Density matrix renormalization group study of the Kitaev honeycomb lattice model

Kazuya Shinjo, S. Sota, Tomonori Shirakawa +2 more

Shigetoshi Sota, Kazuya Sjinjo, Tomonori Shirakawa +2 more

A. V. Kapranov, Ramil S. Akzyanov

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 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 density matrix renormalization group (DMRG) from getting stuck in the low-entangled phases.

Cheng Peng, Yi‐Fan Jiang, Thomas Devereaux +1 more

Abstract We study the effects of doping the Kitaev model on the honeycomb lattice where the spins interact via the bond-directional interaction JK, which is known to have a quantum spin liquid as its exact ground state. The effect of hole doping is studied within the t-JK model on a three-leg cylinder using density-matrix renormalization group. Upon light doping, we find that the ground state of the system has a dominant quasi-long-range charge-density-wave correlations but short-range single-particle correlations. In the pairing channel, the even-parity superconducting correlation is dominant with d-wave-like symmetry, which oscillates in sign as a function of separation with a period equal to that of the spin-density wave and two times the charge-density wave. Although these correlations fall rapidly (possibly exponentially) at long distances, this is never-the-less the example where a pair-density wave is the leading instability in the pairing channel on the honeycomb lattice.

Sei-ichiro Suga, Takafumi J. Suzuki, Takuto Yamada

Kazuya Shinjo