Solvable BCS-Hubbard Liouvillians in arbitrary dimensions

Abstract

We present the construction of a solvable Lindblad model in arbitrary dimensions, wherein the Liouvillian can be mapped to a BCS-Hubbard model featuring an imaginary interaction. The Hilbert space of the system can be divided into multiple sectors, each characterized by an onsite invariant configuration. The model exhibits bistable steady states in all spatial dimensions, which is guaranteed by the fermion-number parity. Notably, the Liouvillian gap exhibits a Zeno transition, below which the Liouvillian gap is linear with respect to the dissipation. We also uncover a generic dimension-dependent gap behavior: In one dimension, the gap originates from multiple sectors with spectral crossing; in higher dimensions, a single sector determines the gap.

arXiv comment7 pages, 2 figures

References in corpus (40)

• Anyons in an exactly solved model and beyond
• An Open-System Quantum Simulator with Trapped Ions
• Quantum trajectories and open many-body quantum systems
• Preparation of Entangled States by Quantum Markov Processes
• Topology by Dissipation in Atomic Quantum Wires
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Exceptional Points of Non-hermitian Operators
• Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Dissipative preparation of entanglement in optical cavities
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Controlling the dynamics of an open many-body quantum system with localized dissipation
• Exact nonequilibrium steady state of a strongly driven open XXZ chain
• Effective operator formalism for open quantum systems
• Theory of Non-Hermitian Fermionic Superfluidity with a Complex-Valued Interaction
• Simulation methods for open quantum many-body systems
• Variational Quantum Monte Carlo Method with a Neural-Network Ansatz for Open Quantum Systems
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Relaxation times of dissipative many-body quantum systems
• Exact Bethe ansatz spectrum of a tight-binding chain with dephasing noise
• Exact matrix product solution for the boundary-driven Lindblad $XXZ$-chain
• Exact solution for a diffusive nonequilibrium steady state of an open quantum chain
• A dissipative quantum Church-Turing theorem
• Exact Liouvillian Spectrum of a One-Dimensional Dissipative Hubbard Model
• A simple tensor network algorithm for two-dimensional steady states
• Scalable Dissipative Preparation of Many-Body Entanglement
• Dissipative spin chain as a non-Hermitian Kitaev ladder
• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• Exact Nonequilibrium Steady State of an Open Hubbard Chain
• Bistability vs. Metastability in Driven Dissipative Rydberg Gases
• Constructing Integrable Lindblad Superoperators
• Dissipation-induced d-Wave Pairing of Fermionic Atoms in an Optical Lattice
• Collective Excitations and Nonequilibrium Phase Transition in Dissipative Fermionic Superfluids
• Signatures of Liouvillian exceptional points in a quantum thermal machine
• Precisely timing dissipative quantum information processing
• Nonequilibrium perturbation theory in Liouville-Fock space for inelastic electron transport
• Enhancing correlation times for edge spins through dissipation
• Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices
• An exactly solvable BCS-Hubbard Model in arbitrary dimensions

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• Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
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