Linked cluster expansions for open quantum systems on a lattice

Abstract

We propose a generalization of the linked-cluster expansions to study driven-dissipative quantum lattice models, directly accessing the thermodynamic limit of the system. Our method leads to the evaluation of the desired extensive property onto small connected clusters of a given size and topology. We first test this approach on the isotropic spin-1/2 Hamiltonian in two dimensions, where each spin is coupled to an independent environment that induces incoherent spin flips. Then we apply it to the study of an anisotropic model displaying a dissipative phase transition from a magnetically ordered to a disordered phase. By means of a Padé analysis on the series expansions for the average magnetization, we provide a viable route to locate the phase transition and to extrapolate the critical exponent for the magnetic susceptibility.

10 pages, 5 figures

References in corpus (67)

• The Dicke Quantum Phase Transition with a Superfluid Gas in an Optical Cavity
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Nonequilibrium dynamical mean-field theory and its applications
• Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm
• Keldysh Field Theory for Driven Open Quantum Systems
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• Symmetries and conserved quantities in Lindblad master equations
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Dynamical Critical Phenomena in Driven-Dissipative Systems
• Quantum many-body dynamics in optomechanical arrays
• Quantum simulations and many-body physics with light
• Fermionized photons in an array of driven dissipative nonlinear cavities
• Matrix product simulations of non-equilibrium steady states of quantum spin chains
• Quantum Simulation with Interacting Photons
• Antiferromagnetic phase transition in a nonequilibrium lattice of Rydberg atoms
• Fractional quantum Hall states of photons in an array of dissipative coupled cavities
• Variational Matrix Product Operators for the Steady State of Dissipative Quantum Systems
• Unconventional magnetism via optical pumping of interacting spin systems
• Variational principle for steady states of dissipative quantum many-body systems
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• A positive tensor network approach for simulating open quantum many-body systems
• Photon solid phases in driven arrays of nonlinearly coupled cavities
• Numerical Linked-Cluster Approach to Quantum Lattice Models
• Nonequilibrium many-body steady states via Keldysh formalism
• Emergent equilibrium in many-body optical bistability
• Polariton crystallization in driven arrays of lossy nonlinear resonators
• A simple tensor network algorithm for two-dimensional steady states
• A Matrix-Product-Operator Approach to the Nonequilibrium Steady State of Driven-Dissipative Quantum Arrays
• Many-body phenomena in QED-cavity arrays
• Nonequilibrium Steady State of Photoexcited Correlated Electrons in the Presence of Dissipation
• Driven Markovian Quantum Criticality
• Quantum Quenches in the Thermodynamic Limit
• Signatures of the super fluid-insulator phase transition in laser driven dissipative nonlinear cavity arrays
• A Short Introduction to Numerical Linked-Cluster Expansions
• Numerical Linked-Cluster Algorithms. I. Spin systems on square, triangular, and kagome lattices
• Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
• Corner space renormalization method for driven-dissipative 2D correlated systems
• Limit cycle phase in driven-dissipative spin systems
• Perturbative approach to Markovian open quantum systems
• Dynamics and universality in noise driven dissipative systems
• Antiferromagnetic long-range order in dissipative Rydberg lattices
• Critical behavior of dissipative two-dimensional spin lattices
• Spontaneous symmetry breaking in a quadratically-driven nonlinear photonic lattice
• Phase diagram of incoherently driven strongly correlated photonic lattices
• Non-equilibrium dynamics of the driven Hubbard model
• Collective phases of strongly interacting cavity photons
• Stabilizing strongly correlated photon fluids with non-Markovian reservoirs
• Incompressible polaritons in a flat band
• Numerical Linked-Cluster Algorithms. II. t-J models on the square lattice
• Steady-state phase diagram of a driven QED-cavity array with cross-Kerr nonlinearities
• Non-equilibrium many-body effects in driven nonlinear resonator arrays
• Photon transport in a dissipative chain of nonlinear cavities
• Self-Consistent Projection Operator Theory for Quantum Many-Body Systems
• Repulsively induced photon super-bunching in driven resonator arrays
• Resummation for Nonequilibrium Perturbation Theory and Application to Open Quantum Lattices
• Spontaneous, collective coherence in driven, dissipative cavity arrays
• Matrix product state techniques for two-dimensional systems at finite temperature
• Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice
• Few-photon transport in many-body photonic systems: A scattering approach
• Numerical linked cluster expansions for quantum quenches in one dimensional lattices
• Truncated correlation hierarchy schemes for driven-dissipative multimode quantum systems
• Nonequilibrium photonic transport and phase transition in an array of optical cavities
• Photonic currents in driven and dissipative resonator lattices
• Cavity-loss induced plateau in coupled cavity QED array
• Emergent transport in a many-body open system driven by interacting quantum baths

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• Spectral theory of Liouvillians for dissipative phase transitions
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• Simulation methods for open quantum many-body systems
• Variational neural network ansatz for steady states in open quantum systems
• Coherent and dissipative dynamics at quantum phase transitions
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation
• Symmetries and conserved quantities of boundary time crystals in generalized spin models
• Universality in driven open quantum matter
• Phase diagram of the dissipative quantum Ising model on a square lattice
• Mean-field validity in a dissipative critical system: Liouvillian gap, $\mathbb{PT}$-symmetric antigap, and permutational symmetry in the $XYZ$ model
• Quantum Quenches and Relaxation Dynamics in the Thermodynamic Limit
• Combining Dynamical Quantum Typicality and Numerical Linked Cluster Expansions
• Dynamical properties of dissipative XYZ Heisenberg lattices
• Entanglement-Optimal Trajectories of Many-Body Quantum Markov Processes
• Phenomenology of a First Order Dark State Phase Transition
• Dissipative phase transitions in the fully-connected Ising model with $p$-spin interaction
• Many-Body Open Quantum Systems
• Gutzwiller Monte Carlo approach for a critical dissipative spin model
• Quantum and classical correlations in open quantum-spin lattices via truncated-cumulant trajectories
• Optimal stochastic unraveling of disordered open quantum systems: application to driven-dissipative photonic lattices
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Synchronization of persistent oscillations in spin systems with non-local dissipations
• Numerical linked cluster expansions for inhomogeneous systems
• Dissipative dynamics in open XXZ Richardson-Gaudin models
• A quantum algorithm for the direct estimation of the steady state of open quantum systems
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits
• Lanczos Boosted Numerical Linked-Cluster Expansion for Quantum Lattice Models
• Nonuniform phases in the geometrically frustrated dissipative XYZ model
• Emergent light crystal from frustration and pump engineering
• Time- and frequency-domain two-particle correlations of a driven dissipative Bose-Hubbard model
• Steady states of a driven dissipative dipolar XXZ chain
• Steady-state susceptibility in continuous phase transitions of dissipative systems
• Many-body localization and delocalization dynamics in the thermodynamic limit
• Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems
• Dissipative quantum phase transitions monitored by current fluctuations
• Dynamics of two-dimensional open quantum lattice models with tensor networks
• Exact Model Reduction for Continuous-Time Open Quantum Dynamics
• Yang-Lee Zeros of 2D Nearest-Neighbor Antiferromagnetic Ising Models: A Numerical Linked Cluster Expansion Study
• Fully differentiable optimization protocols for non-equilibrium steady states
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach
• Quantum phase transition of light in the dissipative Rabi-Hubbard lattice: A dressed-master-equation perspective