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Condensed Matter > Strongly Correlated Electrons
Title: Fermionic skyrmions and bosonization for a Gross-Neveu transition
(Submitted on 26 Apr 2023 (v1), last revised 7 Apr 2024 (this version, v2))
Abstract: We investigate a 2+1-D interacting Dirac semimetal with onsite flavor SU(2) symmetry. Topological considerations imply that the skyrmions in the flavor-symmetry-breaking phase carry electron quantum numbers, motivating a dual bosonized low energy description in terms of two complex scalars coupled to an abelian Chern-Simons field. We propose that the transition between a nearby Chern insulator and the flavor symmetry-broken phase is a bicritical point in the bosonized description, and also suggest that the Gross-Neveu-Heisenberg (GNH) transition between the Dirac semimetal and the flavor symmetry-broken phase is a tricritical point. Heuristically, the dual description corresponds to the gap closing of fermionic skyrmions. We discuss implications and potential issues with our proposal, and motivated from it, perform extensive unbiased Determinantal Quantum Monte Carlo (DQMC) simulations on a lattice regularized Hamiltonian for the GNH transition, extending previously available results. We compare DQMC results with the estimates in the proposed dual from available perturbative renormalization group results. We also numerically demonstrate the presence of fermionic skyrmions in the symmetry-broken phase of our lattice model.
Submission history
From: Xiao Yan Xu [view email][v1] Wed, 26 Apr 2023 17:55:01 GMT (4692kb,D)
[v2] Sun, 7 Apr 2024 06:27:04 GMT (4690kb,D)
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