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CAMP Seminar: Many-Body Localization Transition in Random Quantum Spin Chains with Long-Range Interactions

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Stephen Haas, University of Southern California
When
08 November 2016 from 3:30 PM to 4:30 PM
Where
339 Davey Laboratory
Contact Name
Marcos Rigol
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We have developed a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power α, which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing α. We identify a critical decay exponent α_c for which the full gap distribution coincides with a critical function, separating an insulator phase at larger α where the gap distribution is Poissonian, and a delocalized state at smaller α, where it follows the Wigner surmise. We also derive the temperature dependence of the magnetic susceptibility in this system, and observe a corresponding crossover between a divergent low-temperature susceptibility at large α to a vanishing low-temperature susceptibility at small α, revealing the opening of a pseudogap in the delocalized regime. Furthermore, we show how that the introduction of a finite exponential cut-off length of the power-law interactions suppresses the pseudo-gap, leading to a non-trivial quantum phase diagram.

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