arXiv:cond-mat/0502270

Quantum Theory of Pomeranchuck Transition in Two Dimensional Fermi Liquids via High Dimensional Bosonization

Kun Yang

Published Feb 10, 2005• 1 citation

Abstract

We use high dimensional bosonization to derive an effective field theory that describes the Pomeranchuck transition in two-dimensional Fermi liquids. The bosonization approach explicitly retains all low-energy degrees of freedom of the system. The resultant theory has dynamical exponent z=2 at tree level and upper critical dimension d_c=2, thus in 2D the system is at the upper critical dimension. These results differ from those of an earlier study based on integrating out fermions.

DOI: 10.48550/arxiv.cond-mat/0502270

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arXiv:cond-mat/0502270

Quantum Theory of Pomeranchuck Transition in Two Dimensional Fermi Liquids via High Dimensional Bosonization

Kun Yang

Published Feb 10, 2005• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/0502270

Related papers

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z = 2

and the upper critical dimension is

d_c = 4-z= 2

. As a result the system is at the upper critical dimension in 2D, resulting in a Gaussian fixed point with a marginally irrelevant quartic perturbation.

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 $\ensuremath{\mid}x{\ensuremath{\mid}}^{\ensuremath{-}1}\mathrm{exp}(\ensuremath{-}\mathrm{const}\phantom{\rule{0.3em}{0ex}}\ensuremath{\mid}x{\ensuremath{\mid}}^{1∕3})$ and we verify explicitly the vanishing of the fermion residue utilizing this expression. In contrast, the fermion autocorrelation function has the behavior $\ensuremath{\mid}t{\ensuremath{\mid}}^{\ensuremath{-}1}\mathrm{exp}(\ensuremath{-}\mathrm{const}\phantom{\rule{0.3em}{0ex}}\ensuremath{\mid}t{\ensuremath{\mid}}^{\ensuremath{-}2∕3})$. In this regime we also find that, at low frequency, the single-particle fermion density of states behaves as ${N}^{*}(\ensuremath{\omega})={N}^{*}(0)+B{\ensuremath{\omega}}^{2∕3}\mathrm{ln}\ensuremath{\omega}+\ensuremath{\cdots}$, 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.

{d}_{c}=5/2

. A deviation from the critical dimension is used as a small parameter for a systematic expansion. We apply this method to the theory where two patches of the Fermi surface are coupled with a critical boson, and show that the Ising-nematic critical point is described by a stable non-Fermi liquid state slightly below the critical dimension. Critical exponents are computed up to the two-loop order.

U(1)

gauge theory occurs, which describes a separation of spin-opposite fermionic excitations. It is noted that the first two features have been discussed in a similar way in 2D and that the last one has not been reported in previous papers. The present paper is expected to be useful in understanding the Mott transition happening beyond two space dimensions.