Tensor Renormalization of Quantum Many-Body Systems Using Projected Entangled Simplex States

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 paircorrelation basis of projected entangled pair states to a simplex. PESS are exact representations of the simplex solid states, and they 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.

Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model

“…A natural generalization of the MPS to two dimensions is the projected entangled pair state (PEPS) 5 , which satisfies the area law of entanglement entropy 5 . Besides PEPS, various types of tensor network states have been introduced, such as multi-scale entanglement renormalization ansatz (MERA) 6 , tree tensor network states 18 and projected entangled simplex states 14 . These tensor network wave functions are usually expressed in a real space basis which may become inefficient to capture the large amount of entanglement in itinerant fermionic systems.…”

“…In the past years, the tensor network algorithms have been widely developed [3][4][5][6][7][8][9][10][11][12][13][14][15] , which are shown to be promising numerical tools. One of the simplest tensor network state is the matrix product state (MPS), which is the variational wave function of the DMRG method 16,17 .…”

Spin-ordered ground state and thermodynamic behaviors of the spin-32kagome Heisenberg antiferromagnet

“…Through continuous efforts of many scientists, its ground state is generally believed to be a spin liquid without any symmetry breaking [4,5]. However, whether or not there is a gap in this interesting system still remains controversial [5][6][7][8][9][10][11][12]. Meanwhile, the high spin (S > 1/2) kagome physics has also gained great interest currently.…”

“…Nonetheless, despite a lot of efforts made both experimentally and theoretically, its nature is still ambiguous and controversial up to date. The experimental studies on a number of spin-3/2 KHAF materials such as S rCr 8 Ga 4 O 19 [25], S rCr 8 Ga 4−x M x O 19 (M = Zn, Mg, Cu) [26], Ba 2 S n 2 ZnGa 10−7p Cr 7p O 22 [27], and Crjarosite KCr 3 (OH) 6 (S O 4 ) 2 [28], etc., have produced diverse results, leading to different even contradictory conclusions on the nature of the spin-3/2 KHAF. For instance, there are studies showing that it has no antiferromagnetic long-range order but undergoes a spin-glass transition [25][26][27], while some others reported that it possesses a long-range order with a nearly 120 • structure [28,29].…”

Self-Consistent Spin-Wave Analysis of the 1/3 Magnetization Plateau in the Kagome Antiferromagnet

“…Among the many different frustrated systems, quantum antiferromagnets on the kagome lattice are perhaps the most intriguing, because the combination of strong geometric frustration and weak constraints maximizes quantum fluctuation effects. The kagome antiferromagnet has attracted ever-increasing attention over the last two decades, with many different methods applied and resulting proposals for the nature of the ground state [3][4][5][6] One of the characteristic features of kagome antiferromagnets is the appearance of magnetization plateaus in the presence of an external magnetic field. Irrespective of the method applied and the prediction for the zero-field ground state, all theoretical approaches agree that there exists a robust magnetization plateau at m = 1/3 for all values of the spin quantum number, S. The 1/3 plateau has been investigated theoretically by real-space perturbation theory (RSPT) [14], exact diagonalization (ED) [15,16], density-matrix renormalization-group methods (DMRG) [17], and infinite projected entangled paired states (iPEPS) [18].…”