Wednesday, September 4, 2013

Emergence of dynamical particle-hole asymmetry

Largely due to the work of Sriram Shastry I have recently become aware that particle-hole asymmetry in strongly correlated electron systems is an important issue (and challenge).
This was flagged in an earlier post.

There are a number of experimental anomalies that suggest the asymmetry is much larger than that associated with band structure effects. These include:

-highly asymmetric ARPES line shapes in the cuprates
-the slope of the I-V characteristics for some STM spectra
-a thermoelectric power that is large and changes sign with temperature in some cuprates

Theoretically it has been a puzzle that theoretical calculations for doped Mott insulators often give self energies that have a large particle-hole asymmetry. See for example Figure 3 in this PRL, Figure 13 of this PRB, and the figure below. It is very different from the perfect particle-hole symmetry implicit in Fermi liquid theory and marginal Fermi liquid theory. Also the quadratic frequency dependence only appears over a narrow frequency range, leading to kinks in the quasi-particle dispersions.

There is a new preprint
Extremely Correlated Fermi Liquid study of the U=infinity Anderson Impurity Model
by Sriram Shastry, Edward Perepelitsky, and Alex Hewson

The frequency dependence of the self energy for a range of impurity occupations n is shown below.

The authors show how this asymmetry emerges naturally in terms of Shastry's theory of an Extremely Correlated Fermi liquid that has two Fermi liquid type "self energies", elucidated in this PRB and particularly in this talk. In particular, there is an emergent low-energy scale Delta associated with the asymmetry.

I thank Sriram and Edward for helpful discussions about their work.


  1. Clicked around his Prof. Shastry's webpage yesterday after reading this post. He has a great Mathematica plug-in (apologies if it's not technically called a plug-in) called DiracQ, which allows to do quantum algebra, construct Hamiltonians and many other things. Looks like it might really come in handy at times.

  2. Yes. Sriram told me about this. I had a quick look and was planning a blog post about it. DiracQ looks very useful.