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arXiv:1211.2083 · Modern Physics Letters B

LOCAL ENTANGLEMENT ENTROPY AT THE MOTT METAL-INSULATOR TRANSITION IN INFINITE DIMENSIONS

DAN-DAN SU, Xi Dai, NING-HUA TONG

Published Feb 5, 2013• 7 citations
arXivHTMLPDF

Abstract

We study the critical behavior of the single-site entanglement entropy S at the Mott metal-insulator transition in infinite-dimensional Hubbard model. For this model, the entanglement between a single site and rest of the lattice can be evaluated exactly, using the dynamical mean-field theory (DMFT). Both the numerical solution using exact diagonalization and the analytical one using two-site DMFT gives S - Sc∝ α log2[(1/2 - Dc)/Dc](U - Uc), with Dcthe double occupancy at Ucand α < 0 being different on two sides of the transition.

DOI
10.1142/s0217984913500346

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We study the critical behavior of the single-site entanglement entropy S at the Mott metal-insulator transition in infinite-dimensional Hubbard model. For this model, the entanglement between a single site and rest of the lattice can be evaluated exactly, using the dynamical mean-field theory (DMFT). Both the numerical solution using exact diagonalization and the analytical one using two-site DMFT gives S - Sc∝ α log2[(1/2 - Dc)/Dc](U - Uc), with Dcthe double occupancy at Ucand α < 0 being different on two sides of the transition.
Using dynamical mean field theory (DMFT) in combination with a continuous-time quantum Monte Carlo (DMFT+CTQMC) tool, we studied the von Neumann entanglement entropy (S) in a bilayer Hubbard model on the Bethe lattice. Jump behaviors in S are observed at the critical points among the Fermi liquid, the Mott insulator, and the band insulator at a low temperature, similar to the results in a double occupancy which the DMFT+CTQMC method can easily calculate. As novel results that the double occupancy cannot account for, the behaviors of S in the weak region with metallic states can supply information on the coherence temperature and the Fermi temperature without the need to analyze the transport properties through analytical continuation of the self-energy or differentiation of the energy. In addition, when the strength of the interlayer hopping is tuned in the strong interaction region, S increases in the Mott phase owing to the short-range spatial fluctuations between impurities of bilayers while it decreases in the band phase. These behaviors mean that S might provide a criterion for separation between the Mott insulator and the band insulator as an order parameter in the strong interaction region.
The Mott metal-insulator transition in the two-band Hubbard model in infinite dimensions is studied by using the linearized dynamical mean-field theory. The discontinuity in the chemical potential for the change from hole to electron doping is calculated analytically as a function of the on-site Coulomb interaction UUU at the ddd-orbital and the charge-transfer energy ΔΔΔ between the ddd- and ppp-orbitals. Critical behaviour of the quasiparticle weight is also obtained analytically as a function of UUU and ΔΔΔ. The analytic results are in good agreement with the numerical results of the exact diagonalization method.
Abstract The Mott transition is a paradigmatic phenomenon where Coulomb interactions between electrons drive a metal‐insulator phase transition. It is extensively studied within the Hubbard model, where a quantum critical transition occurs at a finite temperature second‐order critical point. This work investigates the Mott transition in a modified periodic Anderson model that may be viewed as a three‐orbital lattice model including an interacting, localized orbital coupled to a delocalized conduction orbital via a second conduction orbital. Within the dynamical mean field theory, this model possesses a strictly zero temperature quantum critical point separating a Fermi liquid and a Mott insulating phase. By employing a simplified version of the dynamical mean field theory, namely, the two‐site or linearized dynamical mean field theory, an analytical estimate is provided for the critical parameter strengths at which the transition occurs at zero temperature. An analytical estimate of the single‐site von Neumann entanglement entropy is also provided. This measure can be used as a robust identifier for the phase transition. These calculations are extended to their cluster version to incorporate short‐range, spatial correlations and discuss their effects on the transition observed in this model.
We address the nature of the Mott transition in the Hubbard model at half-filling using cluster dynamical mean field theory (DMFT). We compare cluster-DMFT results with those of single-site DMFT. We show that inclusion of the short-range correlations on top of the on-site correlations does not change the order of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical U and modify the shape of the transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition point. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale. The insulating state is characterized by the narrow Mott gap with pronounced peaks at the gap edge.
The possibility to directly measure, in a cold-atom quantum simulator, the von Neumann entropy and mutual information between a site and its environment opens new perspectives on the characterization of the Mott-Hubbard metal-insulator transition, in the framework of quantum information theory. In this work, we provide an alternative view of the Mott transition in the two-dimensional Hubbard model in terms of rigorous quasilocal measures of entanglement and correlation between two spatially separated electronic orbitals, with no contribution from their environment. A space-resolved analysis of cluster dynamical mean-field theory results elucidates the prominent role of the nearest-neighbor entanglement in probing Mott localization: both its lower and upper bounds sharply increase at the metal-insulator transition. The two-site entanglement beyond nearest neighbors is shown to be quickly damped as the intersite distance is increased. These results ultimately resolve a conundrum of previous analyses based on the single-site von Neumann entropy, which has been found to monotonically decrease when the interaction is increased. The quasilocal two-site entanglement recovers instead the distinctive character of Mott insulators as strongly correlated quantum states, demonstrating its central role in the 2d2d2d Hubbard model.
Quantum entanglement, lacking any classical counterpart, provides a fundamental new route to characterize the quantum nature of many-body states. In this work, we discuss an implementation of a new path integral method [Phys. Rev. Res. 2, 033505 (2020)] for fermions to compute entanglement for extended subsystems in the Hubbard model within dynamical mean-field theory (DMFT) in one and two dimensions. The new path integral formulation measures entanglement by applying a ``kick'' to the underlying interacting fermions. We show that the R\'enyi entanglement entropy can be extracted efficiently within the DMFT framework by integrating over the strength of the kick term. Using this method, we compute the second R\'enyi entropy as a function of subsystem size for metallic and Mott insulating phases of the Hubbard model. We explore the thermal entropy to entanglement crossover in the subsystem R\'enyi entropy in the correlated metallic phase. We show that the subsystem-size scaling of the second R\'enyi entropy is well described by the crossover formula which interpolates between the volume-law thermal R\'enyi entropy and the universal boundary-law R\'enyi entanglement entropy with logarithmic violation, as predicted by conformal field theory. We also study the mutual information across the Mott metal-insulator transition.