Interaction effects on 1D fermionic symmetry protected topological phases

Abstract

In free fermion systems with given symmetry and dimension, the possible topological phases are labeled by elements of only three types of Abelian groups, Z_1, Z_2, or Z. For example non-interacting 1D fermionic superconducting phases with S_z spin rotation and time-reversal symmetries are classified by Z. We show that with weak interactions, this classification reduces to Z_4. Using group cohomology, one can additionally show that there are only four distinct phases for such 1D superconductors even with strong interactions. Comparing their projective representations, we find all these four symmetry protected topological phases can be realized with free fermions. Further, we show that 1D fermionic superconducting phases with Z_n discrete S_z spin rotation and time-reversal symmetries are classified by Z_4 when n=even and Z_2 when n=odd; again, all these strongly interacting topological phases can be realized by non-interacting fermions. Our approach can be applied to systems with other symmetries to see which 1D topological phases can be realized by free fermions.

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Cited by in corpus (47)

• Classification of topological quantum matter with symmetries
• A classification of symmetry enriched topological phases with exactly solvable models
• Interacting fermionic topological insulators/superconductors in three dimensions
• Classification of interacting electronic topological insulators in three dimensions
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Breakdown of the topological classification Z for gapped phases of noninteracting fermions by quartic interactions
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Kaleidoscope of symmetry protected topological phases in one-dimensional periodically modulated lattices
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Detecting edge degeneracy in interacting topological insulators through entanglement entropy
• Symmetry protected topological phases of 1D interacting fermions with spin-charge separation
• Stabilizing multiple topological fermions on a quantum computer
• Topological Paramagnetism in Frustrated Spin-One Mott Insulators
• Symmetry Protected Topological Phases in Spin Ladders with Two-body Interactions
• Fragility of Symmetry Protected Topological Order on a Hubbard Ladder
• Interaction effects on the classification of crystalline topological insulators and superconductors
• Entanglement entropy of (3+1)D topological orders with excitations
• Symmetry-protected topological states for interacting fermions in alkaline-earth-like atoms
• Josephson effect in superconducting wires supporting multiple Majorana edge states
• Topological nature of magnetization plateaus in periodically modulated quantum spin chains
• Dimensional hierarchy of fermionic interacting topological phases
• Topological phase in $1D$ topological Kondo insulator: $Z_2$ topological insulator, Haldane-like phase and Kondo breakdown
• Interacting second-order topological insulators in one-dimensional fermions with correlated hopping
• Interacting Symmetry-Protected Topological Phases Out of Equilibrium
• Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains
• A topological mechanism for robust and efficient global oscillations in biological networks
• Edge Modes in One Dimensional Topological Charge Conserving Spin-Triplet Superconductors: Exact Results from Bethe Ansatz
• Hard-core bosons in one-dimensional interacting topological bands
• Boundary-Induced Topological and Mid-Gap States in Charge Conserving One-Dimensional Superconductors
• Interacting Topological Insulators with Synthetic Dimensions
• $8\pi$-periodic dissipationless ac Josephson effect on a quantum spin-Hall edge via a Quantum magnetic impurity
• Topological phases of parafermionic chains with symmetries
• Topological phase transition and the effect of Hubbard interaction on the one-dimensional topological Kondo insulator
• Fermionic Symmetry Protected Topological Phase Induced by Interactions
• Superconductivity in quantum wires: A symmetry analysis
• Bound states of three fermions forming symmetry-protected topological phases
• A Bosonic Analog of a Topological Dirac Semi-Metal: Effective Theory, Neighboring Phases, and Wire Construction
• A search for correlation-induced adiabatic paths between distinct topological insulators
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries
• Topological phases in discrete stochastic systems
• Stability of the boundary zero modes in one-dimensional topological superconductors
• Polynomial description of inhomogeneous topological superconducting wires
• The $\pi$ Berry Phase and Topological Excitation in Interacting Boson-Fermion Mixtures
• Generalized Li-Haldane Correspondence in Critical Dirac-Fermion Systems
• Unsupervised Learning of Symmetry Protected Topological Phase Transitions
• First Order Topological Phase Transitions and Disorder Induced Majorana Modes in Interacting Fermion Chains
• Critical theories connecting gapped phases with ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry from the duality web