Unconventional superconducting correlations in fermionic many-body scars

TL;DR

This work connects unconventional superconductivity with weak ergodicity breaking by constructing group-invariant many-body scar subspaces in two-orbital spinful fermions. It develops four scar families—inter-orbital eta states and two classes of spin-triplet scars—each supporting strong, local, unitary pairing and off-diagonal long-range order under Hamiltonians of the form $H=H_0+\sum_l O_l T_l$, with a unifying $\mathrm{O}(N)$ symmetry. The authors provide analytic, lattice-/dimension-/system-size-independent results for pairing correlations, verify them with exact diagonalization on small lattices, and show how pairing potentials or attractive interactions can make scar states ground states or drive robust superconducting features while keeping scars intact. The findings offer a principled route to realize robust unconventional pairing within non-integrable many-body systems, with potential implications for multi-orbital superconductors and engineered quantum simulators.

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.

Figures (10)

• Figure 1.1: a) Some of the groups $G$ appearing in this work and their inter-dependencies. b) Scar subspaces corresponding to these groups.
• Figure 3.1: Numerical results for the $H^{1}_{\text{i}\eta}$\ref{['eq:Hminimal']} and $N=4$. Horizontal axis in this and all other figures is the energy. a) Entanglement entropy b) Spin-singlet orbital-triplet ($\mu=0$, $\nu=3$) pairing ODLRO. Dashed red line shows the average over the $\ket{\phi_n^{03}}$ states. c) Spin-triplet orbital-singlet ($\mu=1$, $\nu=0$) pairing ODLRO. In both cases, the two-point function is measured between the most distant sites ($i=1$ and $j=N$).
• Figure 3.2: Numerical results for the inter-orbital (${\cal O}_{03}$) pairing potential \ref{['eq:dH0general']} added to the Hamiltonian \ref{['eq:Hminimal']}. a) Entanglement entropy. b) Real part of the 1-point function $\braket{{\cal O}^{\dagger}_{03,j}}$. Horizontal lines indicate analytical values. c) 2-point function $\braket{{\cal O}^{\dagger}_{03,1} {\cal O}_{03,N}}$. Dashed line indicates average over $\ket{z_n^{03}}$ scar subspace. d) Two-point function $\braket{{\cal O}^{\dagger}_{10,1} {\cal O}_{10,N}}$.
• Figure 3.3: $2e$ vs $4e$ clustering with the inter-orbital pairing potential added. a) The absolute value of the expectation value of the quartet creation operator. b) Real part of the expectation value of the pair creation operator. In both cases, the spin-triplet orbital-singlet pairing ${\cal O}^{\dagger}_{20}$ is considered.
• Figure 3.4: Entanglement entropy for an attractive Hubbard interaction with $U=-6.51$. a) $\Delta=0$; b) $\Delta=0.01$. All other parameters are identical to those used in Fig. \ref{['fig:minH1Plots']}.