Many body localization and delocalization in the two dimensional continuum

Rahul Nandkishore

doi:10.1103/physrevb.90.184204

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arXiv · 1408.6235

Many body localization and delocalization in the two dimensional continuum

Rahul Nandkishore

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Abstract

I discuss whether localization in the two dimensional continuum can be stable in the presence of short range interactions. I conclude that, for an impurity model of disorder, if the system is prepared below a critical temperature $T < T_c$, then perturbation theory about the localized phase converges almost everywhere. As a result, the system is at least asymptotically localized, and perhaps even truly many body localized, depending on how certain rare regions behave. Meanwhile, for $T > T_c$, perturbation theory fails to converge, which I interpret as interaction mediated delocalization. I calculate the boundary of the region of perturbative stability of localization in the interaction strength - temperature plane. I also discuss the behavior in a speckle disorder (relevant for cold atoms experiments) and conclude that perturbation theory about the non-interacting phase diverges for arbitrarily weak interactions with speckle disorder, suggesting that many body localization in the two dimensional continuum cannot survive away from the impurity limit.

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Rahul Nandkishore. 2014-08-26. Many body localization and delocalization in the two dimensional continuum. https://doi.org/10.1103/physrevb.90.184204

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