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Fermi-like Liquid From Einstein-DBI-Dilaton System

High Energy Physics - Theory 2013-04-12 v5 Strongly Correlated Electrons

Abstract

We have obtained an expression of the entropy density depending on the scale transformation of the spatial directions in the field theory. It takes the following form in d+1d+1 dimensional bulk spacetime: sTH\fδ(d1)θzs\sim T^{\f{\delta(d-1)-\theta}{z}}_H, where zz and THT_H are the dynamical exponent and temperature in the field theory, respectively. θ\theta is related to the scaling violation exponent, whereas δ\delta gives us the information about the scaling behavior of the spatial field theoretic direction. This we demonstrate by finding solutions to the Einstein-DBI-dilaton system in generic spacetime dimensions. Upon restricting to d=3d=3, we show the linear temperature dependence of the specific heat and inverse quadratic temperature dependence of the resistivity for z=2,θ=0z=2,\theta=0 and δ=1\delta=1, which resembles that of the Fermi-like liquid. Whereas for z=2,θ=2z=2, \theta=-2 and δ=0\delta=0 gives us a solution that is conformal to AdS2R2AdS_2\otimes R^2, which resembles with the non-Fermi-like liquid. Moreover, it shows the logarithmic violation of the entanglement entropy when the entangling region is of the strip type.

Keywords

Cite

@article{arxiv.1209.3559,
  title  = {Fermi-like Liquid From Einstein-DBI-Dilaton System},
  author = {Shesansu Sekhar Pal},
  journal= {arXiv preprint arXiv:1209.3559},
  year   = {2013}
}

Comments

1+39 pages, LATEX, v2: Connection with the BI black holes made, associated references and acknowledgment added, v3: Solutions in arbitrary spacetime both at UV and IR, especially the scale symmetry violating solution, improved presentation, ref added, v4: More improvements and accepted for publication in JHEP

R2 v1 2026-06-21T22:06:02.502Z