Superfluidity and dimensional cross-over in Quasi-1D systems*

1D systems cannot attain long-range order (LRO) but have a wide range of other benefits. One method to cure the missing LRO is to construct an infinite array of weakly coupled 1D systems.
We consider a 3D array of one-dimensional repulsive bosons. If the bosons are hard-core they can model the electron-pairs in e.g. a quasi-1D USC such as the Bechgaard and Fabre salts.
Static Mean-Field (SMF) combined with Density Matrix Renormalization Group (DMRG) reduces the full 3D model to a self-consistently treated 1D one, enabling calculation of ground and thermal equilibrium states. This approach is motivated by the low cost of such an implementation and further allows the simulation of real-time/frequency dynamics.
This model exhibits a phase transition from a 3D superfluid (SF) to a 1D Mott insulator (MI) that forms the basis of the more complex behavior in the USCs. Interestingly, the order parameters indicating the different phases suggest a mix between first- and second-order transitions.

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