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.
Highlights
The theory of tensor-network states is evolving rapidly into an interdisciplinary field involving condensed matter physics, quantum information theory, renormalization group theory, and even quantum gravity
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
As we discuss in detail below, it is difficult to use Projected entangled pair states (PEPS) to represent a quantum state in which the local correlation or entanglement among all the basis states within a cluster containing more than two lattice sites, for example, the simplex solid state proposed by Arovas [21], becomes important. We solve these problems by introducing a new class of tensor-network states. We call these projected entangled simplex states (PESS) because they can be understood in terms of entangled simplex states of virtual systems that are locally projected onto the physical basis states
Summary
The theory of tensor-network states is evolving rapidly into an interdisciplinary field involving condensed matter physics, quantum information theory, renormalization group theory, and even quantum gravity. A MPS may be viewed as a trial wave function arising from virtual entangled pairs formed between two nearest-neighbor sites of a lattice It yields a local description of quantum many-body states based on their entanglement structure. We solve these problems by introducing a new class of tensor-network states We call these projected entangled simplex states (PESS) because they can be understood in terms of entangled simplex states of virtual systems that are locally projected onto the physical basis states. IV a simple update approach for evaluating the PESS wave function based on the HOSVD of tensors By applying this approach to the spin-1=2 Heisenberg model on the kagome lattice, we obtain the ground-state energy as a function of the bond dimension D for simplices with N 1⁄4 3, 5, and 9.
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