Quantum Transport Phenomena and Anderson Localization in Disordered Lattice Models at Finite Temperatures

We present a self-contained theoretical and numerical study of the metal-insulator transition in disordered lattice models at finite temperature, with emphasis on the breakdown of purely single-particle localization pictures once thermal population effects and local multi-particle correlations are taken into account. Starting from the microscopic tight-binding Hamiltonian with on-site diagonal disorder, we construct a finite-temperature Dyson equation whose self-energy is computed through a nonlinear generalization of the self-consistent Born approximation (SCBA). Our central theoretical contribution is a cumulant-resummed correction term, δΣnl, which captures local four-point and six-point disorder correlations beyond the Gaussian (pair-correlation) level and which acquires an explicit, analytically tractable temperature dependence through the Fermi occupation factors entering the Keldysh contour. We derive, with full proofs, a modified diffusion equation for the finite-temperature density propagator and establish existence and uniqueness of its stationary solution below a renormalized mobility edge. Using a rigorous finite-temperature Keldysh-Kubo formalism we obtain the nonequilibrium conductivity tensor and show how thermal broadening shifts the mobility edge Ec(T). In the original analytical results section we derive a closed-form estimate for the thermally dressed localization length $\xi (T)$ and show that the associated critical exponent acquires a temperature-dependent renormalization ν(T)=ν0(1+bTp) within the validity domain of the cumulant expansion. These analytical predictions are then checked against a transfer-matrix numerical protocol based on QR-reorthonormalized Lyapunov exponent computation with finite-size scaling extrapolation.