Abstract
We present an exact Monte Carlo method to simulate the nonequilibrium dynamics of electron-phonon models in the adiabatic limit of zero phonon frequency. The classical nature of the phonons allows us to sample the equilibrium phonon distribution and efficiently evolve the electronic subsystem in a time-dependent electromagnetic field for each phonon configuration. We demonstrate that our approach is particularly useful for charge-density-wave systems experiencing pulsed electric fields, as they appear in pump-probe experiments. For the half-filled Holstein model in one and two dimensions, we calculate the out-of-equilibrium response of the current and the energy after a pulse is applied as well as the photoemission spectrum before and after the pump. Finite-size effects are under control for chains of 162 sites (in one dimension) or 16×16 square lattices (in two dimensions).
Highlights
Electron-phonon interaction plays an important role in strongly correlated materials in which it can give rise to superconductivity, the formation of polarons, or chargedensity-wave (CDW) order
While previous work mainly concentrated on equilibrium properties, we show that this class of models is well suited to study the response of a minimal interacting system to a pulsed electric field as it appears in pump-probe scenarios
Using the example of the Holstein model, we demonstrate that our approach can access timescales that are long enough to reach a steady state after a pulsed electric field has been applied
Summary
Electron-phonon interaction plays an important role in strongly correlated materials in which it can give rise to superconductivity, the formation of polarons, or chargedensity-wave (CDW) order. A recent focus of pumpprobe experiments has been on CDW materials like TaS2 [2–8] or the rare-earth tri-tellurides [9,10] Pumping light into these materials can lead to a long-time ringing of the CDW amplitude mode, as observed in angle-resolved photoemission [2], and even to long-lived metastable phases showing a large change in conductivity [4]. While it is widely debated whether in these materials CDW order arises from the Peierls instability or from a purely electronic mechanism, phonons always play an important role in the out-of-equilibrium dynamics and relaxation toward a steady state.
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