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arXiv:2402.10261 · Physical Review Research

Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model

Christopher Ekman, Emil J. Bergholtz

Published Sep 17, 2024• 13 citations
arXivHTMLPDF

Abstract

Strongly interacting nonequilibrium systems are of great fundamental interest, yet their inherent complexity make them notoriously hard to analyze. We demonstrate that the dynamics of the Bose-Hubbard model, which by itself evades solvability, can be solved exactly at any interaction strength in the presence of loss tuned to a rate matching the hopping amplitude. Remarkably, the full solvability of the corresponding Liouvillian, and the integrability of the pertinent effective non-Hermitian Hamiltonian, survives the addition of disorder and generic boundary conditions. By analyzing the Bethe ansatz solutions we find that even weak interactions change the qualitative features of the system, leading to an intricate dynamical phase diagram featuring non-Hermitian Mott-skin effects, disorder induced localization, highly degenerate exceptional points, and a Bose glasslike phase of fragmented condensates. We discuss realistic implementations of this model with cold atoms. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.l032067

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The non-Hermitian skin effect, in which eigenstates of non-Hermitian Hamiltonians are localized at one boundary in the open boundary condition, has attracted great interest recently. In this paper, we investigate the skin effect in one-dimensional dissipative quantum many-body systems, which we call the Liouvillian skin effect (LSE). We rigorously identify the existence of the LSE for generalized boundary conditions by solving the Liouvillian superoperator of an exactly solvable model with the advantage of the Bethe ansatz. The LSE is sensitive to boundary conditions where the signature is reflected in eigenfunctions of the system. We confirm that the LSE is fragile to a tiny coflow boundary hopping with non-Hermitian current but can survive a counterflow boundary hopping in the thermodynamic limit. Our work provides a prototypical example of exactly solvable dissipative quantum many-body lattice systems exhibiting the LSE for generalized boundary conditions. It can be further extended to other integrable open quantum many-body models.
Non-Hermitian skin effect (NHSE) is a unique feature studied extensively in noninteracting non-Hermitian systems. In this paper, we extend the NHSE originally discovered in noninteracting systems to interacting many-body systems by investigating an exactly solvable non-Hermitian model, i.e., the prototypical Lieb-Liniger Bose gas with imaginary vector potential. We show that this non-Hermitian many-body model can also be exactly solved through the Bethe ansatz. By solving the Bethe ansatz equations accurately, the explicit eigenfunction is obtained, and the model's density profiles and momentum distributions are calculated to characterize the NHSE quantitatively. We find that the NHSE is gradually suppressed on the repulsive side but does not vanish as the repulsive interaction strength increases. On the attractive side, the NHSE for bound-state solutions is enhanced as interaction strength grows. In contrast, for the scattering state the NHSE shows a nonmonotonic behavior in the attractive side. Our paper provides an example of the NHSE in exactly solvable many-body systems, and we envision that it can be extended to other non-Hermitian many-body systems, especially to integrable models.
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Non-Hermitian systems exhibit unique spectral properties, including the non-Hermitian skin effect and exceptional points, often influenced by boundary conditions. The modulation of these phenomena by generalized boundary conditions remains unexplored and not understood. Here, we analyze the Hatano-Nelson model with generalized boundary conditions induced by complex hopping amplitudes at the boundary. Using similarity transformations, we determine the conditions yielding real energy spectra and skin effect, and identify the emergence of exceptional points where spectra transition from real to complex. We demonstrate that tuning the boundary hopping amplitudes precisely controls the non-Hermitian skin effect, i.e., the localization of eigenmodes at the lattice edges. These findings reveal the sensitivity of spectral and localization properties to boundary conditions, providing a framework for engineering quantum lattice models with tailored spectral and localization features, with potential applications in quantum devices.