#
APS March Meeting 2010

## Volume 55, Number 2

##
Monday–Friday, March 15–19, 2010;
Portland, Oregon

### Session L1: Novel Probes of Electron Interactions in One-Dimensional Systems

2:30 PM–5:30 PM,
Tuesday, March 16, 2010

Room: Oregon Ballroom 201

Sponsoring
Unit:
DCMP

Chair: Karyn Le Hur, Yale University

Abstract ID: BAPS.2010.MAR.L1.2

### Abstract: L1.00002 : Theory of Nonlinear Luttinger Liquids*

3:06 PM–3:42 PM

Preview Abstract
Abstract

####
Author:

Leonid Glazman

(Yale University)

We developed a generalization of the Luttinger liquid theory
which allowed us to consider threshold singularities in the
momentum-resolved dynamic response functions at arbitrary momenta
({\it i.e.}, far away from the Fermi points). The main difficulty
the new theory overcomes is the accounting for a generic
non-linear dispersion relation of quantum particles which form
the liquid. We derive an effective ``quantum impurity''
Hamiltonian which adequately describes the dynamics of the system
at the near-threshold energies. The phenomenological theory for
the constants of such Hamiltonian is built; it expresses the
constants in terms of other measurable properties (energy spectra
of the excitations) of the liquid.
One of the most important dynamic correlation functions we
consider is the momentum-resolved electron spectral function at
arbitrary momenta. The spectral function is directly measurable
in tunneling experiments. It is singular at the spectrum of the
lowest-energy excitation branch. In the absence of spin
polarization, this is the branch of spinon excitations. The
derivation of the phenomenological relations for the threshold
exponent uses the $SU(2)$ and Galilean invariance of the electron
liquid. We also consider in detail the case of single-species
fermions, which adequately describes the fully spin-polarized
electron gas [1].
The theory of threshold exponents is valid at arbitrary wave
vectors $k$, including the vicinities of Fermi points $\pm k_F$.
There, the exponents approach universal values [2] which depend
only on the Luttinger liquid parameter $K$. Remarkably, the found
exponents differ from the predictions of the conventional linear
Luttinger liquid theory. The deviations from that theory though
are confined to the region close to the threshold; while being
wide away from the Fermi points, the width of that region scales
as $|k\pm k_F|^3$ at $k\to\pm k_F$ in the absence of spin
polarization, and as $(k\pm k_F)^2$ for polarized electrons.
\\[4pt]
[1] A. Imambekov, L.I. Glazman, Phys. Rev. Lett., {\bf 102},
126405 (2009)\\[0pt]
[2] A. Imambekov, L.I. Glazman, Science, {\bf 323}, 228 (2009)

*Research supported by NSF DMR-0906498.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2010.MAR.L1.2