Solvable Markovian dynamics of lattice quantum spin models

Abstract

We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of quantum spin models exactly in arbitrary dimensions, which is illustrated explicitly with two examples of driven-dissipative systems. We investigate their respective nonequilibrium steady states as well as the full real-time evolution on unprecedented system sizes. Characteristic time scales are derived analytically, which allows us to understand the nontrivial finite-size scaling of the dissipative gap. The corresponding scaling exponents are confirmed by solving numerically for the full real-time evolution of two-point correlation functions.

6 pages, 2 figures; version accepted for publication in PRA

References in corpus (16)

• The density-matrix renormalization group in the age of matrix product states
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Real time evolution using the density matrix renormalization group
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• An Open-System Quantum Simulator with Trapped Ions
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms
• Variational principle for steady states of dissipative quantum many-body systems
• Characterization of dynamical phase transitions in quantum jump trajectories beyond the properties of the stationary state
• A solvable family of driven-dissipative many-body systems
• Noise-driven quantum criticality
• Tailored jump operators for purely dissipative quantum magnetism
• Vortex formation and dynamics in two-dimensional driven-dissipative condensates
• A Monte Carlo Time-Dependent Variational Principle
• Dissipative Preparation of Entangled Many-Body States with Rydberg Atoms

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• Exact density profile in a tight-binding chain with dephasing noise
• Exact solution of a quantum asymmetric exclusion process with particle creation and annihilation
• Complexity of Quantum Trajectories
• Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies