From Bosonic Topological Transition to Symmetric Fermion Mass Generation

Abstract

The bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry protected topological phase and the trivial phase. In this work, we derive a description of this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors ($N_f=4$). This allows us to describe the transition in a lattice model with the maximal microscopic symmetry: an internal SO(4) symmetry. Within a systematic renormalization group analysis, we identify the critical point with the desired O(4) emergent symmetry and all expected deformations. By lowering the microscopic symmetry we recover the previous $N_f=2$ non-compact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an SU(2) quantum chromodynamics-Higgs theory with $N_f=4$ flavors of SU(2) fundamental fermions and one SU(2) fundamental Higgs boson. This provides a consistency check on both theories.

15 pages + references, 6 figures

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Cited by in corpus (37)

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• Confinement transition of ${\mathbb{Z}}_2$ gauge theories coupled to massless fermions: emergent QCD${}_3$ and $SO(5)$ symmetry
• Monte Carlo Study of Lattice Compact Quantum Electrodynamics with Fermionic Matter: the Parent State of Quantum Phases
• Symmetric Mass Generation
• Signatures of a Deconfined Phase Transition on the Shastry-Sutherland Lattice: Applications to Quantum Critical SrCu${}_2$(BO${}_3$)${}_2$
• Emergent Symmetry and Conserved Current at a One Dimensional Incarnation of Deconfined Quantum Critical Point
• Comments on Symmetric Mass Generation in 2d and 4d
• Emmy Noether looks at the deconfined quantum critical point
• Symmetry protected topological phases under decoherence
• Pivot Hamiltonians as generators of symmetry and entanglement
• Symmetry Enforced Self-Learning Monte Carlo Method Applied to the Holstein Model
• Symmetric Mass Generation in the 1+1 Dimensional Chiral Fermion 3-4-5-0 Model
• Gapped Chiral Fermions
• Phase diagram, symmetry breaking, and critical behavior of three-dimensional lattice multiflavor scalar chromodynamics
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• Field-induced QCD${}_3$-Chern-Simons quantum criticalities in Kitaev materials
• Fermion-bag inspired Hamiltonian lattice field theory for fermionic quantum criticality
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• Three-dimensional lattice multiflavor scalar chromodynamics: interplay between global and gauge symmetries
• Gauge Enhanced Quantum Criticality Between Grand Unifications: Categorical Higher Symmetry Retraction
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• Disorder Operator and Rényi Entanglement Entropy of Symmetric Mass Generation
• Strong-Weak Chern-Simons-Matter Dualities from a Lattice Construction
• Deconfined metallic quantum criticality: A $U(2)$ gauge-theoretic approach
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• Fermi Surface Symmetric Mass Generation
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
• What Symmetries are Preserved by a Fermion Boundary State?
• Duality viewpoint of criticality
• Conformal Field Theories generated by Chern Insulators under Quantum Decoherence
• Definition and Classification of Fermi Surface Anomalies
• Notes on 8 Majorana Fermions
• Hamiltonian models of lattice fermions solvable by the meron-cluster algorithm
• Realization of the topological Hopf term in two-dimensional lattice models
• Fermion Mass Generation without Symmetry Breaking
• Deconfined Quantum Criticality among Grand Unified Theories
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