Generalized $η$-pairing approach to interacting non-Hermitian systems in arbitrary dimensions
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911484084224000 |
|---|---|
| author | Lieta, Kai |
| author_facet | Lieta, Kai |
| contents | 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 anomalous localization of 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. To exemplify these findings, we first propose the one-dimensional Hatano-Nelson-Hubbard model (with or without the bulk translation invariance) and show that the right and left two-particle eta-pairing eigenstates are exponentially localized at opposite boundaries of the chain. Then, we generalize this model to two dimensions and find that the eta-pairing eigenstates can exhibit the first- or second-order skin effect. Finally, to realize all of the non-Hermitian eta-pairing phenomena, we construct a general two-sublattice model that is defined on an arbitrary lattice; this model can also reveal the eta-pairing structure 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 novel quantum phenomena in interacting non-Hermitian many-body systems, even in arbitrary spatial dimensions and without the bulk translation symmetry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_04559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized $η$-pairing approach to interacting non-Hermitian systems in arbitrary dimensions Lieta, Kai Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Gases Quantum Physics 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 anomalous localization of 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. To exemplify these findings, we first propose the one-dimensional Hatano-Nelson-Hubbard model (with or without the bulk translation invariance) and show that the right and left two-particle eta-pairing eigenstates are exponentially localized at opposite boundaries of the chain. Then, we generalize this model to two dimensions and find that the eta-pairing eigenstates can exhibit the first- or second-order skin effect. Finally, to realize all of the non-Hermitian eta-pairing phenomena, we construct a general two-sublattice model that is defined on an arbitrary lattice; this model can also reveal the eta-pairing structure 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 novel quantum phenomena in interacting non-Hermitian many-body systems, even in arbitrary spatial dimensions and without the bulk translation symmetry. |
| title | Generalized $η$-pairing approach to interacting non-Hermitian systems in arbitrary dimensions |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Gases Quantum Physics |
| url | https://arxiv.org/abs/2502.04559 |