Holographic Aspects of Dynamical Mean-Field Theory

Abstract

Dynamical mean-field theory (DMFT) is one of the most standard theoretical frameworks for addressing strongly correlated electron systems. In this study, we explore a holographic renormalization-group (RG)-like structure inherent in DMFT, which we refer to as "AdS/DMFT", by focusing on the background Bethe-lattice network behind DMFT for electrons with a semicircle density of states. We formulate an RG transformation for the branch Green's function from the outer edge to the interior of the background Bethe-lattice network, and then find that its fixed point can be interpreted as a self-consistent solution of Green's function in DMFT. Moreover, we clarify that the scaling dimensions for the branch Green's function and the boundary correlation functions of electrons at the outer edge of the Bethe-lattice network are characterized by the fixed-point Green's function, analogous to the behavior of a scalar field in an effective two-dimensional anti-de Sitter space. We also perform DMFT computations for the Bethe-lattice Hubbard model, which illustrate that the scaling dimensions capture the Mott transition in the deep interior.

Comments: 16 pages, 5 figures