Constructing Integrable Lindblad Superoperators

Abstract

We develop a new method for the construction of one-dimensional integrable Lindblad systems, which describe quantum many body models in contact with a Markovian environment. We find several new models with interesting features, such as annihilation-diffusion processes, a mixture of coherent and classical particle propagation, and a rectified steady state current. We also find new ways to represent known classical integrable stochastic equations by integrable Lindblad operators. Our method can be extended to various other situations and it establishes a structured approach to the study of solvable open quantum systems.

arXiv comment11 pages

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• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Unbounded entanglement production via a dissipative impurity
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• Hydrodynamics of quantum entropies in Ising chains with linear dissipation
• Phantom Bethe excitations and spin helix eigenstates in integrable periodic and open spin chains
• Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit
• Many-Body Open Quantum Systems
• The fate of high winding number topological phases in the disordered extended Su-Schrieffer-Heeger model
• Introduction to classical and quantum integrability
• Liouvillian Dynamics of the Open Schwinger Model: String Breaking and Kinetic Dissipation in a Thermal Medium
• Conserved charges in the quantum simulation of integrable spin chains
• Can the Macroscopic Fluctuation Theory be Quantized?
• Quantum many-body scars in spin models with multibody interactions
• Engineering generalized Gibbs ensembles with trapped ions
• Chiral coordinate Bethe ansatz for phantom eigenstates in the open XXZ spin-$\frac{1}{2}$ chain
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space
• Integrable nonunitary quantum circuits
• Criteria for Davies Irreducibility of Markovian Quantum Dynamics
• Dissipative dynamics in open XXZ Richardson-Gaudin models
• The Floquet Baxterisation
• Liouvillian skin effects and fragmented condensates in an integrable dissipative Bose-Hubbard model
• An exactly solvable dissipative spin liquid
• Solvable BCS-Hubbard Liouvillians in arbitrary dimensions
• Free fermions beyond Jordan and Wigner
• Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
• Steady helix states in a resonant XXZ Heisenberg model with Dzyaloshinskii-Moriya interaction
• Traffic models and traffic-jam transition in quantum ($N$+1)-level systems
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• Integrable spin chains and cellular automata with medium range interaction
• Superdiffusive magnetization transport in the XX spin chain with non-local dephasing
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• Integrability of open boundary driven quantum circuits
• Jordan blocks and the Bethe ansatz I: The eclectic spin chain as a limit
• Free fermions with dephasing and boundary driving: Bethe Ansatz results
• Understanding Traffic Jams Using Lindblad Superoperators
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• Exact density profile in a tight-binding chain with dephasing noise
• Information Flow in Non-Unitary Quantum Cellular Automata
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• Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
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• Majorana fermions solve the tetrahedron equations as well as higher simplex equations
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