Zohar Nussinov, Patrick Johnson, Matthias J. Graf, Alexander V. Balatsky
Many electronic systems (e.g., the cuprate superconductors and heavy fermions) exhibit striking features in their dynamical response over a prominent range of experimental parameters. While there are some empirical suggestions of particular increasing length scales that accompany such transitions in some cases, this identification is not universal and in numerous instances no large correlation length is evident. Using a correspondence between dissipative classical and quantum many-body systems, we show that, even in the absence of imposed disorder, many continuum systems (and possible lattice counterparts) may exhibit zero-point "quantum dynamical heterogeneities" wherein the dynamics, at a given instant, is spatially non-uniform. Towards this end, we extend a known mapping between finite temperature classical Fokker-Planck systems and quantum systems at zero temperature to include general non-equilibrium dynamics. While the static length scales accompanying this phenomenon do not seem to exhibit a clear divergence in standard correlation functions, the length scale of the dynamical heterogeneities can increase dramatically. We furthermore show how a hard core bosonic system can undergo a zero temperature quantum critical metal-to-insulator-type transition with an extremely large effective dynamical exponent z>4 that is consistent with length scales that increase far more slowly than the relaxation time as a putative critical transition is approached. We suggest ways to analyze experimental data in order to adduce such phenomena. Our approach may be applied to quenched quantum systems.
View original:
http://arxiv.org/abs/1209.3823
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