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

Abstract

Strongly interacting non-equilibrium systems are of great fundamental interest, yet their inherent complexity make then 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 glass-like phase of fragmented condensates. We discuss realistic implementations of this model with cold atoms.

7+7 pages, 2+4 figures, published version

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• Variational approach to the dynamics of dissipative quantum impurity models
• Interaction-Induced Second-Order Skin Effect
• Lindbladian versus Postselected Non-Hermitian Topology
• Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
• Exact density profile in a tight-binding chain with dephasing noise
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Anatomy of Higher-Order Non-Hermitian Skin and Boundary Modes
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices
• Liouvillian skin effects in two-dimensional electron systems at finite temperatures