Bounded Luttinger liquids as a universality class of quantum critical behavior

Abstract

We show that one-dimensional quantum systems with gapless degrees of freedom and open boundary conditions form a new universality class of quantum critical behavior, which we propose to call ``bounded Luttinger liquids''. They share the following properties with ordinary (periodic) Luttinger liquids: absence of fermionic quasi-particle excitations, charge-spin separation, anomalous power-law correlations with exponents whose scaling relations are parametrized by a single coupling constant per degree of freedom, $K_{\nu }$. The values of $K_{\nu }$ are independent of boundary conditions, but the representation of the critical exponents in terms of these $K_{\nu }$ depends on boundary conditions. We illustrate these scaling relations by exploring general rules for boundary critical exponents derived earlier using the Bethe Ansatz solution of the 1D Hubbard model together with boundary conformal field theory, and the theory of Luttinger liquids in finite-size systems. We apply this theory to the photoemission properties of the organic conductors $(TMTSF{)}_{2}X$, and discuss to what extent the assumption of finite strands with open boundaries at the sample surface can reconcile the experimental results with independent information on the Luttinger liquid state in these materials.

23 pages, no figures, to be published in PRB

References in corpus (5)

• Luttinger Liquid Behavior in Carbon Nanotubes
• On-chain electrodynamics of metallic (TMTSF)_2 X salts: Observation of Tomonaga-Luttinger liquid response
• Spectral functions of the 1D Hubbard model in the U -> \infty limit: How to use the factorized wave-function
• Friedel Oscillations in the Open Hubbard Chain
• Spectrum of boundary states in the open Hubbard chain

Cited by in corpus (19)

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• Theory of quasi-one dimensional imbalanced Fermi gases
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• Surface characterization and surface electronic structure of organic quasi-one-dimensional charge transfer salts
• Self-organized atomic nanowires of noble metals on Ge(001): atomic structure and electronic properties
• Deformed Wigner crystal in a one-dimensional quantum dot
• Small Fermi surface in the one-dimensional Kondo lattice model
• Local Spectral Weight of a Luttinger Liquid: Effects from Edges and Impurities
• Luttinger liquid superlattices: realization of gapless insulating phases
• One dimensional strongly interacting Luttinger liquid of lattice spinless fermions
• Luttinger model approach to interacting one-dimensional fermions in a harmonic trap
• Two-component Fermi gas in a one-dimensional harmonic trap
• Treatment of backscattering in a gas of interacting fermions confined to a one-dimensional harmonic atom trap
• Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap
• Correlation exponent K_rho of the one-dimensional Kondo lattice model
• Phase theory and critical exponents for the Tomonaga-Luttinger model with harmonic confinement
• Renormalization group study of Luttinger liquids with boundaries
• Bipartite Fidelity and Loschmidt Echo of Bosonic Conformal Interface