Effective approach to the Nagaoka regime of the two dimensional t-J model

TL;DR

This paper demonstrates that the Ising version of the t-J model effectively captures the Nagaoka regime's physics, enabling large-scale simulations that reveal phase separation at low doping levels.

Contribution

It shows the equivalence of the Ising and standard t-J models in the Nagaoka regime and uses classical Monte Carlo to analyze phase separation at low doping.

Findings

Ising and t-J models produce compatible results for Nagaoka polarons.

Ground state exhibits phase separation into ferromagnetic and antiferromagnetic regions.

Threshold doping level for phase separation is approximately 0.44 times sqrt(J/t).

Abstract

We argue that the t-J model and the recently proposed Ising version of this model give the same physical picture of the Nagaoka regime for J/t << 1. In particular, both models are shown to give compatible results for a single Nagaoka polaron as well as for a Nagaoka bipolaron. When compared to the standard t-J or t-Jz models, the Ising version allows for a numerical analysis on much larger clusters by means of classical Monte Carlo simulations. Taking the advantage of this fact, we study the low doping regime of t-J model for J/t << 1 and show that the ground state exhibits phase separation into hole-rich ferromagnetic and hole-depleted antiferromagnetic regions. This picture holds true up to a threshold concentration of holes, \delta < \delta_t ~ 0.44 \sqrt{J/t}. Analytical calculations show that \delta_t=\sqrt{J/2\pi t}.