Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the Laughlin parent states, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for ν =
We study the motion of a particle in a periodic potential with Ohmic dissipation. In D = 1 dimension it is well known that there are two phases depending on the dissipation: a localized phase with zero temperature mobility µ = 0 and a fully coherent phase with µ unaffected by the periodic potential. For D > 1, we find that this is also the case for a Bravais lattice. However, for non symmorphic lattices, such as the honeycomb lattice and its D dimensional generalization, there is a new intermediate phase with a universal mobility µ * . We study this intermediate fixed point in perturbatively accessible regimes. In addition, we relate this model to the Toulouse limit of the D+1 channel Kondo problem. This mapping allows us to compute µ * exactly using results known from conformal field theory. Experimental implications are discussed for resonant tunneling in strongly coupled Coulomb blockade structures and for multi channel Luttinger liquids.PACS numbers: 05.40+j, 72.15Qm, 73.40Gk The quantum mechanics of a particle in a periodic potential coupled to a dissipative environment is a fundamental problem in condensed matter physics [1]. A simple theory based on the Caldeira-Leggett model of Ohmic dissipation was proposed in the mid 1980's as a possible description of the motion of a heavy charged particle in a metal [2]. In a one dimensional periodic potential it was shown that there are two zero temperature (T = 0) phases. For weak friction, the particle diffuses freely as if the periodic potential were absent. When the friction exceeds a critical value, however, the particle is localized in one of the minima of the potential.Recently there has been renewed interest in this quantum Brownian motion (QBM) model in connection with quantum impurity problems [3] and boundary conformal field theory [4]. It is isomorphic to the problem of tunneling through a barrier in a Luttinger liquid, which is relevant to experiments in quantum wires [5] and tunneling in quantum Hall edge states [6]. Here the "coordinate" of the "particle" is the number of electrons that tunnel past the barrier. The periodic potential arises from the discreteness of the electron's charge. The Luttinger liquid's modes play the role of the dissipative bath. The particle's mobility corresponds to the electrical conductance.There are often multiple electron channels, due to spin and transverse degrees of freedom. The impurity problem then maps to a multi-dimensional periodic potential. In addition to the extended and localized phases, in two dimensions it has been shown that there can be additional non trivial phases [7,8], which may be accessed by tuning to a resonance. Using a similar analysis, Furusaki and Matveev recently found a similar intermediate phase in a model of resonant tunneling through a Coulomb blockade structure [9]. They argued that the resonance fixed point is that of the multi channel Kondo problem.In this paper we consider the general problem of QBM on periodic lattices. We show that the lattice symmetry plays a crucial role in deter...
We propose a new ground state trial wavefunction for a two-dimensional Wigner crystal in a strong perpendicular magnetic field. The wavefunction includes Laughlin-Jastrow correlations between electron pairs, and may be interpreted as a crystal state of composite fermions or composite bosons. Treating the power $m$ of the Laughlin-Jastrow factor as a variational parameter, we use quantum Monte Carlo simulations to compute the energy of these new states. We find that our wavefunctions have lower energy than existing crystalline wavefunctions in the lowest Landau level. Our results are consistent with experimental observations of the filling factor at which the transition between the fractional quantum Hall liquid and the Wigner crystal occurs for electron systems. Exchange contributions to the wavefunctions are estimated quantitatively and shown to be negligible for sufficiently small filling factors
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.