Efficient mapping for Anderson impurity problems with matrix product states

Abstract

We propose an efficient algorithm to numerically solve Anderson impurity problems using matrix product states. By introducing a modified chain mapping we obtain significantly lower entanglement, as compared to all previous attempts, while keeping the short-range nature of the couplings. Our approach naturally extends to finite temperatures, with applications to dynamical mean field theory, non-equilibrium dynamics and quantum transport.

(6+8) pages, (4+9) figures

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• Tree tensor-network real-time multiorbital impurity solver: Spin-orbit coupling and correlation functions in Sr${}_2$RuO${}_4$
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• MPSDynamics.jl: Tensor network simulations for finite-temperature (non-Markovian) open quantum system dynamics
• Grassmann Time-Evolving Matrix Product Operators for Equilibrium Quantum Impurity Problems
• Disentangling Interacting Systems with Fermionic Gaussian Circuits: Application to Quantum Impurity Models
• Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
• Solving quantum impurity problems on the L-shaped Kadanoff-Baym contour
• Infinite Grassmann Time-Evolving Matrix Product Operator Method in the Steady State
• Efficient construction of the Feynman-Vernon influence functional as matrix product states
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
• Spectral Density Modulation and Universal Markovian Closure of Fermionic Environments
• Making Quantum Collision Models Exact
• Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems
• Infinite Grassmann time-evolving matrix product operators for quantum impurity problems after a quench
• Kondo nanomechanical dissipation in the driven Anderson impurity model
• Scalable tensor network algorithm for quantum impurity problems
• Matrix product state simulations of quantum quenches and transport in Coulomb blockaded superconducting devices
• Natural orbital impurity solver for real-frequency properties at finite temperature
• Tree tensor network impurity solver based on Cayley-tree mapping
• Exact description of fermionic reservoirs via purified damped ancillary fermions