Quasiperiodic Quantum Ising Transitions in 1D

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.

Universality and quantum criticality in quasiperiodic spin chains

“…Remarkably, this corresponds to the observation that weak quasiperiodic modulations are (marginally) irrelevant at the clean Ising critical point. It is indeed known from free fermion numerics 30,31 that the Ising transition in the presence of any such nonsingular quasiperiodic potentials is governed by the clean Ising conformal field theory, in agreement with the predictions of the RG. To see a nontrivial transition in this case, one must take singular distributions of '; one can do this, e.g., by taking J i ¼ W J ða þ cosð2πφði þ 1 2 þ θ J ÞÞÞ and h i = W h (a + cos(2πφi + θ h )), with 0 < a < 1 so ' 2i ¼ ÀlnjJ i j, ' 2iþ1 ¼ Àln h i j j is singular.…”

“…RG methods so far have been restricted to the simplest type of function, a binary substitution sequence [19][20][21][22][23][24][25][26][27] . Criticality for generic quasiperiodic modulation has only been addressed very recently for free fermions [28][29][30][31] .…”

Avalanche induced coexisting localized and thermal regions in disordered chains

“…When the disorder is sufficiently hyperuniform that l is the most divergent length scale, the exponent is thus ν = 1. The quasiperiodic potentials used in previous studies provide access to this case [7,[80][81][82][83][84][85]. Finally, we comment on the implications of this work for the MBL transition [19,[46][47][48]57,[70][71][72][73]80,[86][87][88][89][90][91][92][93].…”

Anomalous Diffusion and Localization in a Positionally Disordered Quantum Spin Array

“…On the other hand, in the case of phases breaking a discrete symmetry (of interest to this work) disorder may have a minimal effect on the ground-state corre-arXiv:1907.12511v1 [cond-mat.dis-nn] 29 Jul 2019 lations, leaving the symmetry broken, and yet lead to localization (partial or total) of the elementary excitations. This fact is seldom recognized in the literature, although a few examples have been reported in the case of (quasi-)disordered quantum Ising models [13][14][15]. In this Letter we present a realistic model, capturing the physics of two-dimensional Rydberg-atom arrays [16][17][18], which precisely manifests this phenomenon.…”