Heisenberg antiferromagnet on the Husimi lattice

Liao, Huijuan; Xie, Z. Y.; Chen, J.; Han, Xiaoyang; Xie, H. D.; Normand, B.; Xiang, Tao

doi:10.1103/physrevb.93.075154

Cited by 26 publications

(36 citation statements)

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“…SII of the SM [20], this ansatz obeys the area law of entanglement and, crucially, allows the construction of a renormalization-group scheme to reach the limit of infinite lattice size. The truncation parameter is the tensor bond dimension, D. We introduced the PESS formulation [55] in order to capture the multipartite entanglement within each lattice unit, or simplex [55][56][57], which is the key element of frustrated systems and is missing in the conventional pairwise projected entangled pair states construction. Summarizing the numerical procedure (Sec.…”

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confidence: 99%

Closing in on the Kagome Magnet

Clark

2017

Physics

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The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S ¼ 1=2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of this result. DOI: 10.1103/PhysRevLett.118.137202 In one spatial dimension (1D), quantum fluctuations dominate any physical system and semiclassical order is destroyed. In higher dimensions, frustrated quantum magnets offer perhaps the cleanest systems for seeking the same physics, including quantum spin-liquid states, fractionalized spin degrees of freedom, and exotic topological properties. This challenge has now become a central focus of efforts spanning theory, numerics, experiment, and materials synthesis [1][2][3][4]. While much has been understood about frustrated systems on the triangular, pyrochlore, Shastry-Sutherland, and other 2D and 3D lattices, it is fair to say that the ground-state properties of the S ¼ 1=2 kagome Heisenberg antiferromagnet (KHAF) remain a complete enigma.An analytical Schwinger-boson approach [5], coupledcluster methods [6], and density-matrix renormalizationgroup (DMRG) calculations [7][8][9], including analysis of the topological entanglement entropy [10], all suggest a gapped spin liquid of Z 2 topology. The most sophisticated DMRG studies [9,11] estimate a triplet spin gap Δ ≥ 0.05J. Analytical large-N expansions [12] and numerical simulations by the variational Monte Carlo (VMC) technique [13,14] suggest a gapless spin liquid with U(1) symmetry and a Dirac spectrum of spinons. Extensive exactdiagonalization calculations conclude that the accessible system sizes are simply too small to judge [15,16]. Debate continues between the gapped Z 2 and gapless U(1) scenarios, with very recent arguments in support of both [17,18], while a study using symmetry-preserving tensor-network states (TNS) favors the gapped Z 2 ground state [19]. Experimental approaches to the kagome conundrum have made considerable progress in recent years, but for the purposes of the current theoretical analysis we defer a review to Sec. SI of the Supplemental Material (SM) [20].In this Letter, we employ the projected entangled simplex states (PESS) description of the entangled many-body ground state to compute the properties of the KHAF. Because we consider an infinite system, our results provide hitherto unavailable insight. As functions of the finite tensor bond dimension, we find algebraic convergence of the ground-state energy and algebraic vanishing of a finite stagger...

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Closing in on the Kagome Magnet

Clark

2017

Physics

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“…Recent numerical studies of the kagome and Husimi lattices by the method of projected entangled simplex states (PESS) [6] have demonstrated very explicitly [13] that the origin of the 1/3-plateau phase is the creation of a semiclassical up-up-down spin configuration on every triangle, as shown in Fig. 1; we stress that this statement holds for all values of S, even S = 1/2.…”

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“…These results indicate that the self-consistent spin-wave theory provides an accurate description of the properties of the magnetization plateau in the kagome antiferromagnet. We suggest that the same type of theory should also be applied to describe the properties of magnetization plateaus in a number of other frustrated systems, including the extended square and honeycomb geometries as well as the triangular [20], checkerboard, Shastry-Sutherland, and Husimi antiferromagnets [13].…”

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confidence: 99%

“…Because U k does not depend on the magnetic field, x is also independent of h in the 1/3-plateau phase, although it does depend on S. As noted above, we need therefore solve Eq. (15) only at h = 2S to obtain the spin-wave spectra, {ω j (k)}, and hence the critical fields h c1 and h c2 (13). The spin-wave spectra for the S = 1/2 case at field h = 2S are shown in Fig.…”

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

Wei

Liao

Chen

et al. 2016

Chinese Phys. Lett.

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We propose a modified spin-wave theory to study the 1/3 magnetization plateau of the antiferromagnetic Heisenberg model on the kagome lattice. By the self-consistent inclusion of quantum corrections, the 1/3 plateau is stabilized over a broad range of magnetic fields for all spin quantum numbers, S. The values of the critical magnetic fields and the widths of the magnetization plateaus are fully consistent with recent numerical results from exact diagonalization and infinite projected entangled paired states. The investigation of low-dimensional frustrated magnetism has become one of the most active frontiers in condensed matter physics. Current frontiers in the field include obtaining full insight into the entanglement structure of quantum many-body wavefunctions for different types of quantum spin liquid [1] and simplex-solid state [2]. 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]. RSPT provides analytical results for the critical magnetic fields and the width of the plateau [14]. However, a qualitative discrepancy has arisen with recent numerical results from ED [15] and iPEPS [18], not least in that the calculated plateau width increases a 1 a 2

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“…They can be approximately determined, for example, through an imaginarytime evolution by taking an entanglement mean-field approximation (also called the simple update method in the literature) [12]. With this approach, a PEPS whose bond dimension is as large as 100 or more can be readily calculated [27]. However, to calculate physical propreties, one needs to evaluate the expectation values of physical observablesÔ using the formula,…”

Section: Introductionmentioning

confidence: 99%

Optimized contraction scheme for tensor-network states

et al. 2017

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In the tensor-network framework, the expectation values of two-dimensional quantum states are evaluated by contracting a double-layer tensor network constructed from initial and final tensornetwork states. The computational cost of carrying out this contraction is generally very high, which limits the largest bond dimension of tensor-network states that can be accurately studied to a relatively small value. We propose an optimized contraction scheme to solve this problem by mapping the double-layer tensor network onto an intersected single-layer tensor network. This reduces greatly the bond dimensions of local tensors to be contracted, and improves dramatically the efficiency and accuracy of the evaluation of expectation values of tensor-network states. It almost doubles the largest bond dimension of tensor-network states whose physical properties can be efficiently and reliably calculated, and it extends significantly the application scope of tensornetwork methods.

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Heisenberg antiferromagnet on the Husimi lattice

Cited by 26 publications

References 70 publications

Closing in on the Kagome Magnet

Closing in on the Kagome Magnet

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

Optimized contraction scheme for tensor-network states

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