Conformal Field Theory Approach to One-Dimensional Quantum Liquids

Abstract
We review the critical behavior of 1D highly correlated electron systems and 1D quantum many-body systems with long-range interactions. These models exhibit the common universal long-distance properties which are characterized as Luttinger liquids. The microscopic foundation of Luttinger liquids is formulated on the basis of conformal field theory and Bethe-ansatz solutions.

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