Fermion disorder operator at Gross-Neveu and deconfined quantum criticalities

TL;DR

This study investigates the scaling behavior of fermion disorder operators in correlated Dirac systems at quantum critical points using large-scale quantum Monte Carlo simulations, revealing insights into conformal field theories and emergent symmetries.

Contribution

It provides the first large-scale numerical analysis of the disorder operator in 2D correlated Dirac systems at quantum critical points, connecting to conformal field theory predictions.

Findings

Logarithmic scaling at Gross-Neveu critical points consistent with CFT.

Negative logarithmic coefficients at deconfined quantum critical point, indicating non-unitary CFT.

Emergent continuous symmetries detected in 1D DQCP model.

Abstract

The fermion disorder operator has been shown to reveal the entanglement information in 1D Luttinger liquids and 2D free and interacting Fermi and non-Fermi liquids emerging at quantum critical points(QCP). Here we study, by means of large-scale quantum Monte Carlo simulation, the scaling behavior of disorder operator in correlated Dirac systems. We first demonstrate the logarithmic scaling behavior of the disorder operator at the Gross-Neveu (GN) chiral Ising and Heisenberg QCPs, where consistent conformal field theory (CFT) content of the GN-QCP in its coefficient is found. Then we study a 2D monopole free deconfined quantum critical point (DQCP) realized between a quantum-spin Hall insulator and a superconductor. Our data point to negative values of the logarithmic coefficients such that the DQCP does not correspond to a unitary CFT. Density matrix renormalization group calculations of the disorder operator on a 1D DQCP model also detect emergent continuous symmetries.