# Unconventional superconducting correlations in fermionic many-body scars

## TL;DR

This paper demonstrates how certain subspaces in two-orbital lattice systems exhibit robust, unconventional superconducting correlations linked to many-body scars, which can be analytically characterized and numerically confirmed.

## Contribution

It introduces a new class of many-body scars with strong superconducting correlations in two-orbital systems, expanding understanding of ergodicity breaking and superconductivity.

## Key findings

- Identification of subspaces with long-range superconducting correlations
- Construction of group-invariant quantum many-body scars
- Analytical and numerical confirmation of unconventional pairing

## Abstract

Weak ergodicity breaking in interacting quantum systems may occur due to the existence of a subspace dynamically decoupled from the rest of the Hilbert space. In two-orbital spinful lattice systems, we construct such subspaces that are in addition distinguished by strongest inter-orbital and spin-singlet or spin-triplet, long-range superconducting pairing correlations. All unconventional pairing types we consider are local in space and unitary. Alternatively to orbitals, the additional degree of freedom could originate from the presence of two layers or through any other mechanism. Required Hamiltonians are rather non-exotic and include chemical potential, Hubbard, and spin-orbit interactions typically used for two-orbital superconducting materials. Each subspace is spanned by a family of group-invariant quantum many-body scars combining both 2e and 4e pairing/clustering contributions. One of the basis states has the form of a BCS wavefunction and can always be made the ground state by adding a mean-field pairing potential. Analytical results in this work are lattice-, dimension- and (mostly) system size-independent. We confirm them by exact numerical diagonalization in small systems.