Bekenstein-Hawking Entropy and Strange Metals (1506.05111v4)

Abstract: We examine models of fermions with infinite-range interactions which realize non-Fermi liquids with a continuously variable U(1) charge density $\mathcal{Q}$, and a non-zero entropy density $\mathcal{S}$ at vanishing temperature. Real time correlators of operators carrying U(1) charge $q$ at a low temperature $T$ are characterized by a $\mathcal{Q}$-dependent frequency $\omega_{\mathcal{S}} = (q \, T/\hbar) (\partial \mathcal{S}/\partial{\mathcal{Q}})$ which determines a spectral asymmetry. We show that the correlators match precisely with those of the AdS$_2$ horizons of extremal charged black holes. On the black hole side, the matching employs $\mathcal{S}$ as the Bekenstein-Hawking entropy density, and the laws of black hole thermodynamics which relate $(\partial{\mathcal{S}}/\partial{\mathcal{Q}})/(2 \pi)$ to the electric field strength in AdS$_2$. The fermion model entropy is computed using the microscopic degrees of freedom of a UV complete theory without supersymmetry.

• The paper establishes a correspondence between the entropy density and spectral asymmetry of the SY state and the thermodynamics of AdS2 black holes.
• It employs an infinite-range fermion model with a large-N limit to explore emergent gauge invariance in non-Fermi liquid regimes.
• The findings suggest holographic duality as a promising framework for unifying condensed matter physics with quantum gravitational insights.

Overview of Bekenstein-Hawking Entropy and Strange Metals

Subir Sachdev's paper presents a detailed examination of the connections between non-Fermi liquid behavior in strongly correlated electron systems, specifically strange metals, and concepts from gravitational physics such as Bekenstein-Hawking entropy. The author effectively utilizes an extended holographic framework to consider the SY state alongside the AdS$_2$ quantum theory, noting the remarkable overlap in their descriptions of entropy and correlation functions.

The paper begins by focusing on non-Fermi liquid systems with special emphasis on strange metals characterized by their lack of quasiparticle excitations and a conserved U(1) charge density $\mathcal{Q}$. These systems exhibit noteworthy properties such as non-zero entropy density $\mathcal{S}$ at zero temperature. A model consisting of fermions with infinite-range interactions, previously developed by Sachdev and Ye (SY), serves as the basis for exploring these properties. The SY state is analyzed through a large-N limit of a fermion Hamiltonian, facilitating a tractable path towards understanding non-Fermi liquid phenomena.

Sachdev draws a compelling parallel between the SY state and the quantum gravitational systems associated with extremal charged black holes. The correlators of the SY state match with those derived from AdS$_2$ horizons, leveraging an equivalence stemming from conformal and gauge invariances. A central finding is the relationship establishes between the entropy density of the SY state and the spectral asymmetry, $\omega_{\mathcal{S}}$, which reflects thermodynamic properties divided by $\hbar$. This relationship holds strong evidential value for a seamless transition between gravitational and non-gravitational descriptions of low-energy states in these complex systems.

Throughout the paper, Sachdev offers extensive numerical solutions and arguments supporting the equivalencies between the SY state and AdS$_2$ gravitational models. For instance, the critical correspondence of $\omega_{\mathcal{S}}$ with changes in entropy is shown to align with black hole thermodynamics, substantiating the density-dependent spectral asymmetry observed in strange metals. Additionally, an infinite-range fermion model is utilized to elucidate the emergent low-energy gauge invariance in highly correlated electronic systems, a stepping stone to probing further connections to holographic dualities.

The paper also explores a spherical black hole configuration, reasserting the theoretical predictions across varying frameworks. In both planar and spherical cases, the crucial link between entropy derivatives and spectral frequency shifts points to a potential gravitational dual description of strange metals. Despite the unique equation of states associated with each configuration, a consistent adherence to the Bekenstein-Hawking entropy underpinned by a statistical mechanical interpretation is observed.

Theoretical and practical ramifications of this research pave the way for alternative methodologies in approaching complex quantum systems, and suggest a promising direction for future inquiries. Future explorations could possibly deepen the alignment of related quantum materials phenomena with aspects of theoretical physics traditionally not associated with condensed matter systems.

Sachdev's work enhances our comprehension of the intertwining between condensed matter physics and quantum gravity, providing a cohesive narrative that could bridge these domains through shared principles of computation, symmetry, and scaling. As holographic duality continues to evolve as a potent tool for inquiry, this paper contributes significantly to the groundwork upon which new interpretations of entropy and spectral character in quantum materials can be understood and operationalized.