Lindbladian dissipation of strongly-correlated quantum matter

Abstract

We propose the Sachdev-Ye-Kitaev Lindbladian as a paradigmatic solvable model of dissipative many-body quantum chaos. It describes $N$ strongly coupled Majorana fermions with random all-to-all interactions, with unitary evolution given by a quartic Hamiltonian and the coupling to the environment described by $M$ quadratic jump operators, rendering the full Lindbladian quartic in the Majorana operators. Analytical progress is possible by developing a dynamical mean-field theory for the Liouvillian time evolution on the Keldysh contour. By disorder-averaging the interactions, we derive an (exact) effective action for two collective fields (Green's function and self-energy). In the large-$N$, large-$M$ limit, we obtain the saddle-point equations satisfied by the collective fields, which determine the typical timescales of the dissipative evolution, particularly, the spectral gap that rules the relaxation of the system to its steady state. We solve the saddle-point equations numerically and find that, for strong or intermediate dissipation, the system relaxes exponentially, with a spectral gap that can be computed analytically, while for weak dissipation, there are oscillatory corrections to the exponential relaxation. In this letter, we illustrate the feasibility of analytical calculations in strongly correlated dissipative quantum matter.

8+21 pages, 3+4 figures. v2: two new appendices in the Supplemental Material, as published

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Cited by in corpus (43)

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• Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond
• Operator dynamics in Lindbladian SYK: a Krylov complexity perspective
• Lindbladian dynamics of the Sachdev-Ye-Kitaev model
• Field Theory of Many-Body Lindbladian Dynamics
• Non-Hermitian skin effect in one-dimensional interacting Bose gas
• Dynamical quantum phase transitions in SYK Lindbladians
• Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
• Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Many-Body Open Quantum Systems
• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
• Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
• Operator growth and spread complexity in open quantum systems
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• The operator growth hypothesis in open quantum systems
• Field theory of non-Hermitian disordered systems
• Probing quantum chaos in multipartite systems
• Spectral and steady-state properties of fermionic random quadratic Liouvillians
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• An exactly solvable dissipative spin liquid
• Universal Properties of the Spectral Form Factor in Open Quantum Systems
• Strong-to-weak Symmetry Breaking and Entanglement Transitions
• Replica Symmetry Breaking for the Integrable Two-Site Sachdev-Ye-Kitaev Model
• Theory of Irreversibility in Quantum Many-Body Systems
• Universal hard-edge statistics of non-Hermitian random matrices
• Operator size growth in Lindbladian SYK
• Localization of Lindbladian Fermions
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Fate of dissipative hierarchy of timescales in the presence of unitary dynamics
• Exactly solvable dissipative dynamics and one-form strong-to-weak spontaneous symmetry breaking in interacting two-dimensional spin systems
• Symmetry classification correspondence between quadratic Lindbladians and their steady states
• Complexity of Quadratic Quantum Chaos
• Dynamics of Loschmidt echoes from operator growth in noisy quantum many-body systems
• Open-system dynamics in local Lindbladians with chaotic spectra
• Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
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• Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$