Nonperturvative behavior of the quantum phase transition to a nematic fluid

M LAWLER; D BARCI; V FERNÁNDEZ; E FRADKIN; L OXMAN

PHYSICAL REVIEW B - CONDENSED MATTER AND MATERIALS PHYSICS

American Physical Society

Año: 2006 vol. 73 p. 85101 - 85101

0163-1829

We discuss shape (Pomeranchuk) instabilities of  the Fermi surface of a two-dimensional Fermi system using bosonization. We consider in detail the quantum critical behavior of the transition of a two dimensional Fermi fluid to a nematic state which breaks spontaneously the rotational invariance of the Fermi liquid. We show that higher dimensional bosonization reproduces the quantum critical behavior expected from the Hertz-Millis analysis, and verify that this theory has dynamic critical exponent $z=3$. Going beyond this framework, we study the behavior of the degrees of freedom directly, and show that at quantum criticality as well as in the the quantum nematic phase (except along a set of measure zero of symmetry-dictated directions) the quasi-particles of the normal Fermi liquid are generally wiped out. Instead, they exhibit short ranged spatial correlations that decay faster than any power-law, with the law $|x|^{-1} exp(- extrm {const.};|x|^{1/3})$. In contrast, the fermion auto-correlation function has the behavior $|t|^{-1}  exp(-{ m const}.; |t|^{-2/3})$. In this regime we also that, at low frequency, the  single-particle fermion density-of-states behaves as $N^*(omega)=N^*(0)+ B; omega^{2/3} log omega +ldots$, where $N^*(0)$ is larger than the Fermi liquid value, $N(0)$, and $B$ is a constant.  These results confirm the non-Fermi liquid nature of both the quantum critical theory and of the nematic phase.