Absence of Coexistence of Superconductivity and Antiferromagnetism of the Hole-Doped Two-Dimensional Extended $t-J$ Model

TL;DR

This study uses variational Monte Carlo methods to investigate the two-dimensional extended t-J model, finding no coexistence of superconductivity and antiferromagnetism in the underdoped regime, with a first-order phase transition at a critical doping level.

Contribution

It demonstrates, through advanced wave functions and Monte Carlo simulations, that superconductivity and antiferromagnetism do not coexist in the studied model, clarifying the phase boundary in the underdoped region.

Findings

No coexistence of SC and AFLRO at the phase boundary.

Phase transition between phases is first-order.

Critical hole density for phase transition is approximately 0.06.

Abstract

The possibility of coexistence of superconductivity (SC) and antiferromagnetic long range order (AFLRO) of the two-dimensional extended $t-J$ model in the very underdoped region is studied by the variational Monte-Carlo (VMC) method. In addition to using previously studied wave functions, a recently proposed new wave function generated from the half-filled Mott insulator is used. For hole-doped systems, the phase boundary between AFLRO and $d-$wave SC for the physical parameters, $J/t=0.3$, $t'/t=-0.3$ and $t''/t=0.2$, is located near hole density $\delta_c = 0.06$, and there is {\it no} coexistence. The phase transition is first-order between these two homogeneous phases at $\delta_c$.