Density-matrix renormalization group study of quantum spin systems with Kitaev-type anisotropic interaction

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.

Satoshi Nishimoto, M. ARIKAWA

Kazuya Shinjo, Shigetoshi Sota, Takami Tohyama

We study an extended Kitaev-Heisenberg model including additional anisotropic couplings by using the two-dimensional density-matrix renormalization group method. Calculating the ground-state energy, entanglement entropy, and spin-spin correlation functions, we make a phase diagram of the extended Kitaev-Heisenberg model around the spin-liquid phase. We find a zigzag antiferromagnetic phase, a ferromagnetic phase, a ${120}^{\ensuremath{\circ}}$ antiferromagnetic phase, and two kinds of incommensurate phases around the Kitaev spin-liquid phase. Furthermore, we study the entanglement spectrum of the model, and we find that entanglement levels in the Kitaev spin-liquid phase are degenerate forming pairs, but those in the magnetically ordered phases are nondegenerate. The Schmidt gap defined as the energy difference between the lowest two levels changes at the phase boundary adjacent to the Kitaev spin-liquid phase. However, we find that phase boundaries between magnetically ordered phases do not necessarily agree with the change of the Schmidt gap.

Jonas A. Kjäll, Michael P. Zaletel, Roger S. K. Mong +2 more

We study the ground-state phase diagram of the quantum spin-2 XXZ chain in the presence of on-site anisotropy using a matrix-product state based infinite-system density matrix renormalization group (iDMRG) algorithm. One of the interests in this system is in connecting the highly quantum-mechanical spin-1 phase diagram with the classical $S=\ensuremath{\infty}$ phase diagram. Several of the recent advances within DMRG make it possible to perform a detailed analysis of the whole phase diagram. We consider different types of on-site anisotropies, which allows us to establish the validity of the following statements: (1) the spin-2 model can be tuned into a phase, which is equivalent to the ``topologically nontrivial'' spin-1 Haldane phase, and (2) the spin-2 Haldane phase at the isotropic Heisenberg point is adiabatically connected to the ``trivial'' large-$D$ phase, with a continuous change of the Hamiltonian parameters. Furthermore, we study the spin-3 XXZ chain to help explain the development of the classical phase diagram. We present details on how to use the iDMRG method to map out the phase diagram and include an extensive discussion of the numerical methods.

Indrani Bose, S. Chatterjee