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

TL;DR

This paper adapts the iPEPS algorithm with CTM for studying ground states and phase diagrams of quantum lattice models on ruby and triangle-honeycomb lattices, providing efficient tools for 2D quantum systems.

Contribution

It introduces a modified iPEPS algorithm combined with CTM for new lattice geometries and demonstrates its effectiveness through benchmarking on the ruby model.

Findings

Successful adaptation of iPEPS to ruby and triangle-honeycomb lattices.

Accurate phase diagram consistent with previous studies.

Effective calculation of fidelity, entanglement entropy, and correlators.

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.