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Physical Review Letters

Conservation Laws and Bosonization in Integrable Luttinger Liquids

J. M. P. Carmelo, A. H. Castro Neto, David K Campbell

Published Apr 10, 1995• 10 citations
Publisher

Abstract

After this Letter had gone into print, I became aware of recent work by Bhattacharjee and Rajasekaran [1 -4]
DOI
10.1103/physrevlett.74.3089.2

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We examine and explain the Luttinger-liquid character of models solvable by the Bethe ansatz by introducing a suitable bosonic operator algebra. In the case of the Hubbard chain, this involves two bosonic algebras which apply to all values of U, electronic density, and magnetization. Only at zero magnetization does not lead to the usual charge-spin separation. We show that our ``pseudoparticle'' operator approach clarifies, unifies, and extends several recent results, including the existence of independent right and left equations of motion and the concept of ``pseudoparticle'' (also known as ``Bethe quasiparticle'').
The low-energy properties of interacting Fermi systems are highly constrained by conservation laws. They generally simplify the structure of the underlying renormalization group by reducing the number of independent renormalization constants. In one dimension, all properties of normal metallic fixed points are uniquely determined by separate charge and spin conservation for states near the left and right Fermi points, respectively. We construct the general Luttinger-liquid theory of one-dimensional (1D) metals directly from these conservation laws. Luttinger-liquid parameters emerge naturally from the velocities associated with the conserved currents at the Luttinger-liquid fixed point. Instead of bosonization, one may thus use techniques familiar from Fermi-liquid theory, i.e., Feynman diagrams, equations of motion, and Ward identities. The choice of a technique comprising both Fermi- and Luttinger-liquid theory makes the similarities and differences of both theories particularly transparent, and sets the stage for constructing non-Fermi-liquid metallic fixed points in d>1. Several generic properties and asymptotic conservation laws of 2D non-Fermi-liquid metals are discussed.
We discuss phases of interacting fermionic Luttinger liquids without particle number conservation, such as those in proximity to a superconductor, subjected to weak continuous measurements of their particle density, in the regime where the bosonization approach is applicable. We show that the phases of these systems are controlled by the competition between measurements, which favor the area-law phase and particle tunneling in and out of the Luttinger liquid, which favors the volume-law phase. The volume-law phase in this system is always charge fuzzy. We show that within this framework, the phase boundary between the two phases is given by a universal dependence of the Luttinger parameter on the measurement rate. This behavior can be contrasted with the non-universal phase boundaries in more generic highly excited one dimensional systems whose behavior is no longer captured by the Luttinger liquid framework.