that uses trial wave-functions that include many-body effects. This new formulation allows us to implement a whole family of generalized mean-field states as constraints. As an example, we calculated superconducting pairing correlation functions for the two-dimensional repulsive Hubbard model using a BCS trial state as the constraint. We compared the results with the case where a free-electron trial wave-function is used. We found that the correlation functions are independent of which state is used as the constraint, which reaffirms the results previously found by Zhang et. al regarding the suppression of long range pairing correlations as the system size increases.