Siddharth Parameswaran

Abstract:

We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three-dimensional systems where absent disorder the noninteracting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a non-Fermi liquid phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak. We find that the non-Fermi liquid fixed point is unstable to disorder, and demonstrate that the problem inevitably flows to strong coupling, outside the regime of applicability of the perturbative RG. An examination of the flow to strong coupling suggests that disorder is asymptotically more important than interactions, so that the low-energy behavior of the system can be described by a noninteracting sigma model in the appropriate symmetry class (which depends on whether exact particle-hole symmetry is imposed on the problem). We close with a discussion of general principles unveiled by our analysis that dictate the interplay of disorder and Coulomb interactions in gapless semiconductors, and of connections to many-body localized systems with long-range interactions.

Abstract:

© 2017 by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim We review recent advances in understanding the universal scaling properties of non-equilibrium phase transitions in non-ergodic disordered systems. We discuss dynamical critical points (also known as eigenstate phase transitions) between different many-body localized (MBL) phases, and between MBL and thermal phases. (Figure presented.).