Quasiperiodic Quantum Ising Transitions in 1D

Physical Review Letters
P J D CrowleyC R Laumann

Abstract

Unlike random potentials, quasiperiodic modulation can induce localization-delocalization transitions in one dimension. In this Letter, we analyze the implications of this for symmetry breaking in the quasiperiodically modulated quantum Ising chain. Although weak modulation is irrelevant, strong modulation induces new ferromagnetic and paramagnetic phases which are fully localized and gapless. The quasiperiodic potential and localized excitations lead to quantum criticality that is intermediate to that of the clean and randomly disordered models with exponents of ν=1^{+} (exact) and z≈1.9, Δ_{σ}≈0.16, and Δ_{γ}≈0.63 (up to logarithmic corrections). Technically, the clean Ising transition is destabilized by logarithmic wandering of the local reduced couplings. We conjecture that the wandering coefficient w controls the universality class of the quasiperiodic transition and show its stability to smooth perturbations that preserve the quasiperiodic structure of the model.

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Citations

Apr 18, 2020·Physical Review Letters·Raphaël Menu, Tommaso Roscilde
Dec 1, 2018·Physical Review Letters·Shi-Xin Zhang, Hong Yao
May 8, 2020·Nature Communications·Utkarsh AgrawalRomain Vasseur
Jan 16, 2021·Physical Review Letters·Utkarsh AgrawalRomain Vasseur
Mar 13, 2021·Physical Review Letters·Yucheng WangDapeng Yu

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