Interaction-Induced Fractionalization and Topological Superconductivity in the Polar Molecules Anisotropic t−J Model

Abstract

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

Homogeneous and domain-wall topological Haldane conductors with dressed Rydberg atoms

“…Restoring now in the ground state the alternated spin orientation of the fermions, one realizes that in the t−J z model all the above phases are also spin gapped. According to the general bosonization analysis reported in previous work [31], the spin gap should be characterized by a non-vanishing Haldane spin string order. The latter is defined as…”

“…In addition to this we investigate by density-matrix-renormalization-group (DMRG) [42] numerical analysis further quantities to enforce our findings related to the topological aspects of the model. As a first countercheck we capture the constant finite value of the string order arXiv:1910.11051v2 [cond-mat.quant-gas] 31 Oct 2019 parameter as well as a double degenerate entanglement spectrum [3,7,43,44] which are both characteristic signatures of symmetry protected topological states. Then we concentrate on the effect of a finite magnetic field which enriches the complexity of the treated system.…”

Out-of-equilibrium phase diagram of long-range superconductors

“…More recent work has extended the use of SOPs in the analysis of topological phases also to bosonic and fermionic systems [77][78][79][80][81]. Recently, within the context of high T c superconductivity, SOPs have been used to theoretically study the topological phases diagram of the t − J model [82]. It has further been proposed to study this model in quantum gas microscopes [83], as they are ideal platforms for the measurement of SOPs [84,85].…”

Enhanced superconductivity and various edge modes in modulated $t$-$J$ chains

“…In parallel, the development of ultracold gases in optical lattices within the last two decades provides a new way to explore the physical phenomena described by theoretical model Hamiltonians [28][29][30][31][32], including quasiperiodic models [33] and extended t-J models [34,35]. The experimental setting with remarkable control and tunability has also brought more flexibilities to the theoretical model, which can be studied with sufficient motivation in a broader range of parameters and in different extended forms [34][35][36][37]. The quasi-periodic t-J Hamiltonian, which has not yet been explicitly proposed in optical lattices, has the potential to be realized in future ex-periments [38].…”