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Register a new userQuantum Impurity in Luttinger Liquid: Universal Conductance with Entanglement Renormalization
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We study numerically the universal conductance of Luttinger liquids wire with a single impurity via the Muti-scale Entanglement Renormalization Ansatz (MERA). The scale invariant MERA provides an efficient way to extract scaling operators and scaling dimensions for both the bulk and the boundary conformal field theories. By utilizing the key relationship between the conductance tensor and ground-state correlation function, the universal conductance can be evaluated within the framework of the boundary MERA. We construct the boundary MERA to compute the correlation functions and scaling dimensions for the Kane-Fisher fixed points by modeling the single impurity as a junction (weak link) of two interacting wires. We show that the universal behavior of the junction can be easily identified within the MERA and argue that the boundary MERA framework has tremendous potential to classify the fixed points in general multi-wire junctions.
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We study the non-equilibrium dynamics and transport of a PT-symmetric Luttinger liquid (LL) after an interaction quench. The system is prepared in domain wall initial state. After a quantum quench to spatially homogeneous, PT-symmetric LL, the domain wall develops into a flat central region that spreads out ballistically faster than the conventional Lieb-Robinson maximal speed. By evaluating the current inside the regular lightcone, we find a universal conductance $e^2/h$, insensitive to the strength of the PT-symmetric interaction. On the other hand, by repeating the very same time evolution with a hermitian LL Hamiltonian, the conductance is heavily renormalized by the hermitian interaction as $e^2/hK$ with $K$ the LL parameter. Our analytical results are tested numerically, confirming the universality of the conductance in the non-hermitian realm.
We investigate the stability of conducting and insulating phases in multichannel Luttinger liquids with respect to embedding a single impurity. We devise a general approach for finding critical exponents of the conductance in the limits of both weak and strong scattering. In contrast to the one-channel Luttinger liquid, the system state in certain parametric regions depends on the scattering strength which results in the emergence of a bistability. Focusing on the two-channel liquid, the method developed here enables us to provide a generic analysis of phase boundaries governed by the most relevant (i.e. not necessarily single-particle) scattering mechanism. The present approach is applicable to channels of different nature as in fermion-boson mixtures, or to identical ones as on the opposite edges of a topological insulator. We show that interaction per se cannot provide protection in particular case of topological insulators realized in narrow Hall bars.
The theoretical model of the short-range interacting Luttinger liquid predicts a power-law scaling of the density of states and the momentum distribution function around the Fermi surface, which can be readily tested through tunneling experiments. However, some physical systems have long-range interaction, most notably the Coulomb interaction, leading to significantly different behaviors from the short-range interacting system. In this paper, we revisit the tunneling theory for the one-dimensional electrons interacting via the long-range Coulomb force. We show that even though in a small dynamic range of temperature and bias voltage, the tunneling conductance may appear to have a power-law decay similar to short-range interacting systems, the effective exponent is scale-dependent and slowly increases with decreasing energy. This factor may lead to the sample-to-sample variation in the measured tunneling exponents. We also discuss the crossover to a free Fermi gas at high energy and the effect of the finite size. Our work demonstrates that experimental tunneling measurements in one-dimensional electron systems should be interpreted with great caution when the system is a Coulomb Luttinger liquid.
Using derived previously effective theory we explore conductance in the Luttinger model with one impurity. A new approach to the renormalization group (RG) analysis of this model is developed. It is based on the original Gell-Mann-Low formulation of RG. We sum up infrared logarithmic contibutions to conductance in the leading and few subsequent approximations. We analyze the validity of widely used ``poor mans scaling approach and find that it is applicable only in the leading approximation. Our results for corrections to this approximation are different from results obtained in other papers. It should be expected beforehand, as Gell-Mann-Low function of the model is not regularization scheme invariant. For this reason the observed quantity (e.g., conductance) can not satisfy the Gell-Mann-Low equation beyond the leading-log approximation as it is supposed in the poor mans approach. We formulate the method to calculate the conductance from renormalized hamiltonian in the post-leading approximations and match results to the case of weak impurity where the answer is known in any order in electron-electron interaction.
The transport dynamics of a quenched Luttinger liquid tunnel-coupled to a fermionic reservoir is investigated. In the transient dynamics, we show that for a sudden quench of the electron interaction universal power-law decay in time of the tunneling current occurs, ascribed to the presence of entangled compound excitations created by the quench. In sharp contrast to the usual non universal power-law behavior of a zero-temperature non-quenched Luttinger liquid, the steady state tunneling current is ohmic and can be explained in terms of an effective quench-activated heating of the system. Our study unveils an unconventional dynamics for a quenched Luttinger liquid that could be identified in quenched cold Fermi gases.
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