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Conductance through a potential barrier embedded in a Luttinger liquid: nonuniversal scaling at strong coupling | | D.N. Aristov
; P. Woelfle
; | | Date: |
24 Feb 2009 | | Abstract: | We calculate the linear response conductance of electrons in a Luttinger
liquid with arbitrary interaction g_2, and subject to a potential barrier of
arbitrary strength, as a function of temperature. We map the Hamiltonian in the
basis of scattering states into an effective low energy Hamiltonian in current
algebra form. First the renormalization group (RG) equation for weak
interaction is derived in the current operator language both using the operator
product expansion and the equation of motion method. To access the strong
coupling regime, two methods of deducing the RG equation from perturbation
theory, based on the scaling hypothesis and on the Callan-Symanzik formulation,
are discussed. The important role of scale independent terms is emphasized. The
latter depend on the regulaization scheme used (length versus temperature
cutoff). Analyzing the perturbation theory in the fermionic representation, the
diagrams contributing to the renormalization group beta-function are
identified. A universal part of the beta-function is given by a ladder series
and summed to all orders in g_2. First non-universal corrections beyond the
ladder series are discussed and are shown to differ from the exact solutions
obtained within conformal field theory which use a different regularization
scheme. The RG equation for the temperature dependent conductance is solved
analytically. Our result agrees with known limiting cases. | | Source: | arXiv, 0902.4170 | | Services: | Forum | Review | PDF | Favorites | |
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