Exact solution of the Bose Hubbard model with unidirectional hopping

Abstract

A one-dimensional Bose Hubbard model with unidirectional hopping is shown to be exactly solvable. Applying the algebraic Bethe ansatz method, we prove the integrability of the model and derive the Bethe ansatz equations. The exact eigenvalue spectrum can be obtained by solving these equations. The distribution of Bethe roots reveals the presence of a superfluid-Mott insulator transition at the ground state, and the critical point is determined. By adjusting the boundary parameter, we demonstrate the existence of non-Hermitian skin effect even in the presence of interaction, but it is completely suppressed for the Mott insulator state in the thermodynamical limit. Our result represents a new class of exactly solvable non-Hermitian many-body systems, which have no Hermitian correspondence and can be used as a benchmark for various numerical techniques developed for non-Hermitian many-body systems.

6+8 pages, 2+6 figures

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• Non-reciprocal dynamics and the non-Hermitian skin effect of repulsively bound pairs
• General criterion for non-Hermitian skin effects and Application: Fock space skin effects in many body systems
• Dynamical suppression of many-body non-Hermitian skin effect in Anyonic systems
• Fate of Two-Particle Bound States in the Continuum in non-Hermitian Systems
• Modulational Instability and Dynamical Growth Blockade in the Nonlinear Hatano-Nelson Model
• Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model
• Numerical instability of non-Hermitian Hamiltonian evolutions
• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
• Design nearly optimal quantum algorithm for linear differential equations via Lindbladians
• Many-Body Non-Hermitian Skin Effect with Exact Steady States in the Dissipative Quantum Link Model
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Topologically compatible non-Hermitian skin effect
• Non-Hermitian skin effect in fragmented Hilbert spaces of one-dimensional fermionic lattices
• Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices
• Effective Bethe Ansatz for Spin-1 Non-integrable Models