Phase diagram of the two-dimensional t--J model at low doping

TL;DR

This paper maps the phase diagram of the two-dimensional t--J model at low doping, revealing various phases including hole pairing liquids, droplet liquids, and phase separation, based on finite size scaling of exact diagonalisation data.

Contribution

It provides a detailed phase diagram of the 2D t--J model at low doping using finite size scaling, highlighting the emergence of multiple phases driven by magnetic correlations.

Findings

Identification of a d-wave hole pair liquid for J/t > 0.2

Discovery of a hole droplet liquid at J/t > 0.5

Observation of phase separation at large J/t

Abstract

The phase diagram of the planar t--J model at small hole doping is investigated by finite size scaling of exact diagonalisation data of NXN clusters (up to 26). Hole-droplet binding energies, compressibility and static spin and charge correlations are calculated. Short range antiferromagnetic correlations can produce attractive forces between holes leading to a very rich phase diagram including a liquid of d-wave hole pairs (for $J/t\gtrsim 0.2$), a liquid of hole droplets (quartets) for larger J/t ratios ($J/t\gtrsim 0.5$) and, at even larger coupling J/t, an instability towards phase separation.