Two-particle calculations with quantics tensor trains - solving the parquet equations

Abstract

Two-particle vertex functions require huge amounts of mem- ory when stored using conventional discretization grids. The quantics tensor train (QTT) representation, based on length/time scale separation, leads to significant dimensional reduction of two-particle quantities, removing memory bot- tlenecks. The computational cost of solving diagrammatic equations (Bethe–Salpeter equation, parquet equation and Schwinger–Dyson equation) becomes logarithmic in grid size and depends strongly only on the maximum bond dimension, which is small enough so that the overall computational cost is significantly reduced. I will present the results of the applica- tion of quantics tensor trains (QTTs) and tensor cross interpo- lation (TCI) to the solution of a full set of parquet equations for Hubbard atom, and for the single impurity Anderson model. I will show that the steps needed to evaluate the equations can be decomposed into basic operations on the QTCI compressed objects and that the iterative scheme converges even for nu- merically demanding parameters.