Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model

Abstract

We investigate the application of matrix product state (MPS) representations of the influence functionals (IF) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff-Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

References in corpus (34)

• A bound on chaos
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• The iTEBD algorithm beyond unitary evolution
• Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
• A Universal Operator Growth Hypothesis
• Non-Markovian quantum processes: complete framework and efficient characterisation
• Minimally Entangled Typical Thermal State Algorithms
• Minimally entangled typical quantum states at finite temperature
• Universal Lindblad equation for open quantum systems
• Microscopic model of quantum butterfly effect: out-of-time-order correlators and traveling combustion waves
• Matrix Product States for dynamical simulation of infinite chains
• Exploiting the causal tensor network structure of quantum processes to efficiently simulate non-Markovian path integrals
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Influence matrix approach to many-body Floquet dynamics
• How to discretize a quantum bath for real-time evolution
• Exact dynamics of non-additive environments in non-Markovian open quantum systems
• Precise extrapolation of the correlation function asymptotics in uniform tensor network states with application to the Bose-Hubbard and XXZ models
• Transfer Matrices and Excitations with Matrix Product States
• Computing vibrational eigenstates with tree tensor network states (TTNS)
• A scaling hypothesis for matrix product states
• Real time evolution of Anderson impurity models via tensor network influence functionals
• Non-equilibrium quantum impurity problems via matrix-product states in the temporal domain
• Constructing Tensor Network Influence Functionals for General Quantum Dynamics
• Light Cone Matrix Product
• Open Quantum System Dynamics from Infinite Tensor Network Contraction
• Sublinear scaling in non-Markovian open quantum systems simulations
• Quantum bounds and fluctuation-dissipation relations
• Symmetric minimally entangled typical thermal states for canonical and grand-canonical ensembles
• Tangent space formulation of the Multi-Configuration Time-Dependent Hartree equations of motion: The projector-splitting algorithm revisited
• Tensor network influence functionals in the continuous-time limit: connections to quantum embedding, bath discretization, and higher-order time propagation
• Fast Time-Evolution of Matrix-Product States using the QR decomposition
• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
• Quantum correlation functions through tensor network path integral

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• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Sixth-order time-convolutionless master equation and beyond: Late-time resummations, two types of divergences, and the limits of validity
• Schwinger-Keldysh non-perturbative field theory of open quantum systems beyond the Markovian regime: Application to spin-boson and spin-chain-boson models
• Verifying Quantum Memory in the Dynamics of Spin Boson Models
• Uniform process tensor approach for the calculation of multi-time correlation functions of non-Markovian open systems
• Beyond mean-field dynamics of the Dicke model with non-Markovian dephasing
• Statistics-encoded tensor network approach in disordered quantum many-body spin chains