Quantum phase transition as an interplay of Kitaev and Ising interactions

2014/10/08 by A. Langari, A. Mohammad-Aghaei, Amir Mohammadaghaei +2
Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Central charge #Condensed matter physics #Critical exponent #Degenerate energy levels #Frustration #Ground state #Ising model #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum critical point #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum phase transition #Renormalization group #Topological order #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevb.91.024415

published as Phys. Rev. B 91, 024415 (2015) · 16 pages, 18 figures

arxiv created 2014/10/08 · openalex publication_date 2015/01/15 · arxiv updated 2015/01/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study the interplay between the Kitaev and Ising interactions on a ladder geometry. We show that the ground state of the Kitaev ladder is a symmetry-protected topological (SPT) phase, which is protected by a ℤ₂\ifmmode×\else\texttimes\fiℤ₂ symmetry. The nature of the SPT phase is confirmed by degeneracy of the entanglement spectrum. Nonlocal order parameters that indirectly measure phase factors (inequivalent projective representations of the symmetries) of the ℤ₂\ifmmode×\else\texttimes\fiℤ₂ symmetry explicitly show the protection of the SPT phase under the ℤ₂\ifmmode×\else\texttimes\fiℤ₂ symmetry. We derive the effective theory to describe the topological phase transition on the ladder geometry, which is given by a transverse field Ising model with/without next-nearest-neighbor coupling based on the primary Ising configurations. The ladder has three phases, namely, the Kitaev SPT, symmetry-broken ferro/antiferromagnetic order, and classical spin liquid. The nonzero quantum critical point and its corresponding central charge are provided by the effective theory, which are in full agreement with the numerical results, i.e., the divergence of entanglement entropy at the critical point and change of the entanglement spectrum degeneracy. The central charge of the critical points are either c=1 or c=2, with the magnetization and correlation exponents being 1/4 and 1/2, respectively. The transition from the classical spin-liquid phase of the frustrated Ising ladder to the Kitaev SPT phase is mediated by a floating phase, which shows strong finite entanglement scaling.

Citations

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