Dielectric breakdown of strongly correlated insulators in one dimension: Universal formula from non-Hermitian sine-Gordon theory

TL;DR

The paper addresses dielectric breakdown in 1D strongly correlated insulators under a DC field by building a low-energy effective field theory based on bosonization and a non-Hermitian sine-Gordon model. It derives a universal threshold-field formula that generalizes the Landau-Zener paradigm to many-body, interacting systems, explicitly incorporating the charge $e^*$ of elementary excitations. The authors validate the formula against integrable lattice models (SSH, XXZ, Hubbard), finding good agreement across a broad parameter range and revealing the impact of fractionalization on breakdown. This work provides a unified framework for universal, nonlinear nonequilibrium transport in 1D quantum systems and suggests experimental avenues to probe fractionalized excitations via dielectric breakdown.

Abstract

Application of a strong electric field to insulators induces a finite current. This phenomenon is called dielectric breakdown and is known as a fundamental nonequilibrium and nonlinear transport phenomenon in solids. Here, we study the dielectric breakdown of generic strongly correlated insulators in one dimension. Combining bosonization techniques with a quantum tunneling theory, we develop an effective field-theoretical description of dielectric breakdown using a non-Hermitian sine-Gordon theory. Then, we derive an analytic formula for the threshold field, which is a many-body generalization of the Landau-Zener formula. Importantly, we point out that the threshold field contains a previously overlooked factor originating from the charges of elementary excitations, which should be significant when a system has fractionalized excitations. We apply our results to integrable lattice models and confirm that our formula is valid in a broad range including the weak coupling regime, indicating its wide potential applicability. Our results unveil universal aspects of nonlinear and nonequilibrium transport phenomena in various strongly correlated insulators.

Figures (3)

• Figure 1: (a) Our setup of a strongly correlated one-dimensional insulator under a DC electric field $\bm E$. (b) A typical current-voltage relation ($I$-$V$ characteristic) of dielectric breakdown phenomena. At the threshold voltage $V_\mathrm{th}$, the nonequilibrium insulator-metal transition occurs.
• Figure 2: (a, b) Schematic picture of pair creation of a soliton and an anti-soliton. The filled (empty) circle denotes a particle (hole). The figure (a) ((b)) is before (after) the pair creation. The yellow arrow and the orange broken lines represent the electric field and the position of the domain walls respectively. (c, d) The field configuration (broken line) and the soliton density (solid line). (c) and (d) correspond to (a) and (b) respectively. First, the field is pinned to one of the potential minima and there is no excitation. After the pair creation, two kinks are generated in the field. The shaded area corresponds to the charge of the (anti-)soliton $e^*$ ($-e^*$).
• Figure 3: Comparison between the predictions [Eqs. (\ref{['eq:h_c']}) and (\ref{['eq:Delta(ih)']})] based on the effective field theory and the exact results calculated from integrable lattice models. (a) is for a band insulator (Su-Schrieffer-Heeger model), (b) is for a CDW insulator (spinless fermions with nearest neighbor interaction), and (c) is for a Mott insulator (Fermi-Hubbard model). The critical value $h_c$ together with the right hand side of Eq. (\ref{['eq:h_c']}) and the change of energy gap $\Delta (ih)/\Delta_0$ together with $\sqrt{1-(h/h_c)^2}$ are shown in (X-1) and (X-2) respectively (X = a, b, c).