Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators

• URL: http://arxiv.org/abs/2401.04880v2
• Date: Tue, 2 Apr 2024 14:36:46 GMT
• Title: Real-time Impurity Solver Using Grassmann Time-Evolving Matrix Product Operators
• Authors: Ruofan Chen, Xiansong Xu, Chu Guo,
• Abstract summary: We present an approach to calculate the equilibrium impurity spectral function based on the recently proposed Grassmann time-evolving matrix product operators method. The accuracy of this method is demonstrated in the single-orbital Anderson impurity model and benchmarked against the continuous-time quantum Monte Carlo method.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: An emergent and promising tensor-network-based impurity solver is to represent the path integral as a matrix product state, where the bath is analytically integrated out using Feynman-Vernon influence functional. Here we present an approach to calculate the equilibrium impurity spectral function based on the recently proposed Grassmann time-evolving matrix product operators method. The central idea is to perform a quench from a separable impurity-bath initial state as in the non-equilibrium scenario. The retarded Green's function $G(t+t_0, t'+t_0)$ is then calculated after an equilibration time $t_0$ such that the impurity and bath are approximately in thermal equilibrium. There are two major advantages of this method. First, since we focus on real-time dynamics, we do not need to perform the numerically ill-posed analytic continuation in the continuous-time quantum Monte Carlo case that relies on imaginary-time evolution. Second, the entanglement growth of the matrix product states in real-time calculations is observed to be much slower than that in imaginary-time calculations, leading to a significant improvement in numerical efficiency. The accuracy of this method is demonstrated in the single-orbital Anderson impurity model and benchmarked against the continuous-time quantum Monte Carlo method.

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