Quantum phase transition at non-zero doping in a random $t$-$J$ model

TL;DR

This paper investigates a random $t$-$J$ model using exact diagonalization, revealing a quantum phase transition at a critical doping level characterized by a spin glass phase and changes in electronic properties.

Contribution

It introduces a random all-to-all $t$-$J$ model capturing local correlations and identifies a quantum phase transition at finite doping with signatures in various physical quantities.

Findings

Existence of a metallic spin glass phase up to $p_c \\approx 1/3$

Signatures of Sachdev-Ye-Kitaev spectrum near $p_c$

Maximum in entropy, entanglement entropy, and compressibility near $p_c$

Abstract

We present exact diagonalization results on finite clusters of a $t$-$J$ model of spin-1/2 electrons with random all-to-all hopping and exchange interactions. We argue that such random models capture qualitatively the strong local correlations needed to describe the cuprates and related compounds, while avoiding lattice space group symmetry breaking orders. The previously known spin glass ordered phase in the insulator at doping $p=0$ extends to a metallic spin glass phase up to a transition $p=p_c \approx 1/3$. The dynamic spin susceptibility shows signatures of the spectrum of the Sachdev-Ye-Kitaev models near $p_c$. We also find signs of the phase transition in the entropy, entanglement entropy and compressibility, all of which exhibit a maximum near $p_c$. The electron energy distribution function in the metallic phase is consistent with a disordered extension of the Luttinger-volume Fermi surface for $p>p_c$, while this breaks down for $p<p_c$.