AUTHOR=Allerdt Andrew , Feiguin Adrian E. 

TITLE=A Numerically Exact Approach to Quantum Impurity Problems in Realistic Lattice Geometries

JOURNAL=Frontiers in Physics

VOLUME=Volume 7 - 2019

YEAR=2019

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00067

DOI=10.3389/fphy.2019.00067

ISSN=2296-424X

ABSTRACT=We review a completely unbiased and controlled numerical approach to quantum impurity problems consisting of exactly mapping the complete lattice Hamiltonian onto an equivalent one dimensional system through a unitary transformation. The resulting dimensional and entanglement reduction allows one to study single particle problems on arbitrary $d$-dimensional lattices using the density matrix renormalization group (DMRG) method. The real-space resolution allows one to position the impurities at the boundary or bulk of the sample and to study screening effects due to edge or surface modes. We describe how to generalize this approach to multi-impurity problems, discuss applications and possible extensions.