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arXiv 1005.4690hep-thcond-mat.str-elgr-qc
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低温condensed matter体系的有效全息理论

Effective Holographic Theories for low-temperature condensed matter systems

C. Charmousis, B. Goutéraux, B. S. Kim, E. Kiritsis, Rene Meyer

摘要:

分析了在强耦合条件下,电荷密度与主导标量算符相互作用的有效全息理论的红外动力学。这样的理论是参数化的两个真正的指数$(γ,δ)$,控制IR动力学。通过研究几类完全包含电荷密度反作用的带电电子黑洞解的热力学、光谱和电导率,描述了这类理论在凝聚态应用中的前景。$(γ,δ)$平面的几个区域可以被排除,因为极值解具有不可接受的奇异性。经典解在零温度下一般熵为零,除了当$γ=δ$在极值点熵为有限时。发现在整个$(γ,δ)$平面上,低温下直流电阻率和低频下交流电导率随温度的变化具有普遍的标度性,存在一个余维一区域,直流电阻率与温度呈线性关系.对于大规模的运营商,它示出,当标量运营商是不是的drons,直流电阻率缩放为平面(3D)系统的热容(和熵)。区域确定在有限密度的理论是一个莫特样绝缘体在T=0。我们还发现,在足够低的温度下,由于载流子的熵一般大于在零电荷密度。

英文摘要:

The IR dynamics of effective holographic theories capturing the interplay between charge density and the leading relevant scalar operator at strong coupling are analyzed. Such theories are parameterized by two real exponents $(γ,δ)$ that control the IR dynamics. By studying the thermodynamics, spectra and conductivities of several classes of charged dilatonic black hole solutions that include the charge density back reaction fully, the landscape of such theories in view of condensed matter applications is characterized. Several regions of the $(γ,δ)$ plane can be excluded as the extremal solutions have unacceptable singularities. The classical solutions have generically zero entropy at zero temperature, except when $γ=δ$ where the entropy at extremality is finite. The general scaling of DC resistivity with temperature at low temperature, and AC conductivity at low frequency and temperature across the whole $(γ,δ)$ plane, is found. There is a codimension-one region where the DC resistivity is linear in the temperature. For massive carriers, it is shown that when the scalar operator is not the dilaton, the DC resistivity scales as the heat capacity (and entropy) for planar (3d) systems. Regions are identified where the theory at finite density is a Mott-like insulator at T=0. We also find that at low enough temperatures the entropy due to the charge carriers is generically larger than at zero charge density.

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