Basis Set Reduction Applied to the Two Dimensional t-Jz Model

TL;DR

This paper introduces a Hilbert space reduction technique for the Lanczos method, enabling accurate ground state energy calculations of the 2D t-Jz model on larger clusters, revealing a finite critical coupling for hole binding.

Contribution

A systematic Hilbert space reduction method is proposed, allowing for more efficient and accurate analysis of the 2D t-Jz model on larger clusters than traditional approaches.

Findings

Accurate ground state energies for up to 50 sites.

Identification of a critical Jz/t value (~0.18) for hole binding.

Implication that phase separation occurs only above a finite coupling.

Abstract

A simple variation of the Lanczos method is discussed. The new technique is based on a systematic reduction of the size of the Hilbert space of the model under consideration. As an example, the two dimensional ${\rm t-J_z}$ model of strongly correlated electrons is studied. Accurate results for the ground state energy can be obtained on clusters of up to 50 sites, which are unreachable by conventional Lanczos approaches. In particular, the energy of one and two holes is analyzed as a function of ${\rm J_z/t}$. In the bulk limit, it is shown that a finite coupling ${\rm J_z/t ]_c} \sim 0.18$ is necessary to induce ``binding'' of holes in the model. It is argued that this result implies that the two dimensional ${\rm t-J}$ model phase separates only for couplings larger than a $finite$ critical value.