Tensor renormalization of quantum many-body systems using projected entangled simplex states

TL;DR

This paper introduces projected entangled simplex states (PESS), a new tensor-network class for efficiently studying quantum lattice models, demonstrating their effectiveness on the kagome lattice antiferromagnetic Heisenberg model.

Contribution

The paper develops PESS, extending PEPS to simplices, and introduces a simple update method for evaluating these states in quantum many-body systems.

Findings

Accurate ground-state energy estimates for the kagome lattice model.

PESS satisfy the area law of entanglement entropy.

Systematic improvement over previous bounds.

Abstract

We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS), for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states (PEPS) to a simplex. PESS are an exact representation of the simplex solid states and provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice, we obtain accurate and systematic results for the ground-state energy, which approach the lowest upper bounds yet estimated for this quantity.