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arXiv:1605.06514 · Mathematical Physics Analysis and Geometry

Localization for the Ising Model in a Transverse Field with Generic Aperiodic Disorder

Rajinder Mavi

Published Feb 12, 2019• 1 citation
arXivHTMLPDF
DOI
10.1007/s11040-019-9303-y

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We investigate the dynamics of two Jordan Wigner solvable models; namely, the one-dimensional chain of hard-core bosons and the one-dimensional transverse field Ising model under coin-toss-like aperiodically driven staggered on-site potential and the transverse field, respectively. It is demonstrated that both the models heat up to the infinite temperature ensemble for a minimal aperiodicity in driving. Consequently, in the case of the hard-core bosons chain, we show that the initial current generated by the application of a twist vanishes in the asymptotic limit for any driving frequency. For the transverse Ising chain, we establish that the system not only reaches the diagonal ensemble but the entanglement entropy also attains the thermal value in the asymptotic limit following initial ballistic growth. All these findings, contrasted with that of the perfectly periodic situation, are analytically established in the asymptotic limit within an exact disorder matrix formalism developed using the uncorrelated binary nature of the coin-toss aperiodicity.
We investigate the transverse field Ising model on a diamond chain using series expansions about the high-field limit and exact diagonalizations. For the unfrustrated case we accurately determine the quantum critical point and its expected 2d Ising universality separating the polarized and the Z2{\mathcal{Z}}_{2}Z2​ symmetry broken phase. In contrast, we find strong evidence for a disorder by disorder scenario for the fully-frustrated transverse field Ising model, i.e., except for the pure Ising model, having an extensive number of ground states, the system is always in a quantum disordered polarized phase. The low-energy excitations in this polarized phase are understood in terms of exact local modes of the model. Furthermore, an effective low-energy description for an infinitesimal transverse field allows us to pinpoint the quantum disordered nature of the ground state via mapping to an effective transverse field Ising chain and to determine the induced gap to the elementary effective domain wall excitation very accurately.