Quantum criticality in Ising chains with random hyperuniform couplings

P. J.D. Crowley, C. R. Laumann, S. Gopalakrishnan

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12 Scopus citations


We study quantum phase transitions in transverse-field Ising spin chains in which the couplings are random but hyperuniform, in the sense that their large-scale fluctuations are suppressed. We construct a one-parameter family of disorder models in which long-wavelength fluctuations are increasingly suppressed as a parameter α is tuned. For α=0, one recovers the familiar infinite-randomness critical point. For 0<α<1, we find a line of infinite-randomness critical points with continuously varying critical exponents; however, the Griffiths phases that flank the critical point at α=0 are absent at any α>0. When α>1, randomness is a dangerously irrelevant perturbation at the clean Ising critical point, leading to a state we call the critical Ising insulator. In this state, thermodynamics and equilibrium correlation functions behave as in the clean system. However, all finite-energy excitations are localized, thermal transport vanishes, and autocorrelation functions remain finite in the long-time limit. We characterize this line of hyperuniform critical points using a combination of perturbation theory, renormalization-group methods, and exact diagonalization.

Original languageEnglish (US)
Article number134206
JournalPhysical Review B
Issue number13
StatePublished - Oct 17 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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