Deconfined critical point in a doped random quantum Heisenberg magnet

TL;DR

This paper investigates a deconfined quantum critical point in a doped, disordered quantum Heisenberg model, revealing fractionalized excitations and phase transitions relevant to cuprate superconductors.

Contribution

It introduces a detailed phase diagram with a novel critical point characterized by fractionalized excitations and analyzes its properties using renormalization group and large M methods.

Findings

Identification of a critical doping point with fractionalized excitations

Existence of confining phases flanking the critical point

Quantitative analysis of critical exponents and phase boundaries

Abstract

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interactions between any pair of sites and a constraint of no double occupancy. A perturbative renormalization group analysis yields a critical point with fractionalized excitations at a non-zero critical value $p_c$ of the hole doping $p$ away from the half-filled insulator. We compute the renormalization group to two loops, but some exponents are obtained to all loop order. We argue that the critical point $p_c$ is flanked by confining phases: a disordered Fermi liquid with carrier density $1+p$ for $p>p_c$, and a metallic spin glass with carrier density $p$ for $p<p_c$. Additional evidence for the critical behavior is obtained from a large $M$ analysis of a model which extends the SU(2) spin symmetry to SU($M$). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.