"Lattices mimicking fractional spatial dimensions: boson dynamics and fate of topological phases"


Masaki Tezuka (Kyoto Univ.)


Interactions with power-law dependence on the spatial distance have been introduced in trapped, low-dimensional ultracold ion gases, in which the exponent has been demonstrated to be widely changed according to the system parameters [1]. Such power-law interactions with variable exponents can realize systems effectively having larger and fractional spatial dimensions. We have demonstrated that even in originally one-dimensional systems, breakdown of continuous symmetries and realization of long-range order, forbidden in short-range models by the Mermin-Wagner-Hohenberg theorem, is expected [2]. Here we investigate, by the time-dependent density-matrix renormalization group method, the dynamics of a Bose condensate after the long-range term is quenched [3].
The spatial dimensionality of the system has been established as a crucial key for studying topologically nontrivial states of matter. Then, how does the topological phase behave when the system effectively has a fractional spatial dimension, as in the systems discussed above? Recently power-law interacting versions of the Ising chain with transverse magnetic field and the Kitaev chain have been investigated [4], and the possibility of a novel topological phase with massive edge modes has been proposed. In this poster, we also present our recent results on the effect of the power-law kinetic term on one-dimensional topological superconductors with Majorana edge fermions.
[1] J. W. Britton et al., Nature 484, 489 (2012); R. Islam et al., Science 340, 583 (2013).
[2] A. M. Lobos, M. Tezuka, and A. M. García-García, Phys. Rev. B 88, 134506 (2013).
[3] M. Tezuka, A. M. García-García, and M. A. Cazalilla, Phys. Rev. A 90, 053618 (2014).
[4] D. Vodola, L. Lepori, E. Ercolessi, and G. Pupillo, arXiv:1508.00820; D. Vodola, L. Lepori, E. Ercolessi, A. V. Gorshkov, and G. Pupillo, Phys. Rev. Lett. 113, 156402 (2014).

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