• Open Access

Deconfined Critical Point in a Doped Random Quantum Heisenberg Magnet

Darshan G. Joshi, Chenyuan Li, Grigory Tarnopolsky, Antoine Georges, and Subir Sachdev
Phys. Rev. X 10, 021033 – Published 12 May 2020

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 value pc 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 pc is flanked by confining phases: a disordered Fermi liquid with carrier density 1+p for p>pc and a metallic spin glass with carrier density p for p<pc. 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.

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  • Received 24 December 2019
  • Revised 18 February 2020
  • Accepted 23 March 2020

DOI:https://doi.org/10.1103/PhysRevX.10.021033

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Darshan G. Joshi1, Chenyuan Li1, Grigory Tarnopolsky1, Antoine Georges2,3,4,5, and Subir Sachdev1

  • 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
  • 3Collège de France, 11 place Marcelin Berthelot, 75005 Paris, France
  • 4CPHT, CNRS, École Polytechnique, IP Paris, F-91128 Palaiseau, France
  • 5DQMP, Université de Genève, 24 quai Ernest Ansermet, CH-1211 Genève, Switzerland

Popular 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.

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Vol. 10, Iss. 2 — April - June 2020

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