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 (58)

• Fault-tolerant quantum computation by anyons
• Topological entanglement entropy
• Efficient classical simulation of slightly entangled quantum computations
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Efficient simulation of one-dimensional quantum many-body systems
• "Deconfined" quantum critical points
• A class of quantum many-body states that can be efficiently simulated
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Competing states in the t-J model: uniform d-wave state versus stripe state
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Quasi-particle Statistics and Braiding from Ground State Entanglement
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• Entanglement spectrum and boundary theories with projected entangled-pair states
• The Loop Algorithm
• Topological Entanglement Renyi Entropy and Reduced Density Matrix Structure
• Variational optimization with infinite projected entangled-pair states
• The iPEPS algorithm, improved: fast full update and gauge fixing
• Algorithms for finite Projected Entangled Pair States
• Gradient methods for variational optimization of projected entangled-pair states
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Isometric Tensor Network States in Two Dimensions
• Tensor renormalization of quantum many-body systems using projected entangled simplex states
• The sign problem in Monte Carlo simulations of frustrated quantum spin systems
• Observation of Four-body Ring-exchange Interactions and Anyonic Fractional Statistics
• Unifying Projected Entangled Pair States contractions
• Effects of biquadratic exchange on the spectrum of elementary excitations in spin ladders
• D-wave correlated Critical Bose Liquids in two dimensions
• Finitely Correlated Generalized Spin Ladders
• Phase Diagram of a Spin Ladder with Cyclic Four Spin Exchange
• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Vortices and quasiparticles near the "superconductor-insulator" transition in thin films
• Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
• Spin Excitations in La2CuO4: Consistent Description by Inclusion of Ring-Exchange
• Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
• Gradient optimization of finite projected entangled pair states
• Perturbation theories for the S=1/2 spin ladder with four-spin ring exchange
• 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
• Bose Metals and Insulators on Multi-Leg Ladders with Ring Exchange
• Exotic Gapless Mott Insulators of Bosons on Multi-Leg Ladders
• Conversion of projected entangled pair states into a canonical form
• Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange
• Spin correlations in the paramagnetic phase and ring exchange in lanthanum cuprate
• Simulating 2+1d ${\mathbb{Z}}_3$ lattice gauge theory with iPEPS
• Quantum Entanglement in the S=1/2 Spin Ladder with Ring Exchange
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Gapless Hamiltonians for the toric code using the PEPS formalism
• Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice
• Chiral phases of two-dimensional hard-core bosons with frustrated ring-exchange
• Exact diagonalization study of the Hubbard-parametrized four-spin ring exchange model on a square lattice
• Gradient optimization of fermionic projected entangled pair states on directed lattices
• The N-Leg spin-S Heisenberg ladders: A DMRG study
• 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