TY - JOUR

T1 - Nonperturbative behavior of the quantum phase transition to a nematic Fermi fluid

AU - Lawler, Michael J.

AU - Barci, Daniel G.

AU - Fernández, Victoria

AU - Fradkin, Eduardo

AU - Oxman, Luis

N1 - Copyright:
Copyright 2012 Elsevier B.V., All rights reserved.

PY - 2006

Y1 - 2006

N2 - 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 fermion degrees of freedom directly, and show that at quantum criticality as well as in the quantum nematic phase (except along a set of measure zero of symmetry-dictated directions) the quasiparticles 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(-const x 13) and we verify explicitly the vanishing of the fermion residue utilizing this expression. In contrast, the fermion autocorrelation function has the behavior t -1 exp(-const t -23). In this regime we also find that, at low frequency, the single-particle fermion density of states behaves as N* (ω)= N* (0)+B ω23 lnω+, where N* (0) is larger than the free Fermi 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.

AB - 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 fermion degrees of freedom directly, and show that at quantum criticality as well as in the quantum nematic phase (except along a set of measure zero of symmetry-dictated directions) the quasiparticles 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(-const x 13) and we verify explicitly the vanishing of the fermion residue utilizing this expression. In contrast, the fermion autocorrelation function has the behavior t -1 exp(-const t -23). In this regime we also find that, at low frequency, the single-particle fermion density of states behaves as N* (ω)= N* (0)+B ω23 lnω+, where N* (0) is larger than the free Fermi 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.

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U2 - 10.1103/PhysRevB.73.085101

DO - 10.1103/PhysRevB.73.085101

M3 - Article

AN - SCOPUS:33244473233

VL - 73

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 8

M1 - 085101

ER -