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arXiv:2509.18563 · Physical review. B./Physical review. B

Exceptional-point induced dynamic sensitivity to particle-number parity

J. Y. Liu-Sun, Z. Song

Published Mar 9, 2026• 0 citations
arXivHTMLPDF

Abstract

As an exclusive feature of a non-Hermitian system, the existence of exceptional points (EPs) depends not only on the details of the Hamiltonian but also on the particle-number filling and the particle statistics. In this paper, we study many-particle EPs in a Bose Hubbard chain with two end-site resonant imaginary potentials. Starting from a single-particle coalescing eigenstate, we construct $n$-particle condensate eigenstates for the cases with zero and infinite $U$. Compared with the free bosonic case, where the $ n $-particle condensate eigenstate is an $(n+1)$-th-order coalescing state, the hardcore-boson counterpart is a second-order coalescing state for odd $n$ , while it is not for even $n$. The difference in particle-number parity results in distinct quenching dynamics of the condensate states, highlighting the role of parity in system behavior. Our finding may stimulate research on the dynamic sensitivity to particle-number parity.

DOI
10.1103/337k-9ntw

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As an exclusive feature of a non-Hermitian system, the existence of exceptional points (EPs) depends not only on the details of the Hamiltonian but also on the particle-number filling and the particle statistics. In this paper, we study many-particle EPs in a Bose Hubbard chain with two end-site resonant imaginary potentials. Starting from a single-particle coalescing eigenstate, we construct nnn-particle condensate eigenstates for the cases with zero and infinite UUU. Compared with the free bosonic case, where the nnn-particle condensate eigenstate is an (n+1)(n+1)(n+1)-th-order coalescing state, the hardcore-boson counterpart is a second-order coalescing state for odd nnn , while it is not for even nnn. The difference in particle-number parity results in distinct quenching dynamics of the condensate states, highlighting the role of parity in system behavior. Our finding may stimulate research on the dynamic sensitivity to particle-number parity.
Exceptional points (EPs), as an exclusive feature of a non-Hermitian system, support coalescing states to be alternative stable state beyond the ground state. In this work, we explore the influence of non-Hermitian impurities on the dynamic formation of condensate states in one-, two-, and three-dimensional extended Bose-Hubbard systems with strong on-site interaction. Based on the solution for the hardcore limit, we show exactly that condensate modes with off-diagonal long-range order (ODLRO) can exist when certain system parameters satisfy specific matching conditions. Under open boundary conditions, the condensate states become coalescing states when the non-Hermitian \mathcal{PT} 𝒫 𝒯 -symmetric boundary gives rise to the EPs. The fundamental mechanism behind this phenomenon is uncovered through analyzing the scattering dynamics of many-particle wavepackets at the non-Hermitian boundaries. The EP dynamics facilitate the dynamic generation of condensate states with non-zero momentum. To further substantiate the theoretical findings, numerical simulations are conducted. This study not only unveils the potential condensation of interacting bosons but also offers an approach for the engineering of condensate states.
The appearance of topological singularities, namely exceptional points (EPs) is an intriguing feature of parameter-dependent open quantum or wave systems. EPs are the special type of nonHermitian degeneracies where two (or more) eigenstates of the underlying system coalesce. In this paper, we present a three level non-Hermitian Hamiltonian which hosts three interacting eigenstates. The matrix elements are optimized in such a way that the intermediate eigenstate interacts with both the other states and the underlying system hosts at least two different second order EPs. The impact of quasi-static parameter variation along a cyclic contour around the embedded EPs on the dynamics of interacting eigenvalues is well investigated in the context of cascaded state conversion. Such dynamics of the eigenvalues shows a clear signature of the third order EP with a combined effect of both the second order EPs. Moreover, we examine the accumulation of phases around the identified EPs and study the hallmark of phase exchange during cascaded state conversions accompanied by the parametric encirclement of the third order EP.
We study a non-Hermitian PT−PT-PT−symmetric generalization of an NNN-particle, two-mode Bose-Hubbard system, modeling for example a Bose-Einstein condensate in a double well potential coupled to a continuum via a sink in one of the wells and a source in the other. The effect of the interplay between the particle interaction and the non-Hermiticity on characteristic features of the spectrum is analyzed drawing special attention to the occurrence and unfolding of exceptional points (EPs). We find that for vanishing particle interaction there are only two EPs of order N+1N+1N+1 which under perturbation unfold either into [(N+1)/2][(N+1)/2][(N+1)/2] eigenvalue pairs (and in case of N+1N+1N+1 odd, into an additional zero-eigenvalue) or into eigenvalue triplets (third-order eigenvalue rings) and (N+1)mod  3(N+1)\mod 3(N+1)mod3 single eigenvalues, depending on the direction of the perturbation in parameter space. This behavior is described analytically using perturbational techniques. More general EP unfoldings into eigenvalue rings up to (N+1)(N+1)(N+1)th order are indicated.
Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly in influencing quantum correlations, remains underexplored. In this work, we investigate how EPs control multimode entanglement in bosonic chains. Using a Bogoliubov-de Gennes (BdG) framework to describe the Heisenberg equations, we identify EPs of varying orders and uncover spectral transitions between purely real, purely imaginary, and mixed eigenvalue spectra. These spectral regions, divided by EPs, correspond to three distinct entanglement dynamics: oscillatory, exponential, and hybrid. Remarkably, we demonstrate that higher-order EPs, realized by non-integer-pi hopping phases or nonuniform interaction strengths, significantly enhance the degree of multimode entanglement compared to second-order EPs. Our findings provide a pathway to leveraging EPs for entanglement control and exhibit the potential of non-Hermitian physics in advancing quantum technologies.
Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly in influencing quantum correlations, remains underexplored. In this work, we investigate how EPs control multimode entanglement in bosonic chains. Using a Bogoliubov-de Gennes (BdG) framework to describe the Heisenberg equations, we identify EPs of varying orders and uncover spectral transitions between purely real, purely imaginary, and mixed eigenvalue spectra. These spectral regions, divided by EPs, correspond to three distinct entanglement dynamics: oscillatory, exponential, and hybrid. Remarkably, we demonstrate that higher-order EPs, realized by non-integer-pi hopping phases or nonuniform interaction strengths, significantly enhance the degree of multimode entanglement compared to second-order EPs. Our findings provide a pathway to leveraging EPs for entanglement control and exhibit the potential of non-Hermitian physics in advancing quantum technologies.
Exceptional points (EPs), arising in non-Hermitian systems, have garnered significant attention in recent years, enabling advancements in sensing, wave manipulation, and mode selectivity. However, their role in quantum systems, particularly in influencing quantum correlations, remains underexplored. In this work, we investigate how EPs control multimode entanglement in bosonic chains. Using a Bogoliubov-de Gennes (BdG) framework to describe the Heisenberg equations, we identify EPs of varying orders and uncover spectral transitions between purely real, purely imaginary, and mixed eigenvalue spectra. These spectral regions, divided by EPs, correspond to three distinct entanglement dynamics: oscillatory, exponential, and hybrid. Remarkably, we demonstrate that higher-order EPs, realized by non-integer- π hopping phases or nonuniform interaction strengths, significantly enhance the degree of multimode entanglement compared to second-order EPs. Our findings provide a pathway to leveraging EPs for entanglement control and exhibit the potential of non-Hermitian physics in advancing quantum technologies.