Infinite Grassmann time-evolving matrix product operator method for zero-temperature equilibrium quantum impurity problems

Abstract

The Grassmann time-evolving matrix product operator (GTEMPO) method has proven to be an accurate and efficient numerical method for the real-time dynamics of quantum impurity problems. Whereas its application for imaginary-time calculations is much less competitive compared to well-established methods such as the continuous-time quantum Monte Carlo (CTQMC). In this work, we unleash the full power of GTEMPO for zero-temperature imaginary-time calculations: the multi-time impurity state is time-translationally invariant with infinite boundary condition, therefore it can be represented as an infinite Grassmann matrix product state (GMPS) with nontrivial unit cell in a single time step, instead of an open boundary GMPS spanning the whole imaginary-time axis. We devise a very efficient infinite GTEMPO algorithm targeted at zero-temperature equilibrium quantum impurity problems, which is known to be a hard regime for quantum Monte Carlo methods. To demonstrate the performance of our method, we benchmark it against exact solutions in the noninteracting limit, and against CTQMC calculations in the Anderson impurity models with up to two orbitals, where we show that the required bond dimension of the infinite GMPS is much smaller than its finite-temperature counterpart.