Abstract
We investigate the phase diagrams of a one-dimensional lattice model of fermions and of a spin chain with interactions extending up to next-nearest neighbour range. In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbour and next-nearest-neighbour interactions. Our analysis is based on analytical calculations in the classical limit, bosonization techniques and large-scale density-matrix renormalization group numerical simulations. The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles. In relation with recent studies, we show several emergent transition lines with a central charge $c = 3/2$ between the Luttinger-liquid and the cluster Luttinger liquid phases. These results could be experimentally investigated using highly-tunable quantum simulators.
Highlights
Whether or not unpaired Majorana zero modes could appear in one-dimensional systems without the coupling to an external superconducting device is a question that has recently triggered a lot of interest
The phase diagram, which is investigated in all relevant filling regimes, displays a remarkably rich collection of phases, including Luttinger liquids, phase separation, charge-density waves, bond-order phases, and exotic cluster Luttinger liquids with paired particles
II we present the explicit form of the model Hamiltonian both in the fermionic and in the spin formulation, we indicate the parameters chosen for the numerical density-matrix renormalization group (DMRG) investigations and the physical observables employed throughout the article
Summary
Whether or not unpaired Majorana zero modes could appear in one-dimensional systems without the coupling to an external superconducting device is a question that has recently triggered a lot of interest. As a main result of this research subject, it has been proposed that the use of inhomogeneous systems where paired phases are coupled to normal phases is expected to reveal zeroenergy Majorana boundary modes, which should be pinned at the interfaces [6] For this reason, the study of pairing physics in one-dimensional fermionic setups has recently become an extremely interesting topic and this observation constitutes the broad motivation of the present work. VI the main features of the phase diagram structure at density commensurability effects are responsible for the disappearance of the liquid behavior observed at lower densities in favor of insulating CDW phases
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