Quantum many-body scars with unconventional superconducting pairing symmetries via multibody interactions

We present a systematic framework to construct model Hamiltonians that have unconventional superconducting pairing states as exact energy eigenstates, by incorporating multibody interactions (i.e., interactions among more than two particles). The multibody interactions are introduced in a form of the local density-density coupling in such a way that any pair configuration in real space has a constant interaction energy by canceling the two-body and multibody interactions. Our approach is applicable to both spinless and spinful models in any spatial dimensions and on any bipartite lattices, facilitating an exhaustive extension of Yang's <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mi>s</a:mi><a:mtext>−</a:mtext><a:mi>wave</a:mi><a:mspace width="4pt"/><a:mi>η</a:mi><a:mtext>−</a:mtext><a:mi>pairing</a:mi></a:mrow></a:math> state to various other unconventional pairing symmetries (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mi>p</c:mi><c:mtext>−</c:mtext><c:mi>wave</c:mi><c:mo>,</c:mo></c:mrow></c:math> <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mi>d</d:mi><d:mtext>−</d:mtext><d:mi>wave</d:mi><d:mo>,</d:mo></d:mrow></d:math> <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mrow><e:mi>f</e:mi><e:mtext>−</e:mtext><e:mi>wave</e:mi><e:mo>,</e:mo></e:mrow></e:math> etc.). Particularly, the constructed eigenstates have off-site pairs with finite center-of-mass momentum, which leads to superconducting states with either even-parity and spin-triplet or odd-parity and spin-singlet symmetry. We verify that the two-dimensional spinful Hubbard model on a square lattice with the multibody interactions has the spin-triplet <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mi>d</f:mi><f:mtext>−</f:mtext><f:mi>wave</f:mi></f:mrow></f:math> pairing state as an energy eigenstate, which can be regarded as a quantum many-body scar state as evidenced from the numerical analysis of the pair correlation function, entanglement entropy, and level statistics. We also discuss other examples, including spin-triplet <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:mi>f</g:mi><g:mtext>−</g:mtext><g:mi>wave</g:mi></g:mrow></g:math> pairing states on a honeycomb lattice and spin-singlet <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>p</h:mi><h:mtext>−</h:mtext><h:mi>wave</h:mi></h:mrow></h:math> pairing states in a one-dimensional chain. These findings open up the possibility of realizing nonequilibrium unconventional superconductivity in a long-lived manner protected against thermalization.