Exact eigenstates of multicomponent Hubbard models: SU(<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>) magnetic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>η</mml:mi></mml:math> pairing, we

We construct exact eigenstates of multicomponent Hubbard models in arbitrary dimensions by generalizing the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>η</a:mi></a:math>-pairing mechanism. Our models include the <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>SU</b:mi><b:mo>(</b:mo><b:mi>N</b:mi><b:mo>)</b:mo></b:mrow></b:math> Hubbard model as a special case. Unlike the conventional two-component case, the generalized <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mi>η</c:mi></c:math>-pairing mechanism permits the construction of eigenstates that feature off-diagonal long-range order and magnetic long-range order. These states form fragmented fermionic condensates due to a simultaneous condensation of multicomponent <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mi>η</d:mi></d:math> pairs. While the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>η</e:mi></e:math>-pairing states in the SU(2) Hubbard model are based on the <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mi>η</f:mi></f:math>-pairing symmetry, the exact eigenstates in the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>N</g:mi></g:math>-component system with <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>N</h:mi><h:mo>≥</h:mo><h:mn>3</h:mn></h:mrow></h:math> arise not from symmetry of the Hamiltonian but from a spectrum generating algebra defined in a restricted Hilbert space. We exploit this fact to show that the generalized <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi>η</i:mi></i:math>-pairing eigenstates do not satisfy the eigenstate thermalization hypothesis and serve as quantum many-body scar states. This result indicates a weak breakdown of ergodicity in the <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mi>N</j:mi></j:math>-component Hubbard models for <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"><k:mrow><k:mi>N</k:mi><k:mo>≥</k:mo><k:mn>3</k:mn></k:mrow></k:math>. Furthermore, we show that these exact eigenstates constitute integrable subsectors in which the Hubbard Hamiltonian effectively reduces to a noninteracting model. This partial integrability causes various multicomponent Hubbard models to weakly break ergodicity. We propose a method of harnessing dissipation to distill the integrable part of the dynamics and elucidate a mechanism of nonthermalization caused by dissipation. This work establishes the coexistence of off-diagonal long-range order and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"><l:mrow><l:mi>SU</l:mi><l:mo>(</l:mo><l:mi>N</l:mi></l:mrow></l:math>) magnetism in excited eigenstates of the multicomponent Hubbard models, which presents a possibility of novel out-of-equilibrium pairing states of multicomponent fermions. These models unveil a unique feature of quantum thermalization of multicomponent fermions, which can experimentally be tested with cold-atom quantum simulators. Published by the American Physical Society 2024