Real Time Evolution in Quantum Many-Body Systems With Unitary Perturbation Theory

Abstract

We develop a new analytical method for solving real time evolution problems of quantum many-body systems. Our approach is a direct generalization of the well-known canonical perturbation theory for classical systems. Similar to canonical perturbation theory, secular terms are avoided in a systematic expansion and one obtains stable long-time behavior. These general ideas are illustrated by applying them to the spin-boson model and studying its non-equilibrium spin dynamics.

Final version as accepted for publication in Phys. Rev. B (4 pages, 3 figures)

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• Finite size effects in global quantum quenches: examples from free bosons in an harmonic trap and the one-dimensional Bose-Hubbard model
• Non-perturbative stochastic method for driven spin-boson model
• Relaxation vs decoherence: Spin and current dynamics in the anisotropic Kondo model at finite bias and magnetic field
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• New theoretical approaches for correlated systems in nonequilibrium
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• Spatiotemporal buildup of the Kondo screening cloud
• Oscillatory dynamics and non-markovian memory in dissipative quantum systems
• Variational principle for quantum impurity systems in and out of equilibrium: application to Kondo problems
• Unitary perturbation theory approach to real-time evolution problems
• Nonequilibrium Spin Dynamics in the Ferromagnetic Kondo Model
• Non-Equilibrium Kondo Model with Voltage Bias in a Magnetic Field
• The quench dynamics of a dissipative quantum system: a renormalization group study
• Flow Equation Calculation of Transient and Steady State Currents in the Anderson Impurity Model
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
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• Unitary long-time evolution with quantum renormalization groups and artificial neural networks
• A perturbative renormalization group approach to driven quantum systems
• Scaling approach for the time-dependent Kondo model
• Dynamics of Disordered Quantum Systems Using Flow Equations
• Non-Equilibrium Scaling Analysis of the Kondo Model with Voltage Bias
• Non-equilibrium magnetization dynamics of ferromagnetically coupled Kondo spins
• Imaginary-time quantum many-body theory out of equilibrium I: Formal equivalence to Keldysh real-time theory and calculation of static properties
• Dynamical renormalization group approach to the spin-boson model
• Dynamics of a Qubit in a High-Impedance Transmission Line from a Bath Perspective
• Flow Equations for Disordered Floquet Systems
• Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
• Non-equilibrium dynamics of a system with Quantum Frustration
• The excitation operator approach to non-Markovian dynamics of quantum impurity models in the Kondo regime
• Flow equation approach to the linear response theory of superconductors
• Non-linear response to electric field in extended Hubbard models
• The excitation operator method in the spin dynamics of the one-dimensional XXZ model
• Entanglement Continuous Unitary Transformations
• Solving real time evolution problems by constructing excitation operators
• Prethermalization of density-density correlations after an interaction quench in the Hubbard model
• Systematic large flavor fTWA approach to interaction quenches in the Hubbard model