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arXiv:1207.4986 · New Journal of Physics

Parafermion excitations in a superfluid of quasi-molecular chains

Alexei M. Tsvelik, Anatoly B. Kuklov

Published Nov 30, 2012• 14 citations

Abstract

We study a quantum phase transition in a system of dipoles confined in a stack of N identical one-dimensional lattices (tubes) polarized perpendicularly to the lattices. In this arrangement, the intra-lattice interaction is purely repulsive, preventing system collapse, and the inter-lattice interaction is attractive. The dipoles may represent polar molecules or indirect excitons. The transition separates two phases; in one of them, superfluidity (understood as algebraic decay of the corresponding correlation functions) takes place in each individual lattice, and in the other (chain superfluid) the order parameter is the product of bosonic operators from all lattices. We argue that in the presence of finite inter-lattice tunneling the transition belongs to the universality class of the q = N two-dimensional classical Potts model. For N = 2,3,4 the corresponding low-energy field theory is the model of Z N parafermions perturbed by the thermal operator. The results of Monte Carlo simulations are consistent with these predictions. The detection scheme for the chain superfluid is outlined.

DOI: 10.1088/1367-2630/14/11/115033

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We study a quantum phase transition in a system of dipoles confined in a stack of N identical one-dimensional lattices (tubes) polarized perpendicularly to the lattices. In this arrangement, the intra-lattice interaction is purely repulsive, preventing system collapse, and the inter-lattice interaction is attractive. The dipoles may represent polar molecules or indirect excitons. The transition separates two phases; in one of them, superfluidity (understood as algebraic decay of the corresponding correlation functions) takes place in each individual lattice, and in the other (chain superfluid) the order parameter is the product of bosonic operators from all lattices. We argue that in the presence of finite inter-lattice tunneling the transition belongs to the universality class of the q = N two-dimensional classical Potts model. For N = 2,3,4 the corresponding low-energy field theory is the model of Z N parafermions perturbed by the thermal operator. The results of Monte Carlo simulations are consistent with these predictions. The detection scheme for the chain superfluid is outlined.

We analyze the nature of quantum phase transition to a superfluid state of flexible chains in a gas of polar bosonic molecules confined in a stack of

N

identical 1d ("cigar" type) optical lattice layers and polarized perpendicularly to the layers. Monte Carlo simulations within the

J

-current model show that, in the absence of the inter-tube tunneling, the transition to the

N

-layered superfluid is in the Berezinskii-Kosterlitz-Thouless universality class in the one-particle density matrix channel. The inter-layer tunneling changes it to the

q=N

2d Potts universality. The low energy field descriptions of the transition are discussed in terms of conformal field theories.

The superfluid to normal fluid transition of dipolar bosons in two dimensions is studied in a broad density range by using path integral Monte Carlo simulations and summarized in the phase diagram. While at low densities we find good agreement with the universal results depending only on the scattering length a{s}, at moderate and high densities the transition temperature is strongly affected by interactions and the excitation spectrum of quasiparticles. The results are expected to be of relevance to dipolar atomic and molecular systems and indirect excitons in quantum wells.

We investigate the zero-temperature phase diagram of the one-dimensional Bose-Hubbard model with power-law hopping decaying with distance as 1/r^{α} using exact large scale quantum Monte Carlo simulations. For all 1<α≤3 the quantum phase transition from a superfluid and a Mott insulator at unit filling is found to be continuous and scale invariant, in marked contrast with the Berezinskii-Kosterlitz-Thouless (BKT) scenario that is recovered only for α>3. By performing finite-size scaling collapses of the superfluid stiffness and extracting dynamical and correlation-length exponents from the low-energy spectrum, we establish that these transitions define a distinct universality class throughout the long-range regime 1<α≤3. Analysis of the single-particle correlation functions and grand canonical phase diagram further reveals a sequence of ordering regimes within the superfluid phase: true long-range order for α≤2, anomalous quasi-long-range order for 2<α≤3, and conventional algebraic decay for α>3. Our exact numerical results provide a benchmark to compare theories of long-range quantum models and are relevant for experiments with cold neutral atom, molecules and ion chains.

We discuss a model of dipolar bosons trapped in a weakly coupled planar array of one-dimensional tubes. We consider the situation where the dipolar moments are aligned by an external field, and we find a rich phase diagram as a function of the angle of this field exhibiting quantum phase transitions between solid, superfluid, and supersolid phases. In the low energy limit, the model turns out to be identical to one describing quasi-one-dimensional superconductivity in condensed matter systems. This opens the possibility of using bosons as a quantum analog simulator of electronic systems, a scenario arising from the intricate relation between statistics and interactions in quasi-one-dimensional systems.

We investigate the finite-temperature phase diagram of polar molecules confined in a quasi-two-dimensional geometry by a harmonic potential along the polarization axis. We employ quantum Monte Carlo simulations to explore the strongly correlated regime accessible with current experimental setups. By tuning temperature and confinement strength, we identify a rich set of phases, including normal fluid, superfluid, supersolid, cluster crystal, and bilayer crystal states. Our results reveal the emergence of crystallization upon increasing temperature, highlighting the nontrivial role of thermal fluctuations in dipolar systems. In particular, we show that a bilayer crystal with one molecule per lattice site can be stabilized by varying the confinement strength at fixed interaction. Moreover, we show evidence of layering of superfluid states with phase coherence between the two layers. These findings provide insight into the interplay between interactions, confinement, and temperature in low-dimensional dipolar systems, and suggest new directions for engineering quantum phases with ultracold polar molecules.