Quantum criticality in Ising chains with random hyperuniform couplings

Abstract

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 $\ensuremath{\alpha}$ is tuned. For $\ensuremath{\alpha}=0$, one recovers the familiar infinite-randomness critical point. For $0<\ensuremath{\alpha}<1$, we find a line of infinite-randomness critical points with continuously varying critical exponents; however, the Griffiths phases that flank the critical point at $\ensuremath{\alpha}=0$ are absent at any $\ensuremath{\alpha}>0$. When $\ensuremath{\alpha}>1$, 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.