The Interplay of Thermal Melting and Pump-Driven Melting of Charge Order: A Two-Temperature Study of the Holstein Model

Abstract

Charge order driven by electron–phonon coupling is well understood at equilibrium but pump-probe experiments raise a new question: how does this order melt and recover after strong photoexcitation? A pump pulse promotes carriers across the charge-order gap and creates a nonequilibrium high-energy electronic population. In a closed system, the subsequent dynamics are constrained by energy conservation. In an ‘open system’—where the system is coupled to a thermal bath at some temperature (Formula presented.) —there are new fluctuation and dissipation processes at play. One can attempt a computational scheme that incorporates coupling of electrons to a laser pump, the coupling of system phonons to a thermal bath, and the Holstein interaction that couples electrons and phonons. We attempt an approximation where the pump-induced electronic excitations are modeled by a slowly time-varying ‘electron temperature’, (Formula presented.), indicative of a quasi-equilibrium electronic state. We solve the problem for different combinations of (Formula presented.) and (Formula presented.), probing the order parameter dynamics, the static properties and excitations in the long-time ‘quasi-steady state’, and establish a ‘phase diagram’ in terms of bath temperature and electron temperature. © 2026 by the authors.