Berry Phase in Quantum Field Theory: Diabolical Points and Boundary Phenomena

Abstract

We study aspects of Berry phase in gapped many-body quantum systems by means of effective field theory. Once the parameters are promoted to spacetime-dependent background fields, such adiabatic phases are described by Wess-Zumino-Witten (WZW) and similar terms. In the presence of symmetries, there are also quantized invariants capturing generalized Thouless pumps. Consideration of these terms provides constraints on the phase diagram of many-body systems, implying the existence of gapless points in the phase diagram which are stable for topological reasons. We describe such diabolical points, realized by free fermions and gauge theories in various dimensions, which act as sources of "higher Berry curvature" and are protected by the quantization of the corresponding WZW terms or Thouless pump terms. These are analogous to Weyl nodes in a semimetal band structure. We argue that in the presence of a boundary, there are boundary diabolical points---parameter values where the boundary gap closes---which occupy arcs ending at the bulk diabolical points. Thus the boundary has an "anomaly in the space of couplings" in the sense of Córdova et al. Consideration of the topological effective action for the parameters also provides some new checks on conjectured infrared dualities and deconfined quantum criticality in 2+1d.

21+7 pages, 4+2 figures

References in corpus (12)

• Generalized Global Symmetries
• "Deconfined" quantum critical points
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Level/rank Duality and Chern-Simons-Matter Theories
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Many-body spin Berry phases emerging from the $\pi$-flux state: antiferromagnetic/valence-bond-solid competition
• Transitions to valence-bond solid order in a honeycomb lattice antiferromagnet
• Higher-dimensional generalizations of the Berry curvature
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Topology and edge states survive quantum criticality between topological insulators

Cited by in corpus (41)

• Intrinsically Gapless Topological Phases
• Generalized Global Symmetries of $T[M]$ Theories. I
• Continuous Generalized Symmetries in Three Dimensions
• Pivot Hamiltonians as generators of symmetry and entanglement
• Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes
• Revisiting Wess-Zumino-Witten terms
• Quantum many-body topology of quasicrystals
• Flow of (higher) Berry curvature and bulk-boundary correspondence in parametrized quantum systems
• Local Noether theorem for quantum lattice systems and topological invariants of gapped states
• Topological Goldstone phases of matter
• On adiabatic cycles of quantum spin systems
• Higher Berry Phase of Fermions and Index Theorem
• Effective field theories of topological crystalline insulators and topological crystals
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• Definition and Classification of Fermi Surface Anomalies
• Higgs-Confinement Transitions in QCD from Symmetry Protected Topological Phases
• Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions
• Generalized Thouless Pumps in 1+1-dimensional Interacting Fermionic Systems
• On Topology of the Moduli Space of Gapped Hamiltonians for Topological Phases
• Plateau transitions of spin pump and bulk-edge correspondence
• Remarks on Berry Connection in QFT, Anomalies, and Applications
• Higher Berry Curvature from the Wave function II: Locally Parameterized States Beyond One Dimension
• Higher Berry Curvature from the Wave Function I: Schmidt Decomposition and Matrix Product States
• Charting the space of ground states with tensor networks
• Classical origins of Landau-incompatible transitions
• Gappability Index for Quantum Many-Body Systems
• Differential models for the Anderson dual to bordism theories and invertible QFT's, II
• Anomaly and Superconnection
• A Long Exact Sequence in Symmetry Breaking: order parameter constraints, defect anomaly-matching, and higher Berry phases
• Higher Berry curvature from matrix product states
• Anomalous continuous symmetries and quantum topology of Goldstone modes
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• Modulating Hamiltonian Approach to Quantum Many-Body Systems and Crystalline Topological Phases Protected by Generalized Magnetic Translations
• Interface Junctions in QCD${}_4$
• Charge pumps, pivot Hamiltonians and symmetry-protected topological phases
• Adiabatic modulation of driving protocols in periodically driven quantum systems
• Equivariant Parameter Families of Spin Chains: A Discrete MPS Formulation
• Effects of quantum geometric phase of a particle in an oscillating hard-wall spherical trap
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice
• From D=3 to D=2 dimensions: a note on topological order