Number-conserving interacting fermion models with exact topological superconducting ground states

Abstract

We present a method to construct number-conserving Hamiltonians whose ground states exactly reproduce an arbitrarily chosen BCS-type mean-field state. Such parent Hamiltonians can be constructed not only for the usual $s$-wave BCS state, but also for more exotic states of this form, including the ground states of Kitaev wires and 2D topological superconductors. This method leads to infinite families of locally-interacting fermion models with exact topological superconducting ground states. After explaining the general technique, we apply this method to construct two specific classes of models. The first one is a one-dimensional double wire lattice model with Majorana-like degenerate ground states. The second one is a two-dimensional $p_x+i{p}_y$ superconducting model, where we also obtain analytic expressions for topologically degenerate ground states in the presence of vortices. Our models may provide a deeper conceptual understanding of how Majorana zero modes could emerge in condensed matter systems, as well as inspire novel routes to realize them in experiment.

5 pages, 2 figures; supplement: 4 pages, 1 figure

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• Boundary deconfined quantum criticality at transitions between symmetry-protected topological chains
• Two-fluid coexistence and phase separation in a one dimensional model with pair hopping and density interactions
• Analytic ground state wavefunctions of mean-field $p_x+i{p}_y$ superconductors with vortices and boundaries
• Interaction-induced phase transitions at topological quantum criticality of an extended Su-Schrieffer-Heeger model
• Topology of superconductors beyond mean-field theory
• Universal Signatures of Majorana-like Quasiparticles in Strongly Correlated Landau-Fermi Liquids
• Generalized Majorana edge modes in a number-conserving periodically driven $p$-wave superconductor
• Majorana edge modes in isolated wires
• Integrable Model of a Superconductor with non-Fermi liquid and Mott Phases