Criticality and Phase Classification for Quadratic Open Quantum Many-Body Systems

Abstract

We study the steady states of translation-invariant open quantum many-body systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasifree and quadratic, respectively. We find that steady states of one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green's functions. For the quasifree case without quadratic Lindblad operators, we show that fermionic systems with finite-range interactions are noncritical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasifree bosonic systems can be critical in $D>1$ dimensions. Last, we address the question of phase transitions in quadratic systems and find that, without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase.

arXiv comment13 pages, 2 figures; minor improvements and additional references; published version. The employed methods for the solution of quasi-free and quadratic open systems are described in arXiv:2112.08344

References in corpus (49)

• Many-Body Physics with Ultracold Gases
• Probing many-body dynamics on a 51-atom quantum simulator
• Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles
• Fast quantum gates for neutral atoms
• Simulated Quantum Computation of Molecular Energies
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Continuous Quantum Phase Transitions
• Experimental One-Way Quantum Computing
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• An Open-System Quantum Simulator with Trapped Ions
• Strongly Interacting Polaritons in Coupled Arrays of Cavities
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Open Quantum Systems. An Introduction
• A Rydberg Quantum Simulator
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Classifying quantum phases using Matrix Product States and PEPS
• Preparation of Entangled States by Quantum Markov Processes
• Quantum phase transitions
• Photon blockade induced Mott transitions and XY spin models in coupled cavity arrays
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• Third quantization: a general method to solve master equations for quadratic open Fermi systems
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Spectral theory of Liouvillians for dissipative phase transitions
• Dissipative Phase Transition in Central Spin Systems
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Dividing Quantum Channels
• Topology by dissipation
• Alkaline earth atoms in optical tweezers
• Quantum Simulation with Interacting Photons
• Microscopic control and detection of ultracold strontium in optical-tweezer arrays
• Steady-state phases and tunneling-induced instabilities in the driven-dissipative Bose-Hubbard model
• Nonequilibrium quantum criticality in open electronic systems
• Spectral theorem for the Lindblad equation for quadratic open fermionic systems
• Preparation of entangled and antiferromagnetic states by dissipative Rydberg pumping
• Dissipative Dynamics and Phase Transitions in Fermionic Systems
• Dark Entangled Steady States of Interacting Rydberg Atoms
• Quantum critical regime in a quadratically-driven nonlinear photonic lattice
• Dissipative preparation of Chern insulators
• Stabilizing a Bell state of two superconducting qubits by dissipation engineering
• Reservoir engineering and dynamical phase transitions in optomechanical arrays
• Quasi-locality and efficient simulation of Markovian quantum dynamics
• Bose-Hubbard Model: Relation Between Driven-Dissipative Steady-States and Equilibrium Quantum Phases
• Photon condensation in circuit QED by engineered dissipation
• Spontaneous symmetry breaking in a quadratically-driven nonlinear photonic lattice
• Collective phases of strongly interacting cavity photons
• Non-equilibrium fixed points of coupled Ising models
• Gaussian trajectory approach to dissipative phase transitions: the case of quadratically driven photonic lattices
• Super-operator structures and no-go theorems for dissipative quantum phase transitions

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