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

## TL;DR

This paper introduces a method to construct number-conserving Hamiltonians with exact topological superconducting ground states, including models with Majorana modes, advancing understanding and potential experimental realization.

## Contribution

The authors develop a general technique to create number-conserving Hamiltonians that exactly reproduce chosen BCS-type states, including topological superconductors like Kitaev wires and 2D p+ip models.

## Key findings

- Constructed 1D double wire model with Majorana-like ground states
- Developed 2D p+ip superconducting model with vortex states
- Provided analytic expressions for topologically degenerate 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 $p_x+ip_y$ 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.