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arXiv:0909.2788 · Physical Review B

Scaling theory of quantum breakdown in solids

Bikas K. Chakrabarti, Debashis Samanta

Published Feb 1, 2010• 1 citation
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Abstract

We propose a notable scaling theory for general quantum breakdown phenomena. We show, taking Landau-Zener-type breakdown as a particular example that the breakdown phenomena can be viewed as a quantum phase transition for which the scaling Ansatz is developed. Its application to Zener-type breakdown in Anderson insulators and quantum quenching has been discussed.

DOI
10.1103/physrevb.81.052301

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We propose a notable scaling theory for general quantum breakdown phenomena. We show, taking Landau-Zener-type breakdown as a particular example that the breakdown phenomena can be viewed as a quantum phase transition for which the scaling Ansatz is developed. Its application to Zener-type breakdown in Anderson insulators and quantum quenching has been discussed.
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The nonadiabatic quantum tunneling picture, which may be called the many-body Schwinger-Landau-Zener mechanism, for the dielectric breakdown of Mott insulators in strong electric fields is studied in the one-dimensional Hubbard model. The tunneling probability is calculated by a method due to Dykhne-Davis-Pechukas with an analytical continuation of the Bethe-ansatz solution for excited states to a non-Hermitian case. A remarkable agreement with the time-dependent density-matrix renormalization-group result is obtained.
This article is aimed at a pedagogical introduction to the physics of quantum phase transitions that is unique to metallic systems. It has been recognized for some time that quantum criticality can result in a breakdown of Landau's Fermi liquid theory. Its converse, however, has not been appreciated until very recently: non-Fermi liquid behavior can in turn lead to new classes of quantum phase transition. A concrete example is provided by ``local quantum critical points''. I summarize the theoretical reasoning and experimental evidence for local quantum criticality, in the context of heavy fermion metals. The underlying physics is likely to be relevant to other correlated electron systems including doped Mott insulators.
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.
We determine transition probabilities in two exactly solvable multistate Landau-Zener (LZ) models and discuss applications of our results to the theory of dynamic passage through a phase transition in the dissipationless quantum mechanical regime. In particular, we show that the statistics of particles in a new phase demonstrate scaling behavior. Our results also reveal a symmetry that we claim is a property of a large class of multistate LZ models, whose explicit solutions are not presently known. We support our arguments by direct numerical simulations.