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arXiv 1209.3559hep-thcond-mat.str-el
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Einstein-DBI-Dilaton系统中的类费米液体

Fermi-like Liquid From Einstein-DBI-Dilaton System

Shesansu Sekhar Pal

摘要:

在场论中,我们得到了依赖于空间方向尺度变换的熵密度的表达式。它在$d+1$维体时空中有如下形式:$s\sim T^{\f{δ(d-1)-θ}{z}}_H$,其中$z$和$T_H$分别是场论中的动力学指数和温度。$θ$与标度破坏指数有关,而$δ$则为我们提供了关于空间场理论方向标度行为的信息。这一点,我们证明了寻找解决方案的爱因斯坦-DBI-介子系统在通用时空维度。在限制到$d=3$,我们显示的线性温度依赖性的比热和反二次温度依赖性的电阻率$z=2,θ=0$和$δ=1$,这类似于费米液体。而对于$z=2, θ=-2$和$δ=0$,我们给出了一个与$AdS_2\otimes R^2$共形的解,这与非类费米液体相似。当纠缠区为条形时,纠缠熵出现对数破坏。

英文摘要:

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 $d+1$ dimensional bulk spacetime: $s\sim T^{\f{δ(d-1)-θ}{z}}_H$, where $z$ and $T_H$ are the dynamical exponent and temperature in the field theory, respectively. $θ$ is related to the scaling violation exponent, whereas $δ$ 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 $d=3$, we show the linear temperature dependence of the specific heat and inverse quadratic temperature dependence of the resistivity for $z=2,θ=0$ and $δ=1$, which resembles that of the Fermi-like liquid. Whereas for $z=2, θ=-2$ and $δ=0$ gives us a solution that is conformal to $AdS_2\otimes R^2$, 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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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