Numerically Exact Simulation of Photodoped Mott Insulators

A description of long-lived photodoped states in Mott insulators is challenging, as it needs to address exponentially separated timescales. We demonstrate how properties of such states can be computed using numerically exact steady state techniques, in particular, the quantum Monte Carlo algorithm, by using a time-local ansatz for the distribution function with separate Fermi functions for the electron and hole quasiparticles. The simulations show that the Mott gap remains robust to large photodoping, and the photodoped state has hole and electron quasiparticles with strongly renormalized properties.

Figure 1

Time evolution of the photoexcited state, initially prepared at $T_i=2.0$. (a) Expectation value of the double occupancy $d(t)$ (left axis) an kinetic energy $K(t)$ (right axis). (b) Spectral function $A(\omega ,t)$ (solid line) and occupied density of states $A^{<}(\omega ,t)$ (shaded area) for different representative times. (c) Distribution function $F(\omega ,t)$ at different times. Dashed lines in (b) show the spectra obtained from the TLFA, with the corresponding distribution function taken from (c).

Figure 2

(a) Comparison of the spectral function $A(\omega )$ for given $n_{\mathrm{ex}}$, obtained by inchworm QMC (solid lines) and by NCA (transparent lines), at temperature $T_{\mathrm{\Delta }}=1/12.5$. (b) Comparison as in (a) with AMEA spectra using six (dashed gray line) and eight bath sites (solid gray line), for $n_{\mathrm{ex}}=0.06$. (c) The Mott gap ${\mathrm{\Delta }}_{\mathrm{g}}$ for all three approaches. The gap is defined by the spectral weight reaching 0.057, which is half of the maximum of the equilibrium spectrum. For a visualization of the inchworm QMC error, the mean of five inchworm DMFT iterations is plotted together with the standard deviation (shaded region).

Figure 3

(a) Spectral function $A(\omega )$ at $n_{\mathrm{ex}}=0.45$, obtained with inchworm QMC (solid lines) and NCA (transparent lines), at temperature $T_{\mathrm{\Delta }}=1/12.5$. The colored areas denote the occupied spectrum $A^{<}(\omega )$. (b) Comparison of the inchworm QMC (solid lines) and NCA (transparent lines) distribution function $F(\omega )$ at $n_{\mathrm{ex}}=0.45$ and temperature $T_{\mathrm{\Delta }}=1/12.5$. The mean of five inchworm DMFT iterations is plotted together with the standard deviation (shaded region).

Figure 4

(a) Distribution function $F(\omega )$ at $n_{\mathrm{ex}}=0.06$, obtained with inchworm QMC (solid lines) and NCA (transparent lines), at temperature $T_{\mathrm{\Delta }}=1/12.5$. (b) Effective temperature $T_{\text{G},\mathrm{NCA}}/T_{\mathrm{\Delta }}$ (left axis) and $T_{\text{G},\mathrm{inch}}/T_{\mathrm{\Delta }}$ (right axis) of the quasiparticle excitations using the two methods in relation to $T_{\mathrm{\Delta }}$. For a visualization of the Monte Carlo error, the mean of five inchworm DMFT iterations is plotted together with the standard deviation (shaded region).