Efficient flow equations for dissipative systems

Abstract

Open quantum systems provide an essential theoretical basis for the development of novel quantum technologies, since any real quantum system inevitably interacts with its environment. Lindblad master equations capture the effect of Markovian environments. Closed quantum systems can be treated using flow equations with the particle conserving generator. We generalize this generator to non-Hermitian matrices and open quantum systems governed by Lindbladians, comparing our results with recently proposed generators by Rosso et al. (arXiv:2007.12044). In comparison, we find that our advocated generator provides an efficient flow with good accuracy in spite of truncations.

arXiv comment35 pages plus appendices, 15 figures, comments welcome, Submission to SciPost; added references, added explanations regarding transformations of observables and definitions of $Q$, $H^{+}$ and $H^{-}$, added App. C and App. D containing analytical arguments

References in corpus (53)

• Quantum fluids of light
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• An Open-System Quantum Simulator with Trapped Ions
• Quantum trajectories and open many-body quantum systems
• A short introduction to the Lindblad Master Equation
• Interaction Quench in the Hubbard model
• Strong dissipation inhibits losses and induces correlations in cold molecular gases
• Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain
• Cluster mean-field approach to the steady-state phase diagram of dissipative spin systems
• Dispersion and Symmetry of Bound States in the Shastry-Sutherland Model
• Scaling and Decoherence in the Out-of-Equilibrium Kondo Model
• A numerical canonical transformation approach to quantum many body problems
• Super-fermion representation of the Lindblad master equation for the electron transport problem
• Excitations in one-dimensional S=1/2 quantum antiferromagnets
• The Structure of Operators in Effective Particle-Conserving Models
• Universal spectra of random Lindblad operators
• On the spin--boson model with a sub--Ohmic bath
• Time Evolution of Many-Body Localized Systems with the Flow Equation Approach
• Fixed points of Wegner-Wilson flows and many-body localization
• Multistability of Driven-Dissipative Quantum Spins
• Flow equations for band--matrices
• Hierarchy of relaxation timescales in local random Liouvillians
• Accurate effective Hamiltonians via unitary flow in Floquet space
• Flow Equations for Electron-Phonon Interactions
• Roton minimum as fingerprint of magnon-Higgs scattering in ordered quantum antiferromagnets
• Low temperature equilibrium correlation functions in dissipative quantum systems
• Mutually attracting spin waves in the square-lattice quantum antiferromagnet
• A flow equation approach to periodically driven quantum systems
• Flow equation solution for the weak to strong-coupling crossover in the sine-Gordon model
• Systematic Mapping of the Hubbard Model to the Generalized t-J Model
• Flow towards diagonalization for Many-Body-Localization models : adaptation of the Toda matrix differential flow to random quantum spin chains
• Enhanced Perturbative Continuous Unitary Transformations
• Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime
• Diagonalization of system plus environment Hamiltonians
• Exploring many-body localization in quantum systems coupled to an environment via Wegner-Wilson flows
• Similarity renormalization of the electron--phonon coupling
• Flow equation approach to the sine-Gordon model
• The Quartic Oscillator: a Non-Perturbative Study by Continuous Unitary Transformations
• Flow equations for the Anderson Hamiltonian
• Calculating critical temperatures of superconductivity from a renormalized Hamiltonian
• Equilibrium Correlation Functions of the Spin-Boson Model with Sub-Ohmic Bath
• High-order series expansion of non-Hermitian quantum spin models
• Three-body bound states in antiferromagnetic spin ladders
• Dissipative flow equations
• Non-trivial topology of the quasi-one-dimensional triplons in the quantum antiferromagnet ${\text{BiCu}}_2{\text{PO}}_6$
• Multi-Particle Spectral Properties in the Transverse Field Ising Model by Continuous Unitary Transformations
• Flow Equations for Disordered Floquet Systems
• Singlet exciton condensation and bond-order-wave phase in the extended Hubbard model
• Time-dependent correlations in quantum magnets at finite temperature
• Topological study of a Bogoliubov-de Gennes system of pseudo spin-$1/2$ bosons with conserved magnetization in a honeycomb lattice
• Massive spinons in $S=1/2$ spin chains: spinon-pair operator representation

Cited by in corpus (7)

• Many-Body Open Quantum Systems
• Periodically Driven Open Quantum Systems: Spectral Properties and Non-Equilibrium Steady States
• Series expansions in closed and open quantum many-body systems with multiple quasiparticle types
• Low-energy spin excitations in field-induced phases of the spin-ladder antiferromagnet BiCu${}_2$PO${}_6$
• Collective modes in superconductors including Coulomb repulsion
• The exact solution of the Wegner flow equation with the Mielke generator for $3\times 3$ Hermitian matrices
• A method to derive material-specific spin-bath model descriptions of materials displaying prevalent spin physics