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arXiv · 1307.5696

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

Z. Y. Xie·J. Chen·J. F. Yu·X. Kong·B. Normand·T. Xiang
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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.

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Z. Y. Xie, J. Chen, J. F. Yu, X. Kong, B. Normand, T. Xiang. 2014-01-02. Tensor renormalization of quantum many-body systems using projected entangled simplex states. https://doi.org/10.1103/physrevx.4.011025

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