A Density Matrix Renormalization Group Study of Ultrasmall Superconducting Grains

TL;DR

This paper applies the DMRG method to study ultrasmall superconducting grains, revealing a smooth crossover from few-electron to bulk BCS behavior using a novel particle-hole based approach.

Contribution

It introduces a DMRG approach tailored for ultrasmall superconducting grains, focusing on particle-hole states around the Fermi level.

Findings

Observed a smooth logarithmic crossover between regimes

Demonstrated the effectiveness of DMRG in this context

Provided insights into the transition from few-electron to bulk superconductivity

Abstract

We apply the DMRG method to the BCS pairing Hamiltonian which describes ultrasmall superconducting grains. Our version of the DMRG uses the particle (hole) states around the Fermi level as the system block (environment). We observe a smooth logarithmic-like crossover between the few electron regime and the BCS-bulk regime.