Driven-dissipative Ising Model: An exact field-theoretical analysis

Abstract

Driven-dissipative many-body systems are difficult to analyze analytically due to their non-equilibrium dynamics, dissipation and many-body interactions. In this paper, we consider a driven-dissipative infinite-range Ising model with local spontaneous emission, which naturally emerges from the open Dicke model in the large-detuning limit. Utilizing an adaptation of the Suzuki-Trotter quantum-to-classical mapping, we develop an exact field-theoretical analysis and a diagrammatic representation of the spin model that can be understood from a simple scattering picture. With this representation, we are able to analyze critical behavior, finite-size scaling and the effective temperature near the respective phase transition. Our formalism further allows a detailed study of the ordered phase where we find a "heating" region within which the effective temperature becomes negative, thereby exhibiting a truly non-equilibrium behavior. At the phase transition, we find two distinct critical behaviors with overdamped and underdamped critical dynamics at generic and weakly-dissipative critical points, respectively. We further show that the underdamped critical behavior is robust against short-range perturbations and is not an artifact of the mean-field nature of the model. To treat such perturbations, we extend our diagrammatic representation to include the coupling to spin waves due to the short-range interactions. The field-theoretical approach and the diagrammatics developed in this work should prove useful in applications to generic short-range driven-dissipative spin systems.

arXiv comment25 pages, 16 figures

References in corpus (56)

• Quantum Computing in the NISQ era and beyond
• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• An Open-System Quantum Simulator with Trapped Ions
• Keldysh Field Theory for Driven Open Quantum Systems
• Proposed realization of the Dicke-model quantum phase transition in an optical cavity QED system
• Exploring Symmetry Breaking at the Dicke Quantum Phase Transition
• Dynamical phase transition in the open Dicke model
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Entanglement and Tunable Spin-Spin Couplings Between Trapped Ions Using Multiple Transverse Modes
• Keldysh approach for non-equilibrium phase transitions in quantum optics: beyond the Dicke model in optical cavities
• Open quantum systems with local and collective incoherent processes: Efficient numerical simulation using permutational invariance
• Exploring dynamical phase transitions with cold atoms in an optical cavity
• Collective quantum jumps of Rydberg atoms
• Steady-state phases and tunneling-induced instabilities in the driven-dissipative Bose-Hubbard model
• Unconventional magnetism via optical pumping of interacting spin systems
• Nonequilibrium quantum criticality in open electronic systems
• Collective Dynamics of Bose--Einstein Condensates in Optical Cavities
• Nonequilibrium many-body steady states via Keldysh formalism
• Dissipative Phase Transition in the Open Quantum Rabi Model
• Suppressing and restoring the Dicke superradiance transition by dephasing and decay
• Dicke time crystals in driven-dissipative quantum many-body systems
• On the critical exponent of a quantum noise driven phase transition: the open system Dicke-model
• Emergent equilibrium in many-body optical bistability
• Verification of a many-ion simulator of the Dicke model through slow quenches across a phase transition
• Quantum critical regime in a quadratically-driven nonlinear photonic lattice
• Driven Markovian Quantum Criticality
• Critical slowing down in driven-dissipative Bose-Hubbard lattices
• Infinite-range Ising ferromagnet in a time-dependent transverse field: quench and ac dynamics near the quantum critical point
• Limit cycle phase in driven-dissipative spin systems
• Impact of non-equilibrium fluctuations on pre-thermal dynamical phase transitions in long-range interacting spin chains
• Time-dependent generalized Gibbs ensembles in open quantum systems
• Atom-only descriptions of the driven-dissipative Dicke model
• Prethermalization Revealed by the Relaxation Dynamics of Full Distribution Functions
• Chaotic dynamical ferromagnetic phase induced by non-equilibrium quantum fluctuations
• Absence of Long-Range Coherence in the Parametric Emission from Photonic Wires
• Multicritical behavior in dissipative Ising models
• Pumping approximately integrable systems
• Collective phases of strongly interacting cavity photons
• Phase diagram of the dissipative quantum Ising model on a square lattice
• A solvable family of driven-dissipative many-body systems
• Perturbative approach to weakly driven many-particle systems in the presence of approximate conservation laws
• Generalised Dicke non-equilibrium dynamics in trapped ions
• Superradiant to subradiant phase transition in the open system Dicke model: Dark state cascades
• Dicke phase transition without total spin conservation
• Non-equilibrium fixed points of coupled Ising models
• Light-shift-induced quantum phase transitions of a Bose-Einstein condensate in the optical cavities
• Many-Body Quantum Optics with Decaying Atomic Spin States: ($\gamma$, $\kappa$) Dicke model
• Quantum correlations and limit cycles in the driven-dissipative Heisenberg lattice
• Thermalization in open many-body systems based on eigenstate thermalization hypothesis
• Non-equilibrium criticality in quench dynamics of infinite-range spin models
• Fermionic formalism for driven-dissipative multi-level systems
• Fluorescence spectrum and thermalization in a driven coupled cavity array
• Finite-size scaling in the quantum phase transition of the open-system Dicke-model
• On the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model
• Thermalization of a Lipkin-Meshkov-Glick model coupled to a bosonic bath
• Flight of a heavy particle nonlinearly coupled to a quantum bath

Cited by in corpus (15)

• Dissipative time crystals with long-range Lindbladians
• Universality class of Ising critical states with long-range losses
• Quantum criticality using a superconducting quantum processor
• Quantum fluctuations and correlations in open quantum Dicke models
• Exact solution of the infinite-range dissipative transverse-field Ising model
• Measurement-induced phase transitions in monitored infinite-range interacting systems
• Feedback-stabilized dynamical steady states in the Bose-Hubbard model
• Theory of magnon-polaritons in quantum Ising materials
• Spin-boson model under dephasing: Markovian vs Non-Markovian dynamics
• Time-reversal symmetry breaking and emergence in driven-dissipative Ising models
• Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems
• Singular transport in non-equilibrium strongly internal-coupled 1D tilted field spin-1/2 chain
• Accelerating the approach of dissipative quantum spin systems towards stationarity through global spin rotations
• Critical Dynamics and Cyclic Memory Retrieval in Non-reciprocal Hopfield Networks
• Generalized stochastic spin-wave theory for open quantum spin systems