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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.21547 |
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| _version_ | 1866909003003461632 |
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| author | Kulkarni, Vinayak M. |
| author_facet | Kulkarni, Vinayak M. |
| contents | We develop a mathematically controlled framework for Yang--Baxter integrability in pseudo-Hermitian quantum impurity systems arising from periodic driving of a Dirac-like bath. The effective impurity Hamiltonian possesses a dynamically generated $\PT$ symmetry and exhibits exceptional points (EPs) where it becomes non-diagonalizable. We construct the Yang--Baxter generator as a rank-one operator on the two-particle contact space, built from biorthogonal impurity eigenvectors, and prove that it satisfies the Temperley-Lieb relations. Its standard Baxterization gives an $R$-matrix, an RLL relation, an RTT structure,and a commuting family of transfer matrices. At the exceptional point(EP), the semisimple biorthogonal eigenvector construction is replaced by a Jordan-chain contact vector, while the Hamiltonian itself develops a nilpotent Jordan block. Within this framework we derive biorthogonal Bethe equations and show that the Gaudin matrix becomes defective at the EP, establishing that the smallest singular value $σ_N(G)\to0$ at the EP while remaining $\OO(1)$ at the Kondo critical point,providing a sharp algebraic diagnostic. We further prove that Bethe rapidities exhibit square-root coalescence and $\mathbb{Z}_2$ monodromy at the EP, reflecting the underlying Jordan structure, and that the effective pseudo-Hermitian Hamiltonian emerges from the periodically driven microscopic system by adiabatic coarse graining of off-shell angular-momentum modes, with corrections controlled by the auxiliary-mode gap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21547 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Yang-Baxter Integrability and Exceptional-Point Structure in Pseudo-Hermitian Quantum Impurity Systems Kulkarni, Vinayak M. Mathematical Physics 81R12, 82B23, 47A55, 46C20 We develop a mathematically controlled framework for Yang--Baxter integrability in pseudo-Hermitian quantum impurity systems arising from periodic driving of a Dirac-like bath. The effective impurity Hamiltonian possesses a dynamically generated $\PT$ symmetry and exhibits exceptional points (EPs) where it becomes non-diagonalizable. We construct the Yang--Baxter generator as a rank-one operator on the two-particle contact space, built from biorthogonal impurity eigenvectors, and prove that it satisfies the Temperley-Lieb relations. Its standard Baxterization gives an $R$-matrix, an RLL relation, an RTT structure,and a commuting family of transfer matrices. At the exceptional point(EP), the semisimple biorthogonal eigenvector construction is replaced by a Jordan-chain contact vector, while the Hamiltonian itself develops a nilpotent Jordan block. Within this framework we derive biorthogonal Bethe equations and show that the Gaudin matrix becomes defective at the EP, establishing that the smallest singular value $σ_N(G)\to0$ at the EP while remaining $\OO(1)$ at the Kondo critical point,providing a sharp algebraic diagnostic. We further prove that Bethe rapidities exhibit square-root coalescence and $\mathbb{Z}_2$ monodromy at the EP, reflecting the underlying Jordan structure, and that the effective pseudo-Hermitian Hamiltonian emerges from the periodically driven microscopic system by adiabatic coarse graining of off-shell angular-momentum modes, with corrections controlled by the auxiliary-mode gap. |
| title | Yang-Baxter Integrability and Exceptional-Point Structure in Pseudo-Hermitian Quantum Impurity Systems |
| topic | Mathematical Physics 81R12, 82B23, 47A55, 46C20 |
| url | https://arxiv.org/abs/2604.21547 |