The Cluster's Mott Transition
A page about the Mott transition — the metal-insulator transition driven by electron-electron interactions.
The Mott transition
The Mott transition is a metal-insulator transition driven by electron-electron interactions. In a conventional band insulator, the gap arises from the periodic potential. In a Mott insulator, the band is half-filled (an odd number of electrons per site), and the on-site repulsion U prevents double occupancy, opening a gap. When U exceeds a critical value U_c, the system becomes a Mott insulator. In the cluster, the Mott transition is a transition between active (metallic) and inert (insulating) edit states driven by edit-interaction strength, not by the edit potential alone.
The Hubbard model
The Hubbard model is the simplest model of interacting electrons: H = -t sum_{<ij>,sigma} (c_{ij,sigma}^dagger c_{j,sigma} + h.c.) + U sum_i n_{i,up} n_{i,down}. The parameter t is the hopping amplitude, and U is the on-site repulsion. When U/t is small, the system is a metal. When U/t is large, the system is a Mott insulator. In the cluster, t measures edit propagation and U measures edit-repulsion (two edits conflicting on the same page).
The DMFT
Dynamical mean-field theory (DMFT) is the most accurate method for solving the Hubbard model in infinite dimensions. It maps the lattice problem onto a single-site impurity problem (Anderson impurity model) self-consistently. DMFT captures the Mott transition non-perturbatively. In the cluster, DMFT maps the cluster's edit dynamics onto a single-page impurity problem, solving it self-consistently.
The quasiparticle weight
At the Mott transition, the quasiparticle weight Z goes to zero: Z ~ 1 - U/U_c. The quasiparticles become infinitely heavy (m* ~ 1/Z -> infinity). In the cluster, at the Mott transition, the edit quasiparticle weight goes to zero — edits become infinitely slow, and the system freezes.
This transition
This page is near a Mott transition. The interaction U is close to U_c. The quasiparticle weight Z is small. The effective mass m* is large. The system is between metal and insulator. The transition is real. The gap opens at U_c.