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arXiv:1202.6541 · Physical Review B

Exotic quantum criticality in one-dimensional coupled dipolar bosons tubes

P. Lecheminant, Heloise Nonne

Published May 10, 2012• 26 citations
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Abstract

The competition between intertube hopping processes and density-density interactions is investigated in one-dimensional quantum dipolar bosons systems of $N$ coupled tubes at zero temperature. Using a phenomenological bosonization approach, we show that the resulting competition leads to an exotic quantum phase transition described by a U(1) $\ifmmode\times\else\texttimes\fi{}$ ${\mathbb{Z}}_{N}$ conformal field theory with a fractional central charge. The emerging ${\mathbb{Z}}_{N}$ parafermionic critical degrees of freedom are highly nontrivial in terms of the original atoms or polar molecules of the model. We further determine the main physical properties of the quantum-critical point in a double-tube system which has central charge $c=3/2$. In triple-tube systems, we show that the competition between the two antagonistic processes is related to the physics of the two-dimensional ${\mathbb{Z}}_{3}$ chiral Potts model. This work opens the possibility to study the exotic properties of the ${\mathbb{Z}}_{N}$ parafermions in the context of ultracold quantum Bose gases.

DOI
10.1103/physrevb.85.195121

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The competition between intertube hopping processes and density-density interactions is investigated in one-dimensional quantum dipolar bosons systems of NNN coupled tubes at zero temperature. Using a phenomenological bosonization approach, we show that the resulting competition leads to an exotic quantum phase transition described by a U(1) \ifmmode×\else\texttimes\fi\ifmmode\times\else\texttimes\fi{}\ifmmode×\else\texttimes\fi ZN{\mathbb{Z}}_{N}ZN​ conformal field theory with a fractional central charge. The emerging ZN{\mathbb{Z}}_{N}ZN​ parafermionic critical degrees of freedom are highly nontrivial in terms of the original atoms or polar molecules of the model. We further determine the main physical properties of the quantum-critical point in a double-tube system which has central charge c=3/2c=3/2c=3/2. In triple-tube systems, we show that the competition between the two antagonistic processes is related to the physics of the two-dimensional Z3{\mathbb{Z}}_{3}Z3​ chiral Potts model. This work opens the possibility to study the exotic properties of the ZN{\mathbb{Z}}_{N}ZN​ parafermions in the context of ultracold quantum Bose gases.
We consider dipolar bosons in two tubes of one-dimensional lattices, where the dipoles are aligned to be maximally repulsive and the particle filling fraction is the same in each tube. In the classical limit of zero intersite hopping, the particles arrange themselves into an ordered crystal for any rational filling fraction, forming a complete devil's staircase like in the single tube case. Turning on hopping within each tube then gives rise to a competition between the crystalline Mott phases and a liquid of defects or solitons. However, for the two-tube case, we find that solitons from different tubes can bind into pairs for certain topologies of the filling fraction. This provides an intriguing example of pairing that is purely driven by correlations close to a Mott insulator.
We systematically study ground-state properties of fermionic dipolar gases in a planar array of one-dimensional potential tubes for arbitrary orientation of dipole moments. Using the Luttinger liquid theory with the generalized Bogoliubov transformation, we calculate the elementary excitations and the Luttinger scaling exponents for various relevant quantum orders. The complete quantum phase diagrams for arbitrary polar angle of the dipole moment are obtained including charge-density wave, ppp-wave superfluid, intertube gauge-phase density wave, and intertube sss-wave superfluid, where the last two break the U(1) gauge symmetry of the system (conservation of particle number in each tube) and occur only when the intertube interaction is larger than the intratube interaction. We then discuss the physical properties and experimental features of these many-body phases.
We consider a mixture of single-component bosonic and fermionic atoms in an array of coupled one-dimensional "tubes." For an attractive Bose-Fermi interaction, we show that the system exhibits phase separation instead of the usual collapse. Moreover, above a critical intertube hopping, all first-order instabilities disappear in both attractive and repulsive mixtures. The possibility of suppressing instabilities in this system suggests a route towards the realization of paired phases, including a superfluid of p-wave pairs unique to the coupled-tube system, and quantum critical phenomena.
We study a two-dimensional (2D) array of coupled 1D tubes of interacting bosons. Such systems can be produced by loading ultracold atoms in anisotropic optical lattices. We investigate the effects of coupling the tubes via hopping of the bosons (i.e. Josephson coupling). In the absence of a periodic potential along the tubes, or when such potential is incommensurate with the boson density, the system undergoes a transition from an array of incoherent Tomonaga–Luttinger liquids at high temperature to an anisotropic Bose–Einstein condensate (BEC), at low temperature. We determine the transition temperature and long wavelength excitations of the BEC. In addition to the usual gapless (Goldstone) mode found in standard superfluids, we also find a gapped mode associated with fluctuations of the amplitude of the order parameter. When a commensurate periodic potential is applied along the tubes, they can become 1D Mott insulators. Intertube hopping leads to a deconfinement quantum phase transition between the 1D Mott insulators and the anisotropic BEC. We also take into account the finite size of the gas tubes as realized in actual experiments. We map out the phase diagram of the quasi-1D lattice and compare our results with the existing experiments on such systems.
We present a theory for a lattice array of weakly coupled one-dimensional ultracold attractive Fermi gases (1D tubes) with spin imbalance, where strong intratube quantum fluctuations invalidate mean-field theory. We first construct an effective field theory, which treats spin-charge mixing exactly, based on the Bethe ansatz solution of the 1D single tube problem. We show that the 1D Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is a two-component Luttinger liquid, and its elementary excitations are fractional states carrying both charge and spin. We analyze the instability of the 1D FFLO state against intertube tunneling by renormalization group analysis, and find that it flows into either a polarized Fermi liquid or a FFLO superfluid, depending on the magnitude of interaction strength and spin imbalance. We obtain the phase diagram of the quasi-1D system and further determine the scaling of the superfluid transition temperature with intertube coupling.
In this thesis exotic phases of models preserving the symmetries of the one-dimensional quantum Ising and three-state Potts chains are considered, the natural habitats of Majorana fermions and parafermions, respectively. Along with numerical techniques, conformal field theory (CFT) is used to study the resulting physics. Chapter 1 gives an introduction to the field and explains the basics of the numerical techniques to be used throughout the thesis. CFT is briefly introduced in Chapter 2 before the key results necessary for the thesis are given. In Chapter 3, self-dual interactions are added to the critical Ising model, giving a range of different phases. A tricritical Ising point separates the Ising phase from an order-disorder coexistence phase on the chirally symmetric line, while a supersymmetric line provides the transition to an incommensurate phase in the general model. The model is solved exactly on a free-fermionic line giving insight into the points where only numerical analysis can be performed. This is supplemented by Appendix A, where the qualitative difference between similar perturbations is considered. Chapters 4 and 5 consider models with the symmetries of the three-state Potts model. Various phases are found including an order-disorder coexistence phase, a second critical Potts phase, a "not-A" phase, and a representation symmetry protected topological phase. The effect of lattice momentum on the stability of phases and the connection with conformal field theory operators is studied. Lattice realizations of several CFTs are found, such as the tricritical Potts CFT and a CFT expressible in two different forms, either in terms of a boson and fermion, or Potts and tricritical Ising CFTs.