Critical behaviour of the quasi-periodic quantum Ising chain. (1st August 2022)

• Record Type: Journal Article
• Authors: Crowley, P J D; Laumann, C R; Chandran, A
• Is Part Of: Journal of statistical mechanics. (2022:Aug.)
• Publication Date: 2022-08-01
• Subjects: quantum disordered systems -- quantum phase transitions -- spin chains, ladders and planes -- heterogeneous materials; Statistical mechanics -- Periodicals; Mechanics -- Statistical methods -- Periodicals; 530.1305
• DOI: 10.1088/1742-5468/ac815d
• Languages: English
• ISSNs: 1742-5468

Abstract

Abstract: The interplay of correlated spatial modulation and symmetry breaking leads to quantum critical phenomena intermediate between those of the clean and randomly disordered cases. By performing a detailed analytic and numerical case study of the quasi-periodically (QP) modulated transverse field Ising chain, we provide evidence for the conjectures of reference (Crowley et al 2018 Phys. Rev. Lett. 120 175702) regarding the QP-Ising universality class. In the generic case, we confirm that the logarithmic wandering coefficient w governs both the macroscopic critical exponents and the energy-dependent localisation length of the critical excitations. However, for special values of the phase difference Δ between the exchange and transverse field couplings, the QP-Ising transition has different properties. For Δ = 0, a generalised Aubry–André duality prevents the finite energy excitations from localising despite the presence of logarithmic wandering. For Δ such that the fields and couplings are related by a lattice shift, the wandering coefficient w vanishes. Nonetheless, the presence of small couplings leads to non-trivial exponents and localised excitations. Our results add to the rich menagerie of quantum Ising transitions in the presence of spatial modulation.