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arXiv:1703.08949 · Physical Review A

Spin-incoherent Luttinger liquid of one-dimensional spin-1 Tonks-Girardeau Bose gases: Spin-dependent properties

H. H. Jen, Sungkit Yip

Published May 25, 2017• 9 citations
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Abstract

Spin-incoherent Luttinger liquid (SILL) is a different universal class from the Luttinger liquid. This difference results from the spin incoherence of the system when the thermal energy of the system is higher than the spin excitation energy. We consider one-dimensional spin-1 Bose gas in the SILL regime and investigate its spin-dependent many-body properties. In Tonks-Girardeau limit, we are able to write down the general wave functions in a harmonic trap. We numerically calculate the spin-dependent (spin-plus, minus, and zero) momentum distributions in the sector of zero magnetization which allows us to demonstrate the most significant spin-incoherent feature compared to the spinless or spin-polarized case. In contrast to the spinless Bose gas, the momentum distributions are broadened and in the large momentum limit follow the same asymptotic $1/{p}^{4}$ dependence but with reduced coefficients. While the density matrices and momentum distributions differ between different spin components for small $N$, at large $N$ they approach each other. We show these by analytic arguments and numerical calculations up to $N=16$.

DOI
10.1103/physreva.95.053631

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Spin-incoherent Luttinger liquid (SILL) is a different universal class from the Luttinger liquid. This difference results from the spin incoherence of the system when the thermal energy of the system is higher than the spin excitation energy. We consider one-dimensional spin-1 Bose gas in the SILL regime and investigate its spin-dependent many-body properties. In Tonks-Girardeau limit, we are able to write down the general wave functions in a harmonic trap. We numerically calculate the spin-dependent (spin-plus, minus, and zero) momentum distributions in the sector of zero magnetization which allows us to demonstrate the most significant spin-incoherent feature compared to the spinless or spin-polarized case. In contrast to the spinless Bose gas, the momentum distributions are broadened and in the large momentum limit follow the same asymptotic 1/p41/{p}^{4}1/p4 dependence but with reduced coefficients. While the density matrices and momentum distributions differ between different spin components for small NNN, at large NNN they approach each other. We show these by analytic arguments and numerical calculations up to N=16N=16N=16.
We investigate spin-incoherent Luttinger liquid of a one-dimensional spin-1 Bose gas in a harmonic trap. In this regime highly degenerate spin configurations emerge since the energy splitting between different spin states is much less than the thermal energy of the system, while the temperature is low enough that the lowest energetic orbitals are occupied. As an example we numerically study the momentum distribution of a one-dimensional spin-1 Bose gas in Tonks-Girardeau gas limit and in the sector of zero magnetization. We find that the momentum distributions broaden as the number of atoms increase due to the averaging of spin function overlaps. Large momentum (ppp) asymptotic is analytically derived, showing the universal 1/p41/{p}^{4}1/p4 dependence. We demonstrate that the spin-incoherent Luttinger liquid has a momentum distribution also distinct from spinless bosons at finite temperature.
We theoretically investigate one-dimensional (1D) $\mathrm{SU}(\ensuremath{\kappa}$) fermions in the regime of spin-incoherent Luttinger liquid. We specifically focus on the Tonks-Girardeau gas limit where its density is sufficiently low that effective repulsions between atoms become infinite. In such case, spin exchange energy of 1D $\mathrm{SU}(\ensuremath{\kappa}$) fermions vanishes and all spin configurations are degenerate, which automatically puts them into a spin-incoherent regime. In this limit, we are able to express the single-particle density matrices in terms of those of anyons. This allows us to numerically simulate the number of particles up to N=32N=32N=32. We numerically calculate single-particle density matrices in two cases: (1) equal populations for each spin components (balanced) and (2) all Sz{S}_{z}Sz​ manifolds included. In contrast to noninteracting multicomponent fermions, the momentum distributions are broadened due to strong interactions. As $\ensuremath{\kappa}$ increases, the momentum distributions are less broadened for fixed NNN, while they are more broadened for fixed number of particles per spin component. We then compare numerically calculated high-momentum tails with analytical predictions which are proportional to 1/p41/{p}^{4}1/p4, in good agreement. Thus, our theoretical study provides a comparison with the experiments of repulsive multicomponent alkaline-earth fermions with a tunable $\mathrm{SU}(\ensuremath{\kappa}$) spin symmetry in the spin-incoherent regime.
