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Series on directions in condensed matter physics

BOSONIZATION AND ITS APPLICATION TO TRANSPORT IN QUANTUM WIRES

Feifei Li

Published Oct 24, 2013• 0 citations
Publisher

Abstract

This paper reviews the method of bosonization for one-dimensional interacting fermions. Example of its application to mesoscopic systems is presented with an explicit calculation of the spin and charge currents in an interacting quantum wire subject to a uniform magnetic field and alternating voltage source. Special emphasis is given to the details of the calculation using bosonization and Keldysh techniques.

DOI
10.1142/9789814520720_0010

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This paper reviews the method of bosonization for one-dimensional interacting fermions. Example of its application to mesoscopic systems is presented with an explicit calculation of the spin and charge currents in an interacting quantum wire subject to a uniform magnetic field and alternating voltage source. Special emphasis is given to the details of the calculation using bosonization and Keldysh techniques.
This chapter discusses the technique of bosonization for studying systems of interacting fermions in one dimension. It reviews the low-energy properties of Fermi and Luttinger liquids and presents some of the relations between bosonic and fermionic operators in one dimension. The chapter explores these relations to calculate the correlation functions and the renormalization group properties of various operators for a system of spinless fermions. It explains the methods of bosonization to study the Heisenberg antiferromagnetic spin 1/2 chain, the Hubbard model in one dimension and transport in clean quantum wires and in the presence of isolated impurities. The basic idea of bosonization is that there are certain objects which can be calculated either in a fermionic theory or in a bosonic theory, and the two calculations give the same answer. The chapter also discusses another application of bosonization, which is to study transport, in particular the DC conductivity in one-dimensional wires of interacting fermions.
We discuss the technique of bosonization for studying systems of interacting fermions in one dimension. After briefly reviewing the low-energy properties of Fermi and Luttinger liquids, we present some of the relations between bosonic and fermionic operators in one dimension. We use these relations to calculate the correlation functions and the renormalization group properties of various operators for a system of spinless fermions. We then apply the methods of bosonization to study the Heisenberg antiferromagnetic spin 1/2 chain, the Hubbard model in one dimension and transport in clean quantum wires and in the presence of isolated impurities.
We discuss the technique of bosonization for studying systems of interacting fermions in one dimension. After briefly reviewing the low-energy properties of Fermi and Luttinger liquids, we present some of the relations between bosonic and fermionic operators in one dimension. We use these relations to calculate the correlation functions and the renormalization group properties of various operators for a system of spinless fermions. We then apply the methods of bosonization to study the Heisenberg antiferromagnetic spin 1/2 chain, the Hubbard model in one dimension, and transport in clean quantum wires and in the presence of isolated impurities.
xi The transport properties of a one dimensional disordered system of interacting spinpolarized electrons is studied using a bosonized field theory. In contrast to other approaches in that field [3], [2], a fully bosonized action on the Keldysh contour is used to calculate disorder averaged observables. After a brief introduction to Fermi and Luttinger liquids, we review bosonization, the Keldysh technique and disorder effects in mesoscopic systems. We calculate the first order correction to the clean conductivity in the disorder strength in order to develop a diagrammatic technique for a bosonized system on the Keldysh contour. Furthermore, the dissipative part of the self energy of the retarded plasmonic Green’s function is calculated via equations of motion in the high temperature regime. Corrections to the Drude conductivity of order = 1−K (weak interactions) and ωβ (high temperature) are calculated representing the terms beyond the saddle point approximation.