Bekenstein-Hawking Entropy and Strange Metals
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The combination of general relativity and quantum theory led Jacob Bekenstein and Stephen Hawking to the startling result that black hole horizons obey thermodynamics and possess an entropy and a temperature. A reasonable interpretation of the black hole entropy is that it is associated with quantum degrees of freedom at the very small Planck length scale. Thus far, this interpretation has only been verified using models that derive from string theory.
In a new article* in Physics Review X, Prof. Subir Sachdev examines a class of models long-studied as simple descriptions of the “strange metal” phase of high-temperature superconductors and other correlated electron compounds. He shows that their quantum correlations and thermodynamic properties match precisely with those of the horizons of “extremal” charged black holes, including Bekenstein-Hawking entropy.
Sachdev focuses on planar, charged black holes described by the Maxwell-Einstein theory, although the findings can also be applied to a large class of charged black holes. The models of fermions which are considered in this study interact over an infinite range, and their entropy is nonzero even at zero temperature. Sachdev mathematically shows that the quantum and thermal properties of the strange metal state, i.e., a quantum state without quasiparticle excitations proposed by Sachdev and Ye in 1993 (and similar to observations in cuprates), map to analogous properties of planar, charged black holes. In particular, the Sachdev and Ye state and the Bekenstein-Hawking entropy can be described by analogous equations.
These findings are expected to increase our understanding of quantum states of matter and the dynamics of black hole horizons.
* see Subir Sachdev, "Bekenstein-Hawking Entropy and Strange Metals," Phys. Rev. X 5, 041025 (2015) DOI: http://dx.doi.org/10.1103/PhysRevX.5.041025