Unwinding Fermionic SPT Phases: Supersymmetry Extension

Abstract

We show how 1+1-dimensional fermionic symmetry-protected topological states (SPTs, i.e. nontrivial short-range entangled gapped phases of quantum matter whose boundary exhibits 't Hooft anomaly and whose bulk cannot be deformed into a trivial tensor product state under finite-depth local unitary transformations only in the presence of global symmetries), indeed can be unwound to a trivial state by enlarging the Hilbert space via adding extra degrees of freedom and suitably extending the global symmetries. The extended projective global symmetry on the boundary can become supersymmetric in a specific sense, i.e., it contains group elements that do not commute with the fermion number parity $(-1{)}^F$, while the anti-unitary time-reversal symmetry becomes fractionalized. This also means we can uplift and remove certain exotic fermionic anomalies (e.g., "parity" anomaly in time-reversal or reflection symmetry) via appropriate supersymmetry extensions in terms of group extensions. We work out explicit examples for multi-layers of 1+1d Majorana fermion chains, then comment on models with Sachdev-Ye-Kitaev (SYK) interactions, intrinsic fermionic gapless SPTs protected by supersymmetry, and generalizations to higher spacetime dimensions via a cobordism theory.

arXiv comment61 pages. Sequel to arXiv:1804.11236, arXiv:1705.06728

References in corpus (70)

• Unpaired Majorana fermions in quantum wires
• Classification of topological quantum matter with symmetries
• Supersymmetry and Quantum Mechanics
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Periodic table for topological insulators and superconductors
• Comments on the Sachdev-Ye-Kitaev model
• Generalized Global Symmetries
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Zoo of quantum-topological phases of matter
• Topological phases of fermions in one dimension
• Quantum criticality
• Symmetry Protected Topological phases of Quantum Matter
• The effects of interactions on the topological classification of free fermion systems
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Classification of Topological Insulators and Superconductors
• Emergent Space-time Supersymmetry at the Boundary of a Topological Phase
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• On gauging finite subgroups
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• The "Parity" Anomaly On An Unorientable Manifold
• Fermionic SPT phases in higher dimensions and bosonization
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Dai-Freed anomalies in particle physics
• Comments on Abelian Higgs Models and Persistent Order
• Intrinsically Gapless Topological Phases
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Symmetry Protected Topological phases and Generalized Cohomology
• Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups
• Symmetric Gapped Interfaces of SPT and SET States: Systematic Constructions
• Cobordism Conjecture, Anomalies, and the String Lamppost Principle
• Emergence of supersymmetry on the surface of three dimensional topological insulators
• Developments in Topological Gravity
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Higher Anomalies, Higher Symmetries, and Cobordisms I: Classification of Higher-Symmetry-Protected Topological States and Their Boundary Fermionic/Bosonic Anomalies via a Generalized Cobordism Theory
• Adjoint QCD${}_4$, Deconfined Critical Phenomena, Symmetry-Enriched Topological Quantum Field Theory, and Higher Symmetry-Extension
• Why are fractional charges of orientifolds compatible with Dirac quantization?
• Fermionic Finite-Group Gauge Theories and Interacting Symmetric/Crystalline Orders via Cobordisms
• Time Reversal, SU(N) Yang-Mills and Cobordisms: Interacting Topological Superconductors/Insulators and Quantum Spin Liquids in 3+1D
• Construction and classification of symmetry protected topological phases in interacting fermion systems
• Beyond Standard Models and Grand Unifications: Anomalies, Topological Terms, and Dynamical Constraints via Cobordisms
• Interacting Topological Insulator and Emergent Grand Unified Theory
• A lattice non-perturbative definition of an SO(10) chiral gauge theory and its induced standard model
• Superconducting quantum criticality of topological surface states at three loops
• Cobordism Classes and the Swampland
• Quantum 4d Yang-Mills Theory and Time-Reversal Symmetric 5d Higher-Gauge Topological Field Theory
• Anomaly Matching in the Symmetry Broken Phase: Domain Walls, CPT, and the Smith Isomorphism
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• A Non-Perturbative Definition of the Standard Models
• Gapped Chiral Fermions
• Topological Superconductors on Superstring Worldsheets
• New Higher Anomalies, SU(N) Yang-Mills Gauge Theory and ${\mathbb{CP}}^{\mathrm{N}-1}$ Sigma Model
• Spin Topological Field Theory and Fermionic Matrix Product States
• On gapped boundaries for SPT phases beyond group cohomology
• Higher Anomalies, Higher Symmetries, and Cobordisms II: Lorentz Symmetry Extension and Enriched Bosonic/Fermionic Quantum Gauge Theory
• Quantum Criticality in Topological Insulators and Superconductors: Emergence of Strongly Coupled Majoranas and Supersymmetry
• GSO projections via SPT phases
• Full Commuting Projector Hamiltonians of Interacting Symmetry-Protected Topological Phases of Fermions
• Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model
• Unwinding Short-Range Entanglement
• Anomaly and Cobordism Constraints Beyond the Standard Model: Topological Force
• Stable Vacua for Tachyonic Strings
• Finite-Scale Emergence of 2+1D Supersymmetry at First-Order Quantum Phase Transition
• Interacting Topological Superconductors and possible Origin of $16n$ Chiral Fermions in the Standard Model
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Boundary supersymmetry of 1+1 d fermionic SPT phases
• Anomaly and Cobordism Constraints Beyond Grand Unification: Energy Hierarchy
• Fractionalized time reversal, parity and charge conjugation symmetry in topological superconductor: a possible origin of three generations of neutrinos and mass mixing
• An elementary proof of 1D LSM theorems

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• Global Anomalies on the Hilbert Space
• Symmetric Mass Generation
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Ultra Unification
• Gauge Enhanced Quantum Criticality Beyond the Standard Model
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• Multiversality and Unnecessary Criticality in One Dimension
• Boundary supersymmetry of 1+1 d fermionic SPT phases
• Emergent space-time supersymmetry at disorder quantum critical point
• Classical origins of Landau-incompatible transitions
• Invertible phases for mixed spatial symmetries and the fermionic crystalline equivalence principle
• C-P-T Fractionalization
• Quotient symmetry protected topological phenomena
• Supersymmetry dynamics on Rydberg atom arrays
• Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
• SPT extension of $Z_2$ quantum Ising model's ferromagnetic phase
• Edge states and anomalous SUSY in (2+1)-dimensional Maxwell Chern-Simons theory
• Emergent spacetime supersymmetry at 2D fractionalized quantum criticality