Loop-Cluster Simulation of the $t$-$J$ Model on the Honeycomb Lattice

TL;DR

This paper investigates the $t$-$J$ model on a honeycomb lattice using loop-cluster algorithms, providing insights into low-energy physics and key parameters relevant to superconducting materials.

Contribution

The study introduces an efficient simulation approach for the $t$-$J$ model on a honeycomb lattice and derives low-energy effective parameters from Monte Carlo data.

Findings

Staggered magnetization per spin: 0.2688(3)

Spin stiffness: 0.102(2) J

Spin wave velocity: 1.297(16) J a

Abstract

Inspired by the lattice structure of the unhydrated variant of the superconducting material Na$_x$CoO$_2 \cdot$yH$_2$O at $ x = {1/3}$, we study the $t$-$J$ model on a honeycomb lattice by using an efficient loop-cluster algorithm. The low-energy physics of the undoped system and of the single hole sector is described by a systematic low-energy effective field theory. The staggered magnetization per spin $\widetilde{{\cal M}}_s = 0.2688(3)$, the spin stiffness $\rho_s = 0.102(2) J$, the spin wave velocity $c= 1.297(16) J a$, and the kinetic mass $M'$ of a hole are obtained by fitting the numerical Monte Carlo data to the effective theory predictions.