Exact Zero Modes in Closed Systems of Interacting Fermions

Abstract

We show that for closed finite sized systems with an odd number of real fermionic modes, even in the presence of interactions, there are always at least two fermionic operators that commute with the Hamiltonian.There is a zero mode corresponding to the fermion parity operator, as shown by Akhmerov, as well as additional linearly independent zero modes, one of which is 1) the one that is continuously connected to the Majorana mode solution in the non-interacting limit, and 2) less prone to decoherence when the system is opened to contact with an infinite bath. We also show that in the idealized situation where there are two or more well separated zero modes each associated with a finite number of fermions at a localized vortex, these modes have non-Abelian Ising statistics under braiding. Furthermore the algebra of the zero mode operators makes them useful for fermionic quantum computation.

4 pages, 1 figure,v2 4.5 pages 1 figure some corrections and extensions,v3 5 pages

References in corpus (2)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Electron fractionalization in two-dimensional graphenelike structures

Cited by in corpus (35)

• Three-dimensional Dirac fermions in quasicrystals as seen via optical conductivity
• Exact ground states and topological order in interacting Kitaev/Majorana chains
• Majorana bound states in magnetic skyrmions
• Wire deconstructionism of two-dimensional topological phases
• Strongly interacting Majorana modes in an array of Josephson junctions
• Majorana wavefunction oscillations, fermion parity switches, and disorder in Kitaev chains
• Exact Solution to Interacting Kitaev Chain at Symmetric Point
• Many-body Majorana operators and the equivalence of parity sectors
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Multi-particle content of Majorana zero-modes in the interacting p-wave wire
• Multiple signatures of topological transitions for interacting fermions in chain lattices
• Topological superconductivity and Majorana states in low-dimensional systems
• Localization-enhanced and degraded topological-order in interacting p-wave wires
• Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model
• Error generation and propagation in Majorana-based topological qubits
• Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study
• The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
• Topological phase diagrams of exactly solvable non-Hermitian interacting Kitaev chains
• Identification of Majorana Modes in Interacting Systems by Local Integrals of Motion
• Simulating Z_2 topological insulators via a one-dimensional cavity optomechanical cells array
• Out of Equilibrium Majoranas in Interacting Kitaev Chains
• Exact zero modes and decoherence in systems of interacting Majorana fermions
• Fermion-Parity-Based Computation and its Majorana-Zero-Mode Implementation
• Symmetry classes, many-body zero modes, and supersymmetry in the complex Sachdev-Ye-Kitaev model
• Constrained thermalisation and topological superconductivity
• Even and odd normalized zero modes in random interacting Majorana models respecting the Parity $P$ and the Time-Reversal-Symmetry $T$
• A new twist on the Majorana surface code: Bosonic and fermionic defects for fault-tolerant quantum computation
• Effects of Quantum Pair Creation and Annihilation on a Classical Exclusion Process: the transverse XY model with TASEP
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Fragmentation, Zero Modes, and Collective Bound States in Constrained Models
• Construction of Many-Body-Localized Models where all the eigenstates are Matrix-Product-States
• Quantifying robustness and locality of Majorana bound states in interacting systems
• Floquet Gauge Pumps as Sensors for Spectral Degeneracies Protected by Symmetry or Topology
• Explicit forms of zero modes in symmetric interacting Kitaev chain without and with dimerization