Helical liquids have been experimentally realized in both nanowires and ultracold atomic chains as the result of strong spin-orbit interactions. In both cases the inner degrees of freedom can be considered as an additional space dimension, providing an interpretation of these systems as chiral synthetic ladders, with artificial magnetic fluxes determined by the spin-orbit terms. In this work, we characterize the helical state which appears at filling ν = 1/2: this state is generated by a gap arising in the spin sector of the corresponding Luttinger liquid and it can be interpreted as the one-dimensional (1D) limit of a fractional quantum Hall state of bosonic pairs of fermions. We study its main features, focusing on entanglement properties and correlation functions. The techniques developed here provide a key example for the study of similar quasi-1D systems beyond the semiclassical approximation commonly adopted in the description of the Laughlin-like states.

In this paper we study the ground state properties of a ladder Hamiltonian with chiral SU (2)invariant spin interactions, a possible first step towards the construction of truly two dimensional non-trivial systems with chiral properties starting from quasi-one dimensional ones. Our analysis uses a recent implementation by us of SU (2) symmetry in tensor network algorithms, specifically for infinite Density Matrix Renormalization Group (iDMRG). After a preliminary analysis with Kadanoff coarse-graining and exact diagonalization for a small-size system, we discuss its bosonization and recap the continuum limit of the model to show that it corresponds to a conformal field theory, in agreement with our numerical findings. In particular, the scaling of the entanglement entropy as well as finite-entanglement scaling data show that the ground state properties match those of the universality class of a c = 1 conformal field theory (CFT) in (1 + 1) dimensions. We also study the algebraic decay of spin-spin and dimer-dimer correlation functions, as well as the algebraic convergence of the ground state energy with the bond dimension, and the entanglement spectrum of half an infinite chain. Our results for the entanglement spectrum are remarkably similar to those of the spin-1/2 Heisenberg chain, which we take as a strong indication that both systems are described by the same CFT at low energies, i.e., an SU (2)1 Wess-Zumino-Witten theory. Moreover, we explain in detail how to construct Matrix Product Operators for SU (2)-invariant three-spin interactions, something that had not been addressed with sufficient depth in the literature. arXiv:1812.01311v3 [cond-mat.str-el] 6 May 2019

In strictly one-dimensional systems, repulsive interactions tend to reduce particle mobility on a lattice. Therefore, the Drude weight, controlling the divergence at zero-frequency of optical conductivities in perfect conductors, is lower than in non-interacting cases. We show that this is not the case when extending to quasi one-dimensional ladder systems. Relying on bosonization, perturbative and matrix product states (MPS) calculations, we show that nearest-neighbor interactions and magnetic fluxes provide a bias between back-and forward-scattering processes, leading to linear corrections to the Drude weight in the interaction strength. As a consequence, Drude weights counter-intuitively increase (decrease) with repulsive (attractive) interactions. Our findings are relevant for the efficient tuning of Drude weights in the framework of ultracold atoms trapped in optical lattices and equally affect topological edge states in condensed matter systems. arXiv:1911.11160v1 [cond-mat.quant-gas]

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