Fermionic transport through a driven quantum point contact: breakdown of Floquet thermalization beyond a critical driving frequency

Abstract

We study a quantum system that consists of two fermionic chains coupled by a driven quantum point contact (QPC). The QPC contains a bond with a periodically varying tunneling amplitude. Initially the left chain is packed with fermions while the right one is empty. We numerically track the evolution of the system and demonstrate that, at frequencies above a critical one, the current through the QPC halts, and the particle imbalance between the chains remains forever. This implies a spectacular breakdown of the Floquet version of the eigenstate thermalization hypothesis which predicts a homogeneous particle density profile at large times. We confirm the effect for various driving protocols and interparticle interactions.

Figures (11)

• Figure 1: The system under study consists of two fermionic tight-binding chains coupled by a bond with a periodically driven tunneling amplitude. The bond constitutes the time-dependent quantum point contact.
• Figure 2: Evolution of particle density for two driving frequencies. For a frequency below the critical one (left column) particles tend to distribute uniformly over sites. For a frequency above the critical one (right column) the particle imbalance between the chains is retained. Dashed horizontal line delineates two chains.
• Figure 3: (a) The number of particles in the right chain, $\langle N_R\rangle_t$, as a function of time for frequencies below ($\omega = 1.5$) and above ($\omega = 2.5$) the critical frequency. Steady state values computed according to eq. (\ref{['eq:steady']}) are shown by horizontal dashed lines. The horizontal black line shows the value of $N_R$ corresponding to the uniform distribution of particles over the chains. The interaction strength is $U=0.5$. The total number of sites and fermions is $2L+1 =15$ and $N=8$, respectively. (b) Diagonal matrix elements of the operator $N_R$ in Floquet basis for different Floquet energies $\epsilon_{\alpha}$.
• Figure 4: The scaling with the system size of (a) the steady state value $\langle N_R\rangle_\infty$ and (b) the maximal deviation of the diagonal matrix element $\langle \Phi_\alpha |N_R| \Phi_\alpha \rangle$ from the uniform value $\overline N_R$. The interaction strength is $U=0.5$. One can see the quantitative difference in the scaling behavior for frequencies below and above the critical frequency $\omega_c\simeq2$.
• Figure S1: Plot of the driving protocols, $f_t$, as a function of time. Here the driving frequency is set to 1.