Showing papers on "Luttinger parameter published in 2013"

Numerical evidence for strong randomness scaling at a superfluid-insulator transition of one-dimensional bosons

Abstract: We present numerical evidence from Monte Carlo simulations that the superfluid-insulator quantum phase transition of interacting bosons subject to strong disorder in one dimension is controlled by the strong-randomness critical point. At this critical point the distribution of superfluid stiffness over disorder realizations develops a power-law tail reflecting a universal distribution of weak links. The Luttinger parameter on the other hand does not take on a universal value at this critical point, in marked contrast to the known Berezinskii-Kosterlitz-Thouless-like superfluid-insulator transition in weakly disordered systems. We develop a finite-size scaling procedure which allows us to directly compare the numerical results from systems of linear size up to 1024 sites with theoretical predictions obtained by Altman et al. [ Phys. Rev. Lett. 93 150402 (2004)] using a strong disorder renormalization group approach. The data shows good agreement with the scaling expected at the strong-randomness critical point.

Classical-field renormalization flow of one-dimensional disordered bosons

Abstract: We show that in the regime when strong disorder is more relevant than field quantization the superfluid--to--Bose-glass criticality of one-dimensional bosons is preceded by the prolonged logarithmically slow classical-field renormalization flow of the superfluid stiffness at mesoscopic scales. With the system compressibility remaining constant, the quantum nature of the system manifests itself only in the renormalization of dilute weak links. On the insulating side, the flow ultimately reaches a value of the Luttinger parameter at which the instanton--anti-instanton pairs start to proliferate, in accordance with the universal quantum scenario. This happens first at astronomic system sizes because of the suppressed instanton fugacity. We illustrate our result by first-principles simulations.

Thermally isolated Luttinger liquids with noisy Hamiltonians

Abstract: We study the dynamics of a quantum-coherent thermally isolated Luttinger liquid with noisy Luttinger parameter. To characterize the fluctuations of the absorbed energy in generic noise-driven systems, we first identify two types of energy moments, which can help tease apart the effects of classical (sample-to-sample) and quantum sources of fluctuations. One type of moment captures the total fluctuations due to both sources, while the other one captures the effect of the classical source only. We then demonstrate that, in the Luttinger liquid case, the two types of moments agree in the thermodynamic limit, indicating that the classical source dominates. In contrast to equilibrium thermodynamics, in this driven system the relative fluctuations of energy do not decay with the system size. Additionally, we study the deviations of equal-time correlation functions from their ground-state value, and find a simple scaling behavior.

Edge properties of principal fractional quantum Hall states in the cylinder geometry

Abstract: We study fractional quantum Hall states in the cylinder geometry with open boundaries. We focus on principal fermionic 1/3 and bosonic 1/2 fractions in the case of hard-core interactions. The gap behavior as a function of the cylinder radius is analyzed. By adding enough orbitals to allow for edge modes we show that it is possible to measure the Luttinger parameter of the non-chiral liquid formed by the combination of the two counterpropagating edges when we add a small confining potential. While we measure a Luttinger exponent consistent with the chiral Luttinger theory prediction for the full hard-core interaction, the exponent remains non-trivial in the Tao-Thouless limit as well as for simple truncated states that can be constructed on the cylinder. If the radius of the cylinder is taken to infinity the problem becomes a Tonks-Girardeau one-dimensional interacting gas in Fermi and Bose cases. Finally we show that the the Tao-Thouless and truncated states have an edge electron propagator which decays spatially with a Fermi-liquid exponent even if the energy spectrum can still be described by a non-trivial Luttinger parameter.

Nonequilibrium transport of helical Luttinger liquids through a quantum dot

Abstract: We study a steady state non-equilibrium transport between two interacting helical edge states of a two dimensional topological insulator, described by helical Luttinger liquids, through a quantum dot. For non-interacting dot the current is obtained analytically by including the self-energy correction to the dot Green's function. For interacting dot we use equation of motion method to study the influence of weak on-site Coulomb interaction on the transport. We find the metal-to-insulator quantum phase transition for attractive or repulsive interactions in the leads when the magnitude of the interaction strength characterized by a charge sector Luttinger parameter $K$ goes beyond a critical value. The critical Luttinger parameter $K_{cr}$ depends on the hoping strength between dot and the leads as well as the energy level of the dot with respect to the Fermi levels of the leads, ranging from weak interaction regime for dot level off resonance to strong interaction regime for dot in resonance with the equilibrium Fermi level. Nearby the transition various singular behaviors of current noise, dot density of state, and the decoherence rate (inverse of lifetime) of the dot are briefly discussed.

Susceptibility at the superfluid-insulator transition for one-dimensional disordered bosons

Abstract: A pair of recent Monte Carlo studies have reported evidence for and against a crossover from weak to strong-disorder criticality in the one-dimensional dirty boson problem. The Monte Carlo analyses rely on measurement of two observables: the effective Luttinger parameter K_(eff) and the superfluid susceptibility χ. The former quantity was previously calculated analytically, using the strong-disorder renormalization group (SDRG), by Altman, Kafri, Polkovnikov, and Refael. Here, we use an extension of the SDRG framework to find a non-universal anomalous dimension η_(sd) characterizing the divergence of the susceptibility with system size: χ ~ L^(2-η_(sd)). We show that η_(sd) obeys the hyperscaling relation η_(sd) = 1/2K_(eff). We also identify an important obstacle to measuring this exponent on finite-size systems and comment on the implications for numerics and experiments.

Phase transitions for a collective coordinate coupled to Luttinger liquids.

Abstract: We study various realizations of collective coordinates, e.g., the position of a particle, the charge of a Coulomb box, or the phase of a Bose or a superconducting condensate, coupled to Luttinger liquids with N flavors. We find that for a Luttinger parameter (1/2) < K < 1 there is a phase transition from a delocalized phase into a phase with a periodic potential at strong coupling. In the delocalized phase the dynamics is dominated by an effective mass, i.e., diffusive in imaginary time, while on the transition line it becomes dissipative. At K = (1/2) there is an additional transition into a localized phase with no diffusion at zero temperature.

Luttinger parameters of interacting fermions in one dimension at high energies

Abstract: Interactions between electrons in one dimension are fully described at low energies by only a few parameters of the Tomonaga-Luttinger model, which is based on linearization of the spectrum. We consider a model of spinless fermions with short-range interaction via the Bethe-Ansatz technique and show that a Luttinger parameter emerges in an observable beyond the low-energy limit. A distinct feature of the spectral function, the edge that marks the lowest possible excitation energy for a given momentum, is parabolic for arbitrary momenta and the prefactor is a function of the Luttinger parameter, $K$.