The experimental realization of time-dependent ultracold lattice systems has paved the way towards the implementation of new Hubbard-like Hamiltonians. We show that in a one-dimensional twocomponents lattice dipolar Fermi gas the competition between long range repulsion and correlated hopping induced by periodically modulated on-site interaction allows for the formation of hidden magnetic phases, with degenerate protected edge modes. The magnetism, characterized solely by string-like nonlocal order parameters, manifests in the charge and/or in the spin degrees of freedom. Such behavior is enlighten by employing Luttinger liquid theory and numerical methods. The range of parameters for which hidden magnetism is present can be reached by means of the currently available experimental setups and probes.
The Mott insulator is characterized by having small deviations around the (integer) average particle density n, with pairs with n-1 and n+1 particles forming bound states. In one dimension, the effect is captured by a nonzero value of a nonlocal "string" of parities, which instead vanishes in the superfluid phase where density fluctuations are large. Here, we investigate the interaction induced transition from the superfluid to the Mott insulator, in the paradigmatic Bose Hubbard model at n=1. By means of quantum Monte Carlo simulations and finite size scaling analysis on L×M ladders, we explore the behavior of "brane" parity operators from one dimension (i.e., M=1 and L→∞) to two dimensions (i.e., M→∞ and L→∞). We confirm the conjecture that, adopting a standard definition, their average value decays to zero in two dimensions also in the insulating phase, evaluating the scaling factor of the "perimeter law" [S. P. Rath et al., Ann. Phys. (Berlin) 334, 256 (2013)ANPYA20003-380410.1016/j.aop.2013.04.006]. Upon introducing a further phase in the brane parity, we show that its expectation value becomes nonzero in the insulator, while still vanishing at the transition to the superfluid phase. These quantities are directly accessible to experimental measures, thus providing an insightful signature of the Mott insulator.
We show that the interplay between antiferromagnetic interaction and hole motion gives rise to a topological superconducting phase. This is captured by the one dimensional anisotropic t − J model which can be experimentally achieved with ultracold polar molecules trapped onto an optical lattice. As a function of the anisotropy strength we find that different quantum phases appear, ranging from a gapless Luttinger liquid to spin gapped conducting and superconducting regimes. In presence of appropriate z-anisotropy, we also prove that a phase characterized by non-trivial topological order takes place. The latter is described uniquely by a finite non local string parameter and presents robust edge spin fractionalization. These results allow to explore quantum phases of matter where topological superconductivity is induced by the interaction. PACS numbers:Introduction. Topological quantum matter has recently attracted huge interest from different research fields [1][2][3]. In this context the presence of gapless edge modes associated to a gapped bulk [4,5] can give rise to unique properties like quantized conductance [6-9] and charge fractionalization [10][11][12]. Thanks to symmetry arguments, a full understanding of the aforementioned features can be obtained for non interacting systems allowing to classify the so called topological insulators [13,14] and superconductors [15,16]. Crucially this approach becomes unstable in presence of interaction [17] and the concept of symmetry protection can be exploited to still classify topological phases [18,19]. In particular it has been proved[20] that, for strongly correlated systems, the appearance of protected localized edge states is identified by a finite value of a nonlocal string order parameter [21]. Furthermore the latter captures the hidden antiferromagnetic ordering of some degrees of freedom (for instance, ↑ and ↓ states of a spin 1 model), diluted in the background of the others (for instance, 0 state). Celebrated example of this is the Haldane phase characteristic of several interacting one dimensional models [22][23][24][25][26][27][28][29][30][31][32][33]. Noticeably these studies all focus on hidden antiferromagnetism in presence of a gapped charge channel, thus describing topological insulating regimes. Therefore finding microscopic interacting Hamiltonians supporting the presence of non trivial topological conducting orders, would be of deep and fundamental interest. Moreover this could also possibly lead to the discovery of further features which differ from the non interacting topological case [34]. Due to the fact that string orders have been measured [35,36], ultracold quantum systems [37] represent an ideal platform to study the possible appearance of topological effects in presence of interaction. Moreover the impressive level of control achieved with such experimental setups has also allowed to trap ultracold particles with long range dipolar interaction [38]. By means of such a platform several spin models [39][40][41] with spin-spin
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