Simulation of the Ring-exchange Models with Projected Entangled Pair States

Abstract

Algorithms to simulate the ring-exchange models using the projected entangled pair states (PEPS) are developed. We generalize the imaginary time evolution (ITE) method to optimize PEPS wave functions for the models with ring-exchange interactions. We compare the effects of different approximations to the environment. To understand the numerical instability during the optimization, we introduce the ``singularity'' of a PEPS and develop a regulation procedure that can effectively reduce the singularity of a PEPS. We benchmark our method with the toric code model, and obtain extremely accurate ground state energies and topological entanglement entropy. We also benchmark our method with the two-dimensional cyclic ring exchange model, and find that the ground state has a strong vector chiral order. The algorithms can be a powerful tool to investigate the models with ring interactions. The methods developed in this work, e.g., the regularization process to reduce the singularity can also be applied to other models.

References in corpus (17)

• "Deconfined" quantum critical points
• A class of quantum many-body states that can be efficiently simulated
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Algorithms for finite Projected Entangled Pair States
• D-wave correlated Critical Bose Liquids in two dimensions
• Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange
• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Strong-Coupling Phases of Frustrated Bosons on a 2-leg Ladder with Ring Exchange
• Neel order, ring exchange and charge fluctuations in the half-filled Hubbard model
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Exotic Gapless Mott Insulators of Bosons on Multi-Leg Ladders
• Quantum Entanglement in the S=1/2 Spin Ladder with Ring Exchange
• Exact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice
• Doped two-leg ladder with ring exchange
• Site Dilution in the Half-Filled One-Band Hubbard Model: Ring Exchange, Charge Fluctuations and Application to La2Cu_{1-x}(Mg/Zn)_xO4
• Multiparticle interactions for ultracold atoms in optical tweezers: Cyclic ring-exchange terms