Density matrix renormalization group on a cylinder in mixed real and momentum space

TL;DR

This paper introduces a mixed real and momentum space DMRG method for 2D cylinders, significantly improving computational efficiency and memory usage by exploiting momentum conservation.

Contribution

The authors develop a novel DMRG variant that combines real and momentum space representations, enabling faster and more memory-efficient simulations of 2D systems.

Findings

Over 20-fold reduction in computation time

Sixfold reduction in memory usage

Effective application to the fermionic Hofstadter model

Abstract

We develop a variant of the density matrix renormalization group (DMRG) algorithm for two-dimensional cylinders that uses a real space representation along the cylinder and a momentum space representation in the perpendicular direction. The mixed representation allows us to use the momentum around the circumference as a conserved quantity in the DMRG algorithm. Compared with the traditional purely real-space approach, we find a significant speedup in computation time and a considerable reduction in memory usage. Applying the method to the interacting fermionic Hofstadter model, we demonstrate a reduction in computation time by over 20-fold, in addition to a sixfold memory reduction.