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This paper establishes a rigorous analytical framework for interacting non-Hermitian many-body systems, extending eta-pairing theory to arbitrary dimensions and revealing unique phenomena absent in Hermitian physics. By unifying various symmetries within the Hubbard model context, it provides critical theoretical tools for understanding complex quantum states like Fock space localization and non-Hermitian angular-momentum operators. These advances are essential for researchers developing next-generation quantum simulators and materials that exploit non-Hermitian effects.
Generalized $\eta$-pairing approach to interacting non-Hermitian systems in arbitrary dimensions
arXiv:2502.04559v5 Announce Type: replace-cross Abstract: Developing a general and rigorous analytical approach to non-Hermitian many-body systems is a challenging task. Here, we generalize the eta-pairing theory to very general non-Hermitian Hubbard models and find many novel phenomena without Hermitian analogs. For instance, the Hermitian conjugate of an eta-pairing eigenoperator may not be an eigenoperator, eta-pairing eigenoperators can be spatially modulated, and the $SU(2)$ pseudospin symmetry may not be possible even if $H$ commutes with the eta-pairing operators. Remarkably, these novel non-Hermitian phenomena are closely related to each other by several theorems we establish and can lead to, for example, new types of eta-pairing operators (e.g., the notion of non-Hermitian angular-momentum operators) and the Fock space localization of many-body eta-pairing eigenstates. Some issues on the $SO(4)$ and particle-hole symmetries are clarified. Our general eta-pairing theory also reveals a previously unnoticed unification of these symmetries of the Hubbard model. These general results can be illustrated with concrete examples such as the generalized Hatano-Nelson-Hubbard models and a general two-sublattice model. In particular, the general two-sublattice model can reveal the eta-pairing structure [e.g., the $SO(4)$ symmetry] in systems with Hermitian hoppings, including the original eta-pairing theory for square lattice, the extension to triangular lattice, and some topological systems. Our results establish a new and rigorous theoretical framework for studying interacting non-Hermitian systems in arbitrary spatial dimensions, even without bulk translation symmetry.
Abstract:Developing a general and rigorous analytical approach to non-Hermitian many-body systems is a challenging task. Here, we generalize the eta-pairing theory to very general non-Hermitian Hubbard models and find many novel phenomena without Hermitian analogs. For instance, the Hermitian conjugate of an eta-pairing eigenoperator may not be an eigenoperator, eta-pairing eigenoperators can be spatially modulated, and the $SU(2)$ pseudospin symmetry may not be possible even if $H$ commutes with the eta-pairing operators. Remarkably, these novel non-Hermitian phenomena are closely related to each other by several theorems we establish and can lead to, for example, new types of eta-pairing operators (e.g., the notion of non-Hermitian angular-momentum operators) and the Fock space localization of many-body eta-pairing eigenstates. Some issues on the $SO(4)$ and particle-hole symmetries are clarified. Our general eta-pairing theory also reveals a previously unnoticed unification of these symmetries of the Hubbard model. These general results can be illustrated with concrete examples such as the generalized Hatano-Nelson-Hubbard models and a general two-sublattice model. In particular, the general two-sublattice model can reveal the eta-pairing structure [e.g., the $SO(4)$ symmetry] in systems with Hermitian hoppings, including the original eta-pairing theory for square lattice, the extension to triangular lattice, and some topological systems. Our results establish a new and rigorous theoretical framework for studying interacting non-Hermitian systems in arbitrary spatial dimensions, even without bulk translation symmetry.
Strongly Correlated Electrons (cond-mat.str-el); Mesoscale and Nanoscale Physics (cond-mat.mes-hall); Quantum Gases (cond-mat.quant-gas); Quantum Physics (quant-ph)
arXiv:2502.04559 [cond-mat.str-el]
(or arXiv:2502.04559v5 [cond-mat.str-el] for this version)
Full text under the publisher's open licence · 245 words
