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arXiv:2012.12393 · Physical Review Letters

Two-Fluid Coexistence in a Spinless Fermions Chain with Pair Hopping

Lorenzo Gotta, Leonardo Mazza, Pascal Simon, Guillaume Roux

Published May 21, 2021• 16 citations
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Abstract

We show that a simple one-dimensional model of spinless fermions with pair hopping displays a phase in which a Luttinger liquid of paired fermions coexists with a Luttinger liquid of unpaired fermions. Our results are based on extensive numerical density-matrix renormalization-group calculations and are supported by a two-fluid model that captures the essence of the coexistence region.

DOI
10.1103/physrevlett.126.206805

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We show that a simple one-dimensional model of spinless fermions with pair hopping displays a phase in which a Luttinger liquid of paired fermions coexists with a Luttinger liquid of unpaired fermions. Our results are based on extensive numerical density-matrix renormalization-group calculations and are supported by a two-fluid model that captures the essence of the coexistence region.
We compute the phase diagram of a one-dimensional model of spinless fermions with pair hopping and nearest-neighbor interaction, first introduced by Ruhman and Altman, using the density-matrix renormalization group combined with various analytical approaches. Although the main phases are a Luttinger liquid of fermions and a Luttinger liquid of pairs, we also find remarkable phases in which only a fraction of the fermions are paired. In such a case, two situations arise: either fermions and pairs coexist spatially in a two-fluid mixture, or they are spatially segregated leading to phase separation. These results are supported by several analytical models that describe in an accurate way various relevant cuts of the phase diagram. Last, we identify relevant microscopic observables that capture the presence of these two fluids: while originally introduced in a phenomenological way, they support a wider application of two-fluid models for describing pairing phenomena.
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-neighbor range.In particular, we investigate the appearance of regions with dominant pairing physics in the presence of nearest-neighbor and next-nearest-neighbor 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.
We revisit the low-energy physics of one-dimensional spinless fermion liquids, showing that with sufficiently strong interactions the conventional Luttinger liquid can give way to a strong-pairing phase. While the density fluctuations in both phases are described by a gapless Luttinger liquid, single fermion excitations are gapped only in the strong-pairing phase. Smooth spatial Interfaces between the two phases lead to topological degeneracies in the ground-state and low-energy spectrum of the density fluctuations. Using a concrete microscopic model, with both single-particle and pair hopping, we show that the strong-pairing state is established through emergence of a new low-energy fermionic mode. We characterize the two phases with numerical calculations using the density matrix renormalization group. In particular we find enhancement of the central charge from c=1c=1c=1 in the two Luttinger liquid phases to c=3/2c=3/2c=3/2 at the critical point, which gives direct evidence for an emergent critical Majorana mode. Finally, we confirm the existence of topological degeneracies in the low-energy phonon spectrum, associated with spatial interfaces between the two phases.
We study the formation of bound states in a one-dimensional, single-component Fermi chain with attractive interactions. The phase diagram, computed from DMRG (density matrix renormalization group), shows not only a superfluid of paired fermions (pair phase) and a liquid of three-fermion bound states (trion phase), but also a phase with two gapless modes. We show that the latter phase is described by a two-component Tomonaga-Luttinger liquid (TLL) theory, consisting of one charged and one neutral mode. We argue based on our numerical data, that the single, pair, and trion phases are descendants of the two-component TLL theory. We speculate on the nature of the phase transitions amongst these phases.
We consider a one-dimensional system of spinless fermions with single particle and pair hoppings in a potential on-site disorder. The pair hopping term violates integrability of the model and enhances superconducting fluctuations in the bulk of the liquid. By means of the Abelian bosonization and extensive numerical density matrix renormalization group calculations we provide evidence that sufficiently large pair hopping amplitude guarantees the survival of the Tomonaga-Luttinger liquid phase at weak disorder. Large disorder drives the system to the Bose-glass phase, realizing the Giamarchi-Schulz scenario in such a system.
We report a two-step density-matrix renormalization-group computation of the equal-time single-particle Green's function, the density-density correlations, and the low-frequency spectral weight function of a spinless fermion model in an anisotropic two-dimensional lattice at half filling. We find that at weak couplings the density-density correlations have the universal decay of a Fermi liquid; the spectral weight function displays a sharp quasiparticle peak. But in the vicinity of a quantum critical point, these correlations strongly deviate from a Fermi-liquid prediction and a pseudogap opens in the spectral weight function.