The quantum Hall transition [1] is one of the simplest and most studied quantum phase transitions. Nevertheless, the experimental observation of a new phase in this regime, the quantum Hall insulator, still remains a puzzle since the first report more than a decade ago [2-8], as it is in contradiction with all theoretical studies based on microscopically coherent quantum calculations [9][10][11][12]. In this work we introduce into the coherent quantum theory a new ingredient -rare incoherent events, in a controlled manner. Using both direct numerical solutions and real-space renormalization, we demonstrate that these decoherence events stabilize the elusive quantum Hall insulator phase, which becomes even more stable with increasing temperature and voltage bias, in agreement with experiments.
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