Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A higher-order coupled cluster treatment

Götze, O.; Farnell, Damian J. J.; Bishop, R. F.; Li, P. H. Y.; Richter, Johannes

doi:10.1103/physrevb.84.224428

Cited by 110 publications

(189 citation statements)

References 58 publications

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“…As candidate S = 1 kagome-lattice systems, m-MPYNM·BF 4 , 30, 31 NaV 3 (OH) 6 40 for S = 2 and NaBa 2 Mn 3 F 11 41 for S = 5/2 have been reported, together with theoretical studies [42][43][44] as well as an analysis based on the semiclassical limit. 13 Under these circumstances, then, we are faced with a question: do any systematic behaviors exist in the spin-S kagome-lattice Heisenberg antiferromagnet under magnetic fields?…”

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confidence: 99%

Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet

Nakano

Sakai

2015

J. Phys. Soc. Jpn.

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The magnetization process of the spin-S Heisenberg antiferromagnet on the kagome lattice is studied by the numerical-diagonalization method. Our numerical-diagonalization data for small finite-size clusters with S = 1, 3/2, 2, and 5/2 suggest that a magnetization plateau appears at one-third of the height of the saturation in the magnetization process irrespective of S. We discuss the S dependences of the edge fields and the width of the plateau in comparison with recent results obtained by real-space perturbation theory.Frustrated spin systems have attracted much attention from many condensed-matter physicists. One of the fascinating systems among them is the kagome-lattice Heisenberg antiferromagnet. Unfortunately, our understanding of this system is still far from complete in spite of many experimental and theoretical studies. In the S = 1/2 system, in particular, discoveries of several realistic materials such as herbertsmithite, 1, 2 volborthite, 3, 4 and vesignieite 5, 6 have accelerated theoretical studies. 7-29 However, there remain some unresolved issues; one of them is the spin-gap problem of whether the spin excitation above the singlet ground state is gapped or gapless.On the other hand, fewer studies on S > 1/2 cases have been carried out. As candidate S = 1 kagome-lattice systems, m-MPYNM·BF 4 , 30, 31, 33 and KV 3 Ge 2 O 9 34 are known. Theoretical studies 9, 35-39 for the S = 1 case are also limited. Studies on the S > 1 cases have only started recently; candidate kagome-lattice systems of Cs 2 Mn 3 LiF 12 40 for S = 2 and NaBa 2 Mn 3 F 11 41 for S = 5/2 have been reported, together with theoretical studies 42-44 as well as an analysis based on the semiclassical limit. 13 Under these circumstances, then, we are faced with a question: do any systematic behaviors exist in the spin-S kagome-lattice Heisenberg antiferromagnet under magnetic fields? The purpose of this letter is to extract such systematic behavior of the magnetization processes of this model for various S by numerical-diagonalization calculations that are unbiased against approximations. With the same motivation, Zhitomirsky recently investigated the frustrated Heisenberg model under magnetic fields by real-space perturbation theory taking into account fluctuations around a classical configuration. 44 He found that in the magnetization process of the kagome-lattice antiferromagnet, the so-called uud state is stable at one-third of the height of the saturation, at which a magnetization plateau appears irrespective of the value of S. He also derived an expression for the 1/S expansion for both the edge fields of this height. The comparison between the * E-mail: hnakano@sci.u-hyogo.ac.jp † present numerical-diagonalization results and the results from real-space perturbation theory should contribute to our understanding of the frustration effect in the kagome-lattice antiferromagnet.The Hamiltonian that we study in this research is given by H = H 0 + H Zeeman , whereandHere, S i denotes the spin operator at site i, where the sites are th...

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confidence: 99%

Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet

Nakano

Sakai

2015

J. Phys. Soc. Jpn.

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“…This model has been extensively studied in recent years. Some of the DMRG [39][40][41], coupled cluster expansion [42] and analytical Schwinger-boson meanfield calculation [43] suggest that its ground state is a gapped quantum spin liquid of Z 2 topology. Other work, including analytical large-N expansions [44], variational Monte Carlo simulations [45,46], and, more recently, tensor renormalization group calculations [24], suggest that the ground state is a gapless spin liquid with U(1) symmetry and a Dirac spectrum of spinons.…”

Section: Resultsmentioning

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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“…In the limit of large S , the ground state of KHAF was argued to be the √ 3 × √ 3 state [that is the state with 120 • spin configuration within a unit cell of area √ 3a × √ 3a containing nine sites as illustrated in Fig. 1(a)] with a long-range magnetic order [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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

Liu

2016

Phys. Rev. E

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Three different tensor network (TN) optimization algorithms are employed to accurately determine the ground state and thermodynamic properties of the spin-3/2 kagome Heisenberg antiferromagnet. We found that the √ 3 × √ 3 state (i.e., the state with 120 • spin configuration within a unit cell containing 9 sites) is the ground state of this system, and such an ordered state is melted at any finite temperature, thereby clarifying the existing experimental controversies. Three magnetization plateaus (m/m s = 1/3, 23/27, and 25/27) were obtained, where the 1/3-magnetization plateau has been observed experimentally. The absence of a zero-magnetization plateau indicates a gapless spin excitation that is further supported by the thermodynamic asymptotic behaviors of the susceptibility and specific heat. At low temperatures, the specific heat is shown to exhibit a T 2 behavior, and the susceptibility approaches a finite constant as T → 0. Our TN results of thermodynamic properties are compared with those from high temperature series expansion. In addition, we disclose a quantum phase transition between q = 0 state (i.e. the state with 120 • spin configuration within a unit cell containing three sites) and √ 3 × √ 3 state in a spin-3/2 kagome XXZ model at the critical point ∆ c = 0.54. This study provides reliable and useful information for further explorations on high spin kagome physics.

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Heisenberg antiferromagnet on the kagome lattice with arbitrary spin: A higher-order coupled cluster treatment

Cited by 110 publications

References 58 publications

Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet

Magnetization Process of the Spin-S Kagome-Lattice Heisenberg Antiferromagnet

Optimized contraction scheme for tensor-network states

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

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