Superfluidity in the one-dimensional Bose-Hubbard model

We study superfluidity in the one-dimensional 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.

Automated summary

The study focused on superfluidity in the one-dimensional Bose-Hubbard model, determining superfluid density by calculating energy cost in the thermodynamic limit, observing power-law decay of correlation functions, and the relationship between entanglement entropy and bond dimension. Comparison of two algorithms optimization algorithms was conducted, explaining the efficiency difference between VUMPS and iDMRG, and discussing the potential realization in cold-atom experiments.