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.

arXiv comment6+8 pages, 2+6 figures

References in corpus (45)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Making Sense of Non-Hermitian Hamiltonians
• Edge states and topological invariants of non-Hermitian systems
• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Physics
• Topological phases of non-Hermitian systems
• Symmetry and Topology in Non-Hermitian Physics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Topological Origin of Non-Hermitian Skin Effects
• Non-Bloch Band Theory of Non-Hermitian Systems
• Correspondence between winding numbers and skin modes in non-hermitian systems
• Anatomy of skin modes and topology in non-Hermitian systems
• Fermi gases in one dimension: From Bethe Ansatz to experiments
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Phases of the one-dimensional Bose-Hubbard model
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model
• Impurity induced scale-free localization
• Skin superfluid, topological Mott insulators, and asymmetric dynamics in interacting non-Hermitian Aubry-Andre-Harper models
• Topological classification of non-Hermitian systems with reflection symmetry
• Many-body topology of non-Hermitian systems
• Dynamic properties of the one-dimensional Bose-Hubbard model
• Non-Hermitian topological Mott insulators in one-dimensional fermionic superlattices
• Symmetry breaking and spectral structure of the interacting Hatano-Nelson model
• Breakdown of the Mott insulator: Exact solution of an asymmetric Hubbard model
• Topological classification of defects in non-Hermitian systems
• Engineering tunable local loss in a synthetic lattice of momentum states
• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Fate of the non-Hermitian skin effect in many-body fermionic systems
• Topological Bose-Mott insulators in one-dimensional non-Hermitian superlattices
• Mixture of bosonic and spin-polarized fermionic atoms in an optical lattice
• Accumulation of scale-free localized states induced by local non-Hermiticity
• Fate of fractional quantum Hall states in open quantum systems: characterization of correlated topological states for the full Liouvillian
• Scale-free localization and PT symmetry breaking from local non-Hermiticity
• Symmetry and topological classification of Floquet non-Hermitian systems
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Interaction induced dynamical $\mathcal{P}\mathcal{T}$ symmetry breaking in dissipative Fermi-Hubbard models
• Reduction of one-dimensional non-Hermitian point-gap topology by correlations
• Scale-free non-Hermitian skin effect in a boundary-dissipated spin chain
• Emergent Mott insulators and non-Hermitian conservation laws in an interacting bosonic chain with noninteger filling and nonreciprocal hopping
• Exact solution of a non-Hermitian $\mathcal{PT}$-symmetric Heisenberg spin chain
• Observation of size-dependent boundary effects in non-Hermitian electric circuits

Cited by in corpus (23)

• Occupation-dependent particle separation in one-dimensional non-Hermitian lattices
• 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
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System
• An Explicit Wavefunction of the Interacting Non-Hermitian Spin-1/2 1D System
• Semiclassical analysis of spin dynamics in the non-Hermitian Hubbard model
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System
• Dissipation induced ergodic-nonergodic transitions in finite-height mosaic Wannier-Stark lattices
• Geometric origin of self-intersection points in non-Hermitian energy spectra
• Effective Bethe Ansatz for Spin-1 Non-integrable Models
• Quench dynamics and quantum flutter properties of one-dimensional attractive single-spin flipped Fermi gases