Kitaev-Ising-$J_1$-$J_2$ model: a density matrix renormalization group study

We numerically study the Kitaev honeycomb model with the additional XX Ising interaction between the nearest and the next nearest neighbors (Kitaev-Ising-$J_1$-$J_2$ model), by using the density matrix renormalization group (DMRG) method. Such additional interaction correspond to the nearest and diagonal interactions on the square lattice. Phase diagram of the bare Kitaev model consist of low entangled commensurate magnetic phases and entangled Kitaev spin liquid. Anisotropic Ising interaction allows the entangled quantum paramagnetic phases in the phase diagram, which in the absence of the magnetic field previously was predicted for more complex type of interaction. We study the scaling law of the entanglement entropy and the bond dimension of the matrix product state with the size of the system. In addition, we propose an optimization algorithm to prevent DMRG from getting stuck in the low-entangled phases.

💡 Research Summary

In this work the authors investigate an extended Kitaev honey‑comb model that incorporates additional XX‑type Ising interactions on both nearest‑neighbor (NN) and next‑nearest‑neighbor (NNN) bonds, denoted as the Kitaev‑Ising‑J₁‑J₂ model. The motivation stems from realistic implementations on superconducting quantum processors where parasitic couplings between qubits generate exactly such NN and NNN XX terms. By mapping the honey‑comb geometry onto a square lattice of qubits, the Hamiltonian becomes
H = K ∑⟨ij⟩γ Sᵢ^γ Sⱼ^γ + J₁ ∑⟨ij⟩ Sᵢˣ Sⱼˣ + J₂ ∑⟨⟨ij⟩⟩ Sᵢˣ Sⱼˣ,
with the parametrisation K = cos φ, J₁ = sin φ cos α, J₂ = sin φ sin α, where φ∈