Hybridization expansion Monte Carlo simulation of multi-orbital quantum impurity problems: matrix product formalism and improved Monte Carlo sampling

摘要

We explore two complementary modifications of the hybridization-expansioncontinuous-time Monte Carlo method, aiming at large multi-orbital quantumimpurity problems. One idea is to compute the imaginary-time propagation usinga matrix product states representation. We show that bond dimensionsconsiderably smaller than the dimension of the Hilbert space are sufficient toobtain accurate results, and that this approach scales polynomially, ratherthan exponentially with the number of orbitals. Based on scaling analyses, weconclude that a matrix product state implementation will outperform theexact-diagonalization based method for quantum impurity problems with more than12 orbitals. The second idea is an improved Monte Carlo sampling scheme whichis applicable to all variants of the hybridization expansion method. We showthat this so-called sliding window sampling scheme speeds up the simulation byat least an order of magnitude for a broad range of model parameters, with thelargest improvements at low temperature.