Bounded Luttinger liquids as a universality class of quantum critical behavior
Johannes Voit, Yupeng Wang, M. Grioni
We show that one-dimensional quantum systems with gapless degrees of freedom and open boundary conditions form a universality class of quantum critical behavior, which we propose to call ``bounded Luttinger liquids.'' They share the following properties with ordinary (periodic) Luttinger liquids: the absence of fermionic quasiparticle excitations, charge-spin separation, and anomalous power-law correlations with exponents whose scaling relations are parametrized by a single coupling constant per degree of freedom, ${K}_{\ensuremath{\nu}}.$ The values of ${K}_{\ensuremath{\nu}}$ are independent of boundary conditions, but the representation of the critical exponents in terms of these ${K}_{\ensuremath{\nu}}'\mathrm{s}$ 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 one-dimensional 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 $(\mathrm{TMTSF}{)}_{2}X,$ where TMTSF is tetramethyltetraselenafulvalene, and $X={\mathrm{ClO}}_{9},$ ${\mathrm{PF}}_{6},$ $\mathrm{Re}{\mathrm{O}}_{4},$ 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.
arXiv:cond-mat/9912392•Physical review. B, Condensed matter•Mar 15, 2000•34 citations