Bounded Luttinger liquids as a universality class of quantum critical behavior

TL;DR

This paper introduces 'bounded Luttinger liquids' as a new universality class for one-dimensional quantum systems with open boundaries, sharing key properties with traditional Luttinger liquids but exhibiting boundary-dependent critical exponents.

Contribution

It defines and characterizes bounded Luttinger liquids, extending the understanding of quantum critical behavior in 1D systems with open boundary conditions, and relates theory to experimental observations.

Findings

Bounded Luttinger liquids share key properties with traditional Luttinger liquids.

Critical exponents depend on boundary conditions but are parametrized by boundary-independent constants.

Application to organic conductors shows potential reconciliation of theory with experimental photoemission data.

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 $(TMTSF)_2X$, 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.