Exact Derivation of Luttinger Liquid Relation in a One-Dimensional Two-Component Quantum System with Hyperbolic Interactions

Abstract

We present an exact calculation of the Luttinger liquid relation for the one-dimensional, two-component SC model in the interaction strength range $-1<s<0$ by appropriately varying the limits of the integral Bethe Ansatz equations. The result is confirmed by numerical and conformal methods. By a related study of the transport properties of the SC model, we can give an exact formula for the susceptibility. Our method is applicable to a wide range of models such as, e.g., the Heisenberg-Ising chain.

10 REVTeX pages + 1 uuencoded figure, UoU-0010294

References in corpus (5)

• Quantum Inverse Scattering Method and Correlation Functions
• Exiton, Spinon and Spin Wave Modes in an Exactly Soluble One-Dimensional Quantum Many-Body System
• Twisted Boundary Conditions and the Adiabatic Ground State for the Attractive XXZ Luttinger Liquid
• Test of Conformal Invariance in One-Dimensional Quantum Liquid with Long-Range Interaction
• Critical Exponents for the SC-Model in the Zero Sector

Cited by in corpus (3)

• The Aharonov-Bohm effect for an exciton
• Absence of backscattering at integrable impurities in one-dimensional quantum many-body systems
• Transport Properties of a One-Dimensional Two-Component Quantum Liquid with Hyperbolic Interactions