Quantum phase transition as an interplay of Kitaev and Ising interactions

Abstract

We study the interplay between the Kitaev and Ising interactions on both ladder and two dimensional lattices. We show that the ground state of the Kitaev ladder is a symmetry-protected topological (SPT) phase, which is protected by a ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ symmetry. It is confirmed by the degeneracy of the entanglement spectrum and non-trivial phase factors (inequivalent projective representations of the symmetries), which are obtained within infinite matrix-product representation of numerical density matrix renormalization group. We derive the effective theory to describe the topological phase transition on both ladder and two-dimensional lattices, which is given by the transverse field Ising model with/without next-nearest neighbor coupling. The ladder has three phases, namely, the Kitaev SPT, symmetry broken ferro/antiferromagnetic order and classical spin-liquid. The non-zero 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, change of the entanglement spectrum degeneracy and a drop in the ground-state fidelity. 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. In the absence of frustration, the 2D lattice shows a topological phase transition from the ${\mathbb{Z}}_2$ spin-liquid state to the long-range ordered Ising phase at finite ratio of couplings, while in the presence of frustration, an order-by-disorder transition is induced by the Kitaev term. The 2D classical spin-liquid phase is unstable against the addition of Kitaev term toward an ordered phase before the transition to the ${\mathbb{Z}}_2$ spin-liquid state.

16 pages, 18 figures

References in corpus (26)

• Non-Abelian Anyons and Topological Quantum Computation
• The density-matrix renormalization group in the age of matrix product states
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Matrix product states represent ground states faithfully
• Topological Quantum Distillation
• The iTEBD algorithm beyond unitary evolution
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Optimal Resources for Topological 2D Stabilizer Codes: Comparative Study
• Ground state fidelity from tensor network representations
• Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• Emergent Fermions and Anyons in the Kitaev Model
• Creation and Manipulation of Anyons in the Kitaev Model
• Perturbative study of the Kitaev model with spontaneous time-reversal symmetry breaking
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Evidence for a floating phase of the transverse ANNNI model at high frustration
• Robustness of a topological phase: Topological color code in parallel magnetic field
• Entanglement properties of topological color codes
• Floating Phase in 1D Transverse ANNNI Model
• The adaptive nature of liquidity taking in limit order books
• Exploring phase transitions by finite-entanglement scaling of MPS in the 1D ANNNI model
• The Kitaev-Ising model, Transition between topological and ferromagnetic order
• Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-$1/2$ Heisenberg chain
• Modulation of Local Magnetization in two-dimensional Axial-Next-Nearest-Neighbor Ising model
• Floating Phase in 2D ANNNI Model
• Interaction and thermodynamics of spinons in the XX chain

Cited by in corpus (4)

• Topological spin liquids in the ruby lattice with anisotropic Kitaev interactions
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model
• Layer-by-layer disentangling two-dimensional topological quantum codes
• Charge current and phase diagram of the disordered open longer-range Kitaev chain