Deconfined Critical Point in a Doped Random Quantum Heisenberg Magnet

Abstract

We describe the phase diagram of electrons on a fully connected lattice with random hopping, subject to a random Heisenberg spin exchange interaction 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 nonzero critical valuepcof the hole dopingpaway 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 pointpcis flanked by confining phases: a disordered Fermi liquid with carrier density1+pforp>pcand a metallic spin glass with carrier densitypforp<pc. Additional evidence for the critical behavior is obtained from a large-Manalysis of a model which extends the SU(2) spin symmetry toSU(M). We discuss the relationship of the vicinity of this deconfined quantum critical point to key aspects of cuprate phenomenology.

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Plain Language Summary

Cuprate superconductors are copper oxide materials prized for the ability to conduct electricity with zero resistance at relatively high temperature. Near the optimal hole doping needed for the highest superconducting temperature, these materials undergo a remarkable transformation, primarily characterized by a change in the mobile charge density. However, the underlying cause of this transformation remains a puzzle. Here, we examine a model of a cupratelike system and show that the transformation is likely tied to a novel quantum phase transition.

To study this cuprate transformation, we consider a fully connected cluster of sites, with each electron able to tunnel between any pair of sites or exchange its spin with any other electron, all with a random amplitude. We argue that this simple model has a phase transition with varying density at zero temperature with many similarities to low-temperature observations in the cuprates: In addition to the change in the mobile charge density, it yields a peak in the specific heat and weak spin-glass order at low mobile charge densities.

Most phase transitions are characterized almost completely by an “order parameter,” such as the ferromagnetic order that vanishes above a particular temperature. In contrast, our phase transition is fundamentally characterized by fractionalization of the electron at the critical point into “partons” that carry its spin and charge and a statistical transmutation: The primary spin excitations change from bosonic to fermionic across the phase transition.

Our model predicts that the critical spin correlations are similar to those of the Sachdev-Ye-Kitaev model, a common mathematical description of strongly interacting quantum systems. This connection needs to be understood better, for it may shed light on higher temperature properties, including the “strange-metal” behavior, where an unusual connection between temperature and resistance arises.