Langevin approach to lattice dynamics in a charge-ordered polaronic system

摘要: We use a Langevin approach to treat the finite temperature dynamics of displacement variables in half-filled spinless Holstein model. Working adiabatic regime we exploit smallness parameter simplify memory effects and estimate costs from an "instantaneous" electronic Hamiltonian. phenomenological damping rate, uncorrelated thermal noise. The low state has checkerboard charge order (CO) scheme generates equilibrium thermodynamic properties that accurately match Monte Carlo results. It additionally yields dynamical structure factor, $D({\bf q}, \omega)$, field $x({\bf r}, t)$. observe four regimes with increasing temperature, $T$, classified relation ordering $T_c$, `polaron formation' $T_P$, $ T_c \ll T_P$. For $T T_c$ oscillations are harmonic, leading dispersive phonons, $T$ bringing anharmonic, momentum dependent, corrections. \sim T_c$, tunneling events r})$ occur, propagating `domain' pattern at wavevector ${\bf q} (\pi, \pi)$ energy weight \omega)$. When $T_c < T T_P$, disordered polaron regime, domain structures vanish, dispersion narrows, is lost. \gtrsim T_P$ essentially have local oscillations. propose simple models analyse this rich dynamics.