Superconductivity in the Two-Dimensional $t$-$J$ Model at Low Hole Doping

TL;DR

This study investigates the emergence of d-wave superconductivity in the two-dimensional $t$-$J$ model at low hole doping levels using advanced numerical methods, revealing a finite superconducting order in certain parameter regimes.

Contribution

It introduces a combined Lanczos and variational Monte Carlo approach to analyze the $t$-$J$ model's ground state properties, especially its long-range order.

Findings

Finite d-wave superconducting long-range order identified

Reliable analysis at hole densities down to 0.16

Long-range order depends on the coupling constant $J/t$

Abstract

By combining a generalized Lanczos scheme with the variational Monte Carlo method we can optimize the short- and long-range properties of the groundstate separately. This allows us to measure the long-range order of the groundstate of the $t$-$J$ model as a function of the coupling constant $J/t$, and identify a region of finite d-wave superconducting long-range order. With a lattice size of 50 sites we can reliably examine hole densities down to 0.16.