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arXiv:2404.13297 · SciPost Physics Core

Coalescing hardcore-boson condensate states with nonzero momentum

C.H. Zhang, Zhi Song

Published Jan 31, 2025• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.21468/scipostphyscore.8.1.013

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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.
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 $ n $-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.
The cooperation between non-Hermiticity and interaction brings about a lot of counterintuitive behaviors, which are impossible to exist in the framework of the Hermitian system. We study the effect of a non-Hermitian impurity on the Hubbard model in the context of $\ensuremath{\eta}$ symmetry. We show that the non-Hermitian Hubbard Hamiltonian can respect a full real spectrum even if a local non-Hermitian impurity is applied to. The balance between dissipation of single fermion and on-site pair fluctuation results in a highest-order coalescing state with off-diagonal long-range order (ODLRO). Based on the characteristic of high-order EP, the critical non-Hermitian Hubbard model allows the generation of such a steady superconducting-like state through the time evolution from an arbitrary initial state, including the vacuum state. Remarkably, this dynamic scheme is insensitive to the on-site interaction and entirely independent of the locations of particle dissipation and pair fluctuation. Our results lay the groundwork for the dynamical generation of a steady ODLRO state through the critical non-Hermitian strongly correlated system.
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.
Neither hardcore bosons nor fermions can occupy the same lattice site-state. However, a nearest neighbour interaction may counteract the hardcore effect, resulting in condensate states in a bosonic system. In this work, we unveil the underlying mechanism by developing a general method to construct the condensate eigenstates from those of sub-Hamiltonians. As an application, we find that a local on-site potential can induce an evanescent condensate mode. Based on this, exact condensate ground states of hardcore bosons, possessing off-diagonal long-range order, can be constructed when an array of impurities is applied. The effect of the off-resonance impurity on the condensate ground states is also investigated using numerical simulations of the dynamic response.
An exceptional point (EP) is exclusive for non-Hermitian systems and distinct from that at a degeneracy point (DP), supporting intriguing dynamics which can be utilized to probe quantum phase transitions and prepare eigenstates in a Hermitian many-body system. In this paper, we investigate the transition from a DP for a Hermitian system to an EP driven by non-Hermitian terms. We present a theorem on the existence of a transition between a DP and EP for a general system. Specifically, one of twofold degenerate eigenstates of a Hermitian system becomes a coalescing state when a selected non-Hermitian term is added. The obtained EP is robust to the strength of non-Hermitian terms. We illustrate the theorem by an exactly solvable quasi-one-dimensional model, which allows for the existence of a transition between fully degenerate and exceptional spectra driven by non-Hermitian tunnelings in real and kkk spaces, respectively. We also study the EP dynamics for generating coalescing edge modes in Su-Schrieffer-Heeger-like models. This finding reveals the ubiquitous connection between DPs and EPs.
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.