Reducing entanglement with symmetries: application to persistent currents in impurity problems

TL;DR

This paper introduces a method using canonical transformations to reduce entanglement in impurity problems, significantly enhancing the efficiency of DMRG for studying persistent currents in quantum rings.

Contribution

The authors develop a transformation technique that maps impurity problems with periodic boundaries to open boundaries, optimizing DMRG performance for these systems.

Findings

Enhanced DMRG efficiency for impurity problems

Application to one-channel and two-channel Kondo models

Discovery of connections between different Kondo problems

Abstract

We show how canonical transformations can map problems with impurities coupled to non-interacting rings onto a similar problem with open boundary conditions. The consequent reduction of entanglement, and the fact the density matrix renormalization group (DMRG) is optimally suited for open boundary conditions, increases the efficiency of the method exponentially, making it an unprecedented tool to study persistent currents. We demonstrate its application to the case of the one-channel and two-channel Kondo problems, finding interesting connections between the two.