Michael Knap^1,2, Erez Berg^1,3, Martin Ganahl^1,2, and Eugene Demler^1,2

¹ Department of Physics, Harvard University, Cambridge MA 02138, USA

² Institute of Theoretical and Computational Physics, Graz University of Technology, 8010 Graz, Austria

³ Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel 

Cold polar molecules allow to study exciting new phenomena which arise from the long-range and anisotropic nature of their mutual interactions. Here, we analyze theoretically polar molecules confined in planar arrays of one dimensional tubes [1]. In the classical limit, if the number of tubes is finite, new types of "clustered Wigner crystals" with increasingly many molecules per unit cell can be stabilized by tuning the in-plane angle between the dipolar moments and the tube direction. Quantum mechanically, these phases melt into distinct "clustered Luttinger liquids." We calculate the phase diagram of the system and study the quantum melting of the clustered phases. We find that the requirements for exploring these phases are reachable in current experiments and discuss possible experimental signatures. 

[1] Michael Knap, Erez Berg, Martin Ganahl, and Eugene Demler, Phys. Rev. B 86, 064501 (2012).