Infinite Projected Entangled-Pair State algorithm for ruby and triangle-honeycomb lattices

Abstract

The infinite Projected Entangled-Pair State (iPEPS) algorithm is one of the most efficient techniques for studying the ground-state properties of two-dimensional quantum lattice Hamiltonians in the thermodynamic limit. Here, we show how the algorithm can be adapted to explore nearest-neighbor local Hamiltonians on the ruby and triangle-honeycomb lattices, using the Corner Transfer Matrix (CTM) renormalization group for 2D tensor network contraction. Additionally, we show how the CTM method can be used to calculate the ground state fidelity per lattice site and the boundary density operator and entanglement entropy (EE) on an infinite cylinder. As a benchmark, we apply the iPEPS method to the ruby model with anisotropic interactions and explore the ground-state properties of the system. We further extract the phase diagram of the model in different regimes of the couplings by measuring two-point correlators, ground state fidelity and EE on an infinite cylinder. Our phase diagram is in agreement with previous studies of the model by exact diagonalization.

12 pages, 18 figure

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Cited by in corpus (25)

• Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
• Spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the star lattice: Competing valence-bond-solid phases studied by means of tensor networks
• A universal tensor network algorithm for any infinite lattice
• Detecting a $Z_2$ topologically ordered phase from unbiased infinite projected entangled-pair state simulations
• Single-layer tensor network study of the Heisenberg model with chiral interactions on a kagome lattice
• Time Evolution of an Infinite Projected Entangled Pair State: an Algorithm from First Principles
• Theory of competing Chern-Simons orders and emergent phase transitions
• Ground-state phase diagram of the Kitaev-Heisenberg model on a kagome lattice
• The classical two-dimensional Heisenberg model revisited: An $SU(2)$-symmetric tensor network study
• Variational optimization of tensor-network states with the honeycomb-lattice corner transfer matrix
• Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
• Spin-$\frac{1}{2}$ kagome Heisenberg antiferromagnet with strong breathing anisotropy
• Topological ${\mathbb{Z}}_2$ RVB quantum spin liquid on the ruby lattice
• Variational corner transfer matrix renormalization group method for classical statistical models
• Critical line of the triangular Ising antiferromagnet in a field from a $C_3$-symmetric corner transfer matrix algorithm
• Fine-Grained Tensor Network Methods
• Thermal bosons in 3d optical lattices via tensor networks
• Topological magnons in Kitaev magnets with finite Dzyaloshinskii-Moriya interaction at high field
• Kitaev-Heisenberg model on the star lattice: From chiral Majorana fermions to chiral triplons
• Susceptibility indicator for chiral topological orders emergent from correlated fermions
• Thermal Hall conductivity with sign change in the Heisenberg-Kitaev kagome magnet
• Kitaev honeycomb antiferromagnet in a field: quantum phase diagram for general spin
• All-mode Renormalization for Tensor Network with Stochastic Noise
• Quantum phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the square-kagome lattice: a tensor network study
• Grassmann tensor networks