arXiv 1306.38162013-06hep-th

用D-膜探测全息半局域量子液体

Probing holographic semi-local quantum liquids with D-branes

Da-Wei Pang

备注：: 18 pages, typos corrected, to appear in PRD
DOI：: 10.1103/PhysRevD.88.046002

摘要：

研究了具有一般半定域性的$(d+2)$维背景下探测D-膜的动力学性质。背景由参数$η$表征并且与$AdS_{2}\times\mathbb{R}^{d}$共形。我们讨论了探测D膜的热力学性质，发现在极值处熵密度为零，这表明背景可能对应于系统的真实基态。我们还阐明了比热与费米液体或玻色液体的行为相匹配的条件。我们计算了电流-电流和密度-密度延迟格林函数，由此可以得到交流电导率和零声模。当$d/η<2$和$d/η>2$时，交流电导率分别按$ω^{-1}$和$ω^{-2η/d}$换算，而当$d/η=2$时，其在$ω$中包含对数项。我们还观察到，有没有准粒子激发时，$d/η\geq2$和分类的条件下，准粒子描述是有效的时，$d/η<2$。

英文摘要：

We study dynamics of probe D-branes in $(d+2)$-dimensional background with general semi-locality. The background is characterized by a parameter $η$ and is conformal to $AdS_{2}\times\mathbb{R}^{d}$. We discuss thermodynamics of the probe D-branes and find that the entropy density is vanishing in the extremal limit, which indicates that the background may correspond to the true ground state of the system. We also clarify the conditions under which the specific heat matches to the behavior of a Fermi liquid or a Bose liquid. We calculate the current-current and density-density retarded Green's functions, from which we can obtain the AC conductivity and the zero sound mode. The AC conductivity scales as $ω^{-1}$ when $d/η<2$ and $ω^{-2η/d}$ when $d/η>2$, while it contains a logarithmic term in $ω$ when $d/η=2$. We also observe that there is no quasi-particle excitation when $d/η\geq2$ and classify the conditions under which the quasi-particle description is valid when $d/η<2$.

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