Fermion Disorder Operator at Gross-Neveu and Deconfined Quantum Criticalities

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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 (QCPs) [W. Jiang et al., arXiv:2209.07103]. Here we study, by means of large-scale quantum Monte Carlo simulation, the scaling behavior of the 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.
Funding Information
  • Research Grants Council, University Grants Committee (17301420, 17301721, AoE/P-701/20, 17309822, HKU C7037-22G, A_HKU703/22)
  • Agence Nationale de la Recherche (ANR-22-CE30-0042-01)
  • Chinese Academy of Sciences (XDB33000000)
  • K. C. Wong Education Foundation (GJTD-2020-01)
  • Deutsche Forschungsgemeinschaft
  • National Supercomputer Centre in Guangzhou
  • Cluster of Excellence on Complexity and Topology (EXC 2147, 390858490)
  • Topological and Correlated Electronics at Surfaces and Interfaces (258499086)

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