Pseudomode expansion of many-body correlation functions

Abstract

We present an expansion of a many-body correlation function in a sum of pseudomodes -- exponents with complex frequencies that encompass both decay and oscillations. The pseudomode expansion emerges in the framework of the Heisenberg version of the recursion method. This method essentially solves Heisenberg equations in a Lanczos tridiagonal basis constructed in the Krylov space of a given observable. To obtain pseudomodes, we first add artificial dissipation satisfying the dissipative generalization of the universal operator growth hypothesis, and then take the limit of the vanishing dissipation strength. Fast convergence of the pseudomode expansion is facilitated by the localization in the Krylov space, which is generic in the presence of dissipation and can survive the limit of the vanishing dissipation strength. As an illustration, we present pseudomode expansions of infinite-temperature autocorrelation functions in the quantum Ising and $XX$ spin-$1/2$ models on the square lattice. It turns out that it is enough to take a few first pseudomodes to obtain a good approximation to the correlation function.

References in corpus (37)

• A Universal Operator Growth Hypothesis
• Exact mapping between system-reservoir quantum models and semi-infinite discrete chains using orthogonal polynomials
• Quantum chaos and the complexity of spread of states
• Non-perturbative treatment of non-Markovian dynamics of open quantum systems
• Theory of Pseudomodes in Quantum Optical Processes
• Efficient simulation of finite-temperature open quantum systems
• Krylov Localization and suppression of complexity
• Operator growth and Krylov construction in dissipative open quantum systems
• Operator growth in open quantum systems: lessons from the dissipative SYK
• Quantum Dynamics in Krylov Space: Methods and Applications
• Krylov Complexity in Open Quantum Systems
• Spin transport of weakly disordered Heisenberg chain at infinite temperature
• Generalized theory of pseudomodes for exact descriptions of non-Markovian quantum processes
• Chaos and Complexity of quantum motion
• Dynamics of almost strong edge modes in spin chains away from integrability
• Lifetime of almost strong edge-mode operators in one dimensional, interacting, symmetry protected topological phases
• Operator growth in the transverse-field Ising spin chain with integrability-breaking longitudinal field
• Unified theory of local quantum many-body dynamics: Eigenoperator thermalization theorems
• Universal Long-time Behavior of Nuclear Spin Decays in a Solid
• On the long-time behavior of spin echo and its relation to free induction decay
• Long-time Behavior of Nuclear Spin Decays in Various Lattices
• Signatures of Chaos in Time Series Generated by Many-Spin Systems at High Temperatures
• Eigenmodes in the long-time behavior of a coupled spin system measured with nuclear magnetic resonance
• Long-Time Relaxation on Spin Lattice as Manifestation of Chaotic Dynamics
• Pseudomode approach and vibronic non-Markovian phenomena in light harvesting complexes
• Diffusion constants from the recursion method
• Momentum dependent quantum Ruelle-Pollicott resonances in translationally invariant many-body systems
• Quantum dynamics in one and two dimensions via recursion method
• Robustness of quantum chaos and anomalous relaxation in open quantum circuits
• Comparing numerical methods for hydrodynamics in a one-dimensional lattice spin model
• Exact dynamics of quantum dissipative $XX$ models: Wannier-Stark localization in the fragmented operator space
• Quantum many-body simulations with PauliStrings.jl
• Effective dissipation rate in a Liouvillian graph picture of high-temperature quantum hydrodynamics
• Estimation of equilibration time scales from nested fraction approximations
• Metallic transport of hard core bosons
• Stochastic Sampling of Operator Growth Dynamics
• A standard form of master equations for general non-Markovian jump processes: the Laplace-space embedding framework and asymptotic solution

Cited by in corpus (6)

• Quantum many-body simulations with PauliStrings.jl
• Ringdown in the SYK model
• Ruelle-Pollicott resonances of diffusive U(1)-invariant qubit circuits
• Subexponential decay of local correlations from diffusion-limited dephasing
• Resonant level model from a Krylov perspective: Lanczos coefficients in a quadratic model
• Krylov complexity and Wightman power spectrum with positive chemical potential in Schrödinger field theory