Electronic Mechanism that Quenches Field-Driven Heating as Illustrated with the Static Holstein Model

Time-dependent driving of quantum systems has emerged as a powerful tool to engineer exotic phases far from thermal equilibrium, but in the presence of many-body interactions it also leads to runaway heating, so that generic systems are believed to heat up until they reach a featureless infinite-temperature state. Understanding the mechanisms by which such a heat death can be slowed down or even avoided is a major goal—one such mechanism is to drive toward an even distribution of electrons in momentum space. Here we show how such a mechanism avoids runaway heating for an interacting charge-density-wave chain with a macroscopic number of conserved quantities when driven by a strong dc electric field; minibands with nontrivial distribution functions develop as the current is prematurely driven to zero. Moreover, when approaching a zero-temperature resonance, the field strength can tune between positive, negative, or close-to-infinite effective temperatures for each miniband. Our results suggest that nontrivial metastable distribution functions should be realized in the prethermal regime of quantum systems coupled to slow bosonic modes.

Figure 1

Steady-state spectral functions. Density of states, occupation, and distribution function for electric field strengths of (a) $E=1.0$, (b) $E=2.0$, and (c) $E=3.0$. Here, $k_{B}T=0.01$, $L=42$, $\lambda =0.5$.

Figure 2

Transient nonequilibrium dynamics: (a) Electronic energy and (b) current as a function of time for different initial temperatures. The dashed line in (a) represents the time average of $E_{\mathrm{el}}(t)$ at $k_{B}T=0$. (c) Gauge-invariant momentum distribution function at $k_{B}T=0.05$. (d) Comparison of the equilibrium and steady-state electronic energies as a function of temperature. (e) Steady-state momentum distribution function for different temperatures. The labels in (a) also apply to (b) and (e). Here, $E=1.0$, $L=42$, $\lambda =0.5$.

Figure 3

Steady-state distribution functions for zero initial temperature. (a) The two quasienergies per Floquet energy window show (anti)crossings as a function of inverse field. The color coding corresponds to the spectral distribution function $f_{\infty }(\omega )$. (b) The momentum distribution function $n_{\infty }(k)$ becomes flat when $f_{\infty }({\epsilon }_{\nu })=1/2$. Dashed lines indicate the parameters chosen in Figs. 1 and 4. Here $\lambda =0.5$.

Figure 4

Steady-state distribution functions for different initial temperatures and electric field strengths of (a) $E=1.0$, (b) $E=2.0$, and (c) $E=3.0$. Here, $L=42$ and $\lambda =0.5$.