A strongly correlated Luttinger-liquid behavior is found to emerge well beyond the Tonks-Girardeau (TG) regime in a one-dimensional Bose gas with dipolar repulsions at T=0T=0T=0, persisting for a wide range of densities. After combining reptation quantum Monte Carlo and bosonization techniques, we provide a unifying theory of the underlying crossover physics, evolving from the TG gas at low density into a classical quasiordered state at high density. The density dependent Luttinger parameters extracted from the numerical data provide all that is needed to determine the low-energy behavior from analytical expressions. Our quantitative predictions, in the whole crossover, for measurable quantities such as the structure factor and the momentum distribution, are estimated to be accessible in underway experiments with ultracold polar molecules.
Although the one-dimensional repulsive Fermi-Hubbard model has been intensively studied over many decades, a rigorous understanding of many aspects of the model is still lacking. In this work, based on the solutions to the thermodynamic Bethe ansatz equations, we provide a rigorous study on the following. (1) We calculate the fractional excitations of the system in various phases, from which we identify the parameter regime featuring the spin-incoherent Luttinger liquid (SILL). We investigate the universal properties and the asymptotic of correlation functions of the SILL. (2) We study the interaction-driven phase transition and the associated criticality, and build up an essential connection between the contact susceptibilities and the variations of density, magnetization, and entropy with respect to the interaction strength. As an application of these concepts, which hold true for higher-dimensional systems, we propose a quantum cooling scheme based on the interaction-driven refrigeration cycle.
We investigate the universal thermodynamics of the two-component one-dimensional Bose gas with contact interactions in the vicinity of the quantum critical point separating the vacuum and the ferromagnetic liquid regime. We find that the quantum critical region belongs to the universality class of the spin-degenerate impenetrable particle gas which, surprisingly, is very different from the single-component case and identify its boundaries with the peaks of the specific heat. In addition, we show that the compressibility Wilson ratio, which quantifies the relative strength of thermal and quantum fluctuations, serves as a good discriminator of the quantum regimes near the quantum critical point. Remarkably, in the Tonks-Girardeau regime, the universal contact develops a pronounced minimum, reflected in a counterintuitive narrowing of the momentum distribution as we increase the temperature. This momentum reconstruction, also present at low and intermediate momenta, signals the transition from the ferromagnetic to the spin-incoherent Luttinger liquid phase and can be detected in current experiments with ultracold atomic gases in optical lattices.
In contrast to the well-known Fermi-liquid theory of three dimensions, interacting one-dimensional and quasi-one-dimensional systems of fermions are described at low energy by an effective theory known as Luttinger liquid theory. This theory is expressed in terms of collective many-body excitations that show exotic behavior such as spin-charge separation. Luttinger liquid theory is commonly applied on the premise that ``low energy'' describes both the spin and charge sectors. However, when the interactions in the system are very strong, as they typically are at low particle densities, the ratio of spin to charge energy may become exponentially small. It is then possible at very low temperatures for the single-spin excitation energy to be low compared to the characteristic single excitation charge energy, but still high compared to the characteristic spin energy. This energy window of near ground-state charge degrees of freedom but highly thermally excited spin degrees of freedom is called a spin-incoherent Luttinger liquid. The spin-incoherent Luttinger liquid exhibits a higher degree of universality than the Luttinger liquid and its properties are qualitatively distinct. In this Colloquium some recent theoretical developments in the field are detailed and experimental indications of such a regime in gated semiconductor quantum wires are described.