Superfluidity in the 1D Bose-Hubbard Model

TL;DR

This paper investigates superfluidity in the one-dimensional Bose-Hubbard model using variational matrix product states, analyzing superfluid density, correlation decay, and entanglement scaling, with implications for cold atom experiments.

Contribution

It introduces a variational matrix product state approach to quantify superfluid density and compares optimization algorithms, providing insights into critical behavior and finite-temperature effects.

Findings

Superfluid density varies with Hubbard parameters.

VUMPS algorithm is more efficient than iDMRG.

Scaling laws relate entanglement entropy to superfluidity.

Abstract

We study superfluidity in the 1D Bose-Hubbard model using a variational matrix product state technique. We determine the superfluid density as a function of the Hubbard parameters by calculating the energy cost of phase twists in the thermodynamic limit. As the system is critical, correlation functions decay as power laws and the entanglement entropy grows with the bond dimension of our variational state. We relate the resulting scaling laws to the superfluid density. We compare two different algorithms for optimizing the infinite matrix product state and develop a physical explanation why one of them (VUMPS) is more efficient than the other (iDMRG). Finally, we comment on finite-temperature superfluidity in one dimension and how our results can be realized in cold atom experiments.