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, weak ergodicity breaking, and partial integrability

Abstract

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

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