Dates: Thursday April 7, 14 & 21
Time: 16h00 - 18h00
Location: Maison des Magistères
Synopsis
In the presence of interactions, one-dimensional systems behave very differently from their higher-dimensional counterparts.
First the pecularities of one dimension will be discussed. We will see that Fermi liquid theory breaks down: the elementary excitations in 1D are not electron-like. Instead the 1D system is a so-called Tomonaga-Luttinger liquid (TLL) with collective excitations (spin & charge density waves). The basic properties of the TLL will be introduced.
Then the powerful method of bosonization will be presented. Furthermore, we will discuss the properties of correlation functions and the manifestation of TLL physics in transport properties.
We will also have a look at other methods to describe 1D physics and then discuss regimes where the TLL description is not applicable. The latter is an area of active research. Finally, we will address what happens beyond the strictly 1D limit.
Please find below a list of articles and books that address the topics presented in this course (to be completed ...):
ORIGINAL ARTICLES
S. Tomonaga, Remarks on Bloch's Method of
Sound Waves applied to Many-Fermion Problems, Prog. Theor. Phys.
5, 544 (1950).
J.M. Luttinger, An Exactly Soluble Model of
a Many-Fermion System, J. Math. Phys. 4, 1154 (1963).
F.D.M. Haldane, `Luttinger Liquid
Theory' of One-Dimensional Quantum Fluids. I. Properties of the
Luttinger Model and their Extension to the General 1D Interacting
Spinless Fermi Gas, J. Phys. C 14, 2585 (1981).
BOOKS & REVIEW ARTICLES
T. Giamarchi, Quantum Physics in One Dimension (Clarendon Press, Oxford, 2004).
A.O. Gogolin, A.A. Nersesyan & A.M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, 1998).
H.J. Schulz, G. Cuniberti & P. Pieri, Fermi liquids and Luttinger liquids, cond-mat/9807366.
M.P.A. Fisher & L.I. Glazman, Transport in a one-dimensional Luttinger liquid, cond-mat/9610037.
...
BEYOND LUTTINGER
G.A. Fiete,
The spin-incoherent Luttinger liquid, Rev. Mod. Phys. 79, 801 (2007); cond-mat/0611597.
J.S. Meyer & K.A. Matveev, Wigner crystal physics in quantum wires, J. Phys.: Condens. Matter 21, 023203 (2009); arXiv:0808.2076.
V.V. Deshpande, M. Bockrath, L.I. Glazman & A. Yacoby, Electron liquids and solids in one dimension, Nature 464, 209 (2010).
...
RECENT EXPERIMENTS
O. Auslaender, H. Steinberg, A. Yacoby, Y. Tserkovnyak, B. I. Halperin, K. W. Baldwin, L. N. Pfeiffer & K. W. West, Spin - Charge Separation and Localization in One-Dimension, Science 308, 88 (2005).
G. Barak, H. Steinberg, L.N. Pfeiffer, K.W. West, L.I. Glazman, F. von Oppen & A. Yacoby, Interacting electrons in one dimension beyond the Luttinger-liquid limit, Nature Physics 6, 489 (2010).
...
I will also post lecture notes. No guarantee for completeness and/or correctness!