Probing dielectric breakdown in Mott insulators through current oscillations

(1) The paper presents a systematic numerical study of dielectric breakdown in one-dimensional Mott insulators across a wide parameter range using the Fermi-Hubbard model.

(2) By applying the Landau-Zener formalism, the authors accurately extract excitation gaps from current oscillations, with results consistent with exact diagonalization.

(3) The work provides detailed comparisons between numerical results and theoretical predictions, clarifying the conditions under which the Landau-Zener tunneling picture holds and highlighting finite-size effects.

(1) Conceptual novelty is not very high.

(2) There is room for improvement in terms of providing information and making the paper more accessible to readers by adding additional figures.

In this paper, the authors study the dielectric breakdown of
one-dimensional Mott insulators, using the Fermi-Hubbard model
with a mesoscopic size.
They numerically calculate the time evolution of current
when the magnetic flux is inserted in the ring of the Hubbard chain
(i.e., the linear sweep of the Peierls phase).

First they determine the excitation gap of the system
through the Landau-Zener formalism.
The authors regard the excitation process
from the ground state to the first excited state
as the tunneling between the two level system,
and extract the excitation gap for the oscillation of current,
which agrees with the value obtained from exact diagonalization.
They also confirm that the amplitude of the oscillation of current
scales as $\log A \propto -1/E$ concerning with the applied electric field.
They further investigate the dependence of the threshold of field strength
on the gap, which is compared with the formula predicted by
the tunneling probability formula in the Landau-Zener process.
The agreement between numerics and the formula is good
for the small gap regime, but they show deviation
when the gap is large and the correlation length becomes
shorter than the system size.

While the idea that the dielectric breakdown in a Mott insulator
is described by a Landau-Zener tunneling process is already known,
and the idea of utilizing the expression for tunneling probability
arises naturally, the present work provides a systematic numerical
investigation over a wide range of parameter region.
The detailed comparison with the numerical results and prediction
by the formula helps to clarify the picture of excitation process
of Mott insulators, and the results should be of interest
to researchers of nonequilibrium phenomena in strongly correlated systems.
Thus I think that the manuscript is suitable for publication.
Before its publication, I would like the authors
to consider the following points.

(1) Adding the figures for the Fourier transform of current
shown in Figs. 3 and 5 would be helpful for the readers.

(2) In Fig. 8, I am interested in how the numerical data starts to
deviate from the formula as the gap increases.
I would like to ask the authors to take more data points
between the filled marker and open marker
($1.8<\Delta<2$ for $L=6$ and $1.0<\Delta<1.1$ for $L=10$).

(3) In Fig. 8, the open marker is used for $\xi<L$.
Is Eq.(10) used for the estimation of $\xi$?
If so, is it possible to evaluate $\xi$ numerically
from Eq.(10) by calculating $E_0$ while varying $\Phi$?

Ask for minor revision

This study investigates the threshold electric field strength at which dielectric breakdown occurs when a magnetic flux is applied to a Hubbard model on a ring, thereby generating an electric field along the ring. Employing the Landau-Zener model, the authors clarify the relationship between the charge gap and the breakdown threshold. Furthermore, they point out that the charge gap and the breakdown threshold can be estimated from the frequency and amplitude of the current induced by the flux, respectively. These two approaches to assess the threshold are numerically validated to demonstrate their reliability.

The novelty of this paper lies in its elucidation of how the threshold behavior is affected in finite systems, in contrast to previous studies that mainly focused on the one-dimensional Hubbard model in the thermodynamic limit. I believe that this study is suitable for publication. However, I request the authors to address the following comments.

1- Equation (17) relates the charge gap to the threshold field. Could the authors quantitatively clarify the parameter range (regarding the interaction strength $U$ and the system size $L$) over which this relation remains valid?

2- Equation (24) is an expansion in terms of $E_{th}/E$. Could the authors clarify the range of electric field strength $E$ over which this approximation is quantitatively reliable?

3- While the present study focuses on Mott insulators, the approach may be extendable to other gapped systems such as semiconductors. Could the authors comment on whether there are qualitative differences in the threshold behavior due to many-body effects that would not appear in single-particle gapped systems?

4- In Fig. 2(a), the part of the energy spectrum with $E \gtrsim -3$ appears to be omitted. Including the full spectrum within the displayed range might improve clarity unless there is a specific reason for excluding it.

Ask for minor revision