Topological order in paired states of fermions in two-dimensions with breaking of parity and time-reversal symmetries

Abstract

We numerically evaluate the entanglement spectrum (singular value decomposition of the wavefunction) of paired states of fermions in two dimensions that break parity and time-reversal symmetries, focusing on the spin-polarized $p_x+i{p}_y$ case. The entanglement spectrum of the weak-pairing (BCS) phase contains a Majorana zero mode, indicating non-Abelian topological order. In contrast, for the strong-pairing (BEC) phase, we find no such mode, consistent with Abelian topological order.

4 pages, 4 figures; submitted version

References in corpus (8)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Area laws in quantum systems: mutual information and correlations
• Entanglement entropy of 2D conformal quantum critical points: hearing the shape of a quantum drum
• Quantum Computation Using Vortices and Majorana Zero Modes of a $p_x$ + $i{p}_y$ Superfluid of Fermionic Cold Atoms
• Anisotropic Fermi Superfluid via p-wave Feshbach Resonance
• Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model
• Topological phases and topological entropy of two-dimensional systems with finite correlation length
• Subarea law of entanglement in nodal fermionic systems

Cited by in corpus (41)

• Inversion Symmetric Topological Insulators
• Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator
• Observation of topological order in a Superconducting doped topological insulator (based on the Bi2Se3 class)
• Entanglement spectrum of topological insulators and superconductors
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Edge modes in band topological insulators
• How universal is the entanglement spectrum?
• Trace Index and Spectral Flow in the Entanglement Spectrum
• Entanglement spectrum of the two dimensional Bose-Hubbard model
• Dissipation-induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice
• Boundary-locality and perturbative structure of entanglement spectra in gapped systems
• Decomposition of fractional quantum Hall states: New symmetries and approximations
• Bound states and entanglement in the excited states of quantum spin chains
• Entanglement spectra of complex paired superfluids
• Low-energy sub-gap states in multi-channel Majorana wires
• Entanglement spectroscopy of SU(2)-broken phases in two dimensions
• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Driven-dissipative many-body pairing states for cold fermionic atoms in an optical lattice
• Entanglement Spectroscopy using Quantum Monte Carlo
• Hierarchical structure in the orbital entanglement spectrum in Fractional Quantum Hall systems
• Spin-orbital groundstates of Superconducting doped topological insulators (A Majorana Platform)
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Many-body entanglement in a topological chiral ladder
• Signatures of metal-insulator and topological phase transitions in the entanglement of one-dimensional disordered fermions
• Matrix product states for Hartree-Fock-Bogoliubov wave functions
• Frustration and time reversal symmetry breaking for Fermi and Bose-Fermi systems
• Entanglement Spectrum as a Probe for the Topology of a Spin-Orbit Coupled Superconductor
• Topological order, entanglement, and quantum memory at finite temperature
• Entanglement entropy and entanglement spectrum of triplet topological superconductors
• Different temperature-dependence for the edge and bulk of entanglement Hamiltonian
• Bosonic Gaussian states from conformal field theory
• Constrained thermalisation and topological superconductivity
• Detection of Topology via Entanglement Oscillations
• Analytic Expression for the Entanglement Entropy of a 2D Topological Superconductor
• The BCS wave function, matrix product states, and the Ising conformal field theory
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Energy space entanglement spectrum of pairing models with s-wave and p-wave symmetry
• Entanglement spectra of superconductivity ground states on the honeycomb lattice
• Ground-State Analysis for an Exactly Solvable Coupled-Spin Hamiltonian
• Standard Temperature and Pressure Superconductivity