Strong many-particle localization by constructed disorder

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The goal of the proposed research is to study localization in a many-particle system. Of central interest is on-site localization of all many-particle states, with effective localization length smaller than the intersite distance. Besides localization of stationary states, it is proposed to study the localization lifetime. Bounded sequences of on-site energies will be constructed that efficiently suppress resonant hopping. For these sequences, the single-particle localization transition will be analyzed and sharp bounds on the decay length will be obtained. Strong on-site localization of all many-particle states will be studied for a finite length chain. For an infinite system and an arbitrary number of particles, of primary interest will be the localization lifetime. It will be shown to scale as a high power of the ratio of the bandwidth of site energies to the intersite hopping integral, both for weak and strong particle-particle interaction. For a finite chain, optimization of the energy sequence in order to obtain maximal lifetime for a given bandwidth will be considered. Stability with respect to errors in site energies, the effect of long-range interaction, and the role of decoherence due to coupling to an external reservoir will be studied. In addition to graduate training, carried out jointly by a physicist and a mathematician, the research topic includes undergraduate participation. The students involved in the proposed research should benefit from a weekly interdisciplinary seminar of the Institute for Quantum Sciences organized by the PI at MSU.