Grassmann Time-Evolving Matrix Product Operators for Quantum Impurity Models

Abstract

The time-evolving matrix product operators (TEMPO) method, which makes full use of the Feynman-Vernon influence functional, is the state-of-the-art tensor network method for bosonic impurity problems. However, for fermionic impurity problems the Grassmann path integral prohibits application of this method. We develop Grassmann time-evolving matrix product operators, a full fermionic analog of TEMPO, that can directly manipulates Grassmann path integrals with similar numerical cost as the bosonic counterpart. We further propose a zipup algorithm to compute expectation values on the fly without explicitly building a single large augmented density tensor, which boosts our efficiency on top of the vanilla TEMPO. Our method has a favorable complexity scaling over existing tensor network methods, and we demonstrate its performance on the non-equilibrium dynamics of the single impurity Anderson models. Our method solves the long standing problem of turning Grassmann path integrals into efficient numerical algorithms, which could significantly change the application landscape of tensor network based impurity solvers, and could also be applied for broader problems in open quantum physics and condensed matter physics.

4 pages, 3 figures

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• Steady-state dynamical mean field theory based on influence functional matrix product states
• Semi-group influence matrices for non-equilibrium quantum impurity models
• Simulating quantum dynamics in two-dimensional lattices with tensor network influence functional belief propagation
• Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations
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• Third-order strong-coupling impurity solver for real-frequency DMFT: Accurate spectral functions for antiferromagnetic and photo-doped states
• Verifying Quantum Memory in the Dynamics of Spin Boson Models
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• Summing Real Time Feynman Paths of Lattice Polaron with Matrix Product States
• Improved Memory Truncation Scheme for Quasi-Adiabatic Propagator Path Integral via Influence Functional Renormalization
• Uniform process tensor approach for the calculation of multi-time correlation functions of non-Markovian open systems