Absence of static stripes in the two-dimensional $t{-}J$ model by an accurate and systematic quantum Monte Carlo approach

TL;DR

This study uses advanced quantum Monte Carlo methods to investigate the two-dimensional $t{-}J$ model, finding no static stripe order and evidence of coexisting antiferromagnetism and superconductivity at low doping.

Contribution

It provides a systematic and accurate quantum Monte Carlo analysis that challenges previous claims of stripe order in the $t{-}J$ model.

Findings

No static stripe order at $J/t=0.4$.

Evidence of coexistence of antiferromagnetism and superconductivity at low doping.

Contradicts recent density-matrix renormalization group results.

Abstract

We examine the two-dimensional $t{-}J$ model by using variational approach combined with well established quantum Monte Carlo techniques [S. Sorella {\it et al.}, \prl {\bf 88}, 117002 (2002)] that are used to improve systematically the accuracy of the variational ansatz. Contrary to recent density-matrix renormalization group and projected entangled-pair state calculations [P. Corboz {\it et al.}, \prb {\bf 84}, 041108(R) (2011)], a uniform phase is found for $J/t=0.4$, even when the calculation is biased with an ansatz that explicitly contains stripe order. Moreover, in the small hole doping regime, i.e., $\delta \lesssim 0.1$, our results support the coexistence of antiferromagnetism and superconductivity.