The coupled cluster method applied to quantum magnetism

Starting with Wannier's 1) and Anderson's 2) seminal papers the triangular-lattice antiferromagnet has attracted a lot of attention. One spectacular feature of this model system for a strongly frustrated magnet is the unconventional magnetization process of the triangular-lattice Heisenberg antiferromagnet. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] While for the classical isotropic Heisenberg model at zero temperature the magnetization M increases linearly with the applied magnetic field H, thermal or quantum fluctuations induce a plateau at 1/3 of the saturation magnetization M sat (''order from disorder'' phenomenon). For the extreme quantum case, i.e., spin quantum number s ¼ 1=2, this plateau at T ¼ 0 has been widely discussed. Very recently an almost perfect experimental realization of an s ¼ 1=2 triangular-lattice Heisenberg antiferromagnet has been reported for Ba 3 CoSb 2 O 9 , 17) where the entire measured magnetization curve MðHÞ including the 1/3 plateau is in excellent agreement with theoretical predictions. In particular, the theoretical magnetization data obtained by high-order coupled-cluster approximation 11) and by large-scale exact diagonalization approach 15) almost coincide with the measured ones over a wide range of the magnetic field.Another interesting triangular-lattice magnet is Ba 3 -NiSb 2 O 9 that is considered as a good candidate of an s ¼ 1 triangular-lattice Heisenberg antiferromagnet. 16,18,19) In Ba 3 NiSb 2 O 9 , the uniform triangular lattice of magnetic ions is realized as in Ba 3 CoSb 2 O 9 . Indeed, recently it has been found that the magnetization curve of this compound also exhibits a clear 1/3 plateau. 16) By contrast to the wellinvestigated spin-half case there are much less reliable theoretical studies of the s ¼ 1 model relevant for Ba 3 NiSb 2 O 9 . Motivated by the excellent agreement of theoretical predictions based on exact diagonalization (ED) and coupled-cluster method (CCM) and experimental results for the spin-half compound Ba 3 CoSb 2 O 9 reported in Ref. 17 we apply in this paper these methods to the s ¼ 1 model to provide theoretical data to compare with experimental results.For the s ¼ 1 model the Lanczos ED for N ¼ 27 sites and the CCM-SUBn-n approximation 20) for n ¼ 2; 4; 6; 8 are used to calculate the field-dependent properties of the model.In this short note we will not explain details of the Lanczos ED and the CCM. We refer the interested reader e.g., to Refs. 15,21, 22 and 11,[23][24][25] respectively. First we report the main theoretical results. The saturation field is H sat ¼ 9Js ¼ 9J, where J is the nearest-neighbor exchange coupling. The zero-field uniform susceptibility calculated with CCM-SUBn-n approximation is ¼ 0:10790, 0.09932, 0.09785, and 0.09679 for n ¼ 2, 4, 6, and 8, respectively. Moreover, it is useful to extrapolate the ''raw'' SUBn-n data to n ! 1 by ðnÞ ¼ c 0 þ c 1 ð1=nÞ þ c 2 ð1=nÞ 2 which yields finally our CCM estimate for the susceptibility CCM ¼ 0:0956. This value is in excellent agreement with the spin-wave res...

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“…We refer the interested reader e.g., to Refs. 15,21, 22 and 11,[23][24][25] respectively. First we report the main theoretical results.…”

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confidence: 99%

The Magnetization Process of the Spin-One Triangular-Lattice Heisenberg Antiferromagnet

et al. 2013

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“…The CCM [58][59][60][61][62][63][64][65][66][67][68][69] is one of the very few size-extensive and size-consistent techniques of quantum many-body theory. It thereby provides results in the N → ∞ limit (where N is the number of particles, i.e., lattice spins in our case) from the outset, at all levels of approximation.…”

Section: The Coupled Cluster Methodsmentioning

confidence: 99%

“…The quantum correlations present in the exact GS or excited-state (ES) wave function of the system are then systematically incorporated on top of the model state in a hierarchical scheme that becomes exact in some limit, which is usually unattainable at particular levels of computational implementation. Appropriate conditions for a state to be a suitable CCM model state have been discussed extensively in the literature [61,63,[66][67][68][69]. For spin-lattice models, however, all (quasi)classical states with perfect magnetic LRO are suitable CCM model states.…”

Section: The Coupled Cluster Methodsmentioning

confidence: 99%

“…[41,[58][59][60][61][62][63][64][65][66][67][68][69] for a fuller description. It is very convenient to be able to treat each lattice spin in each model state as being equivalent to one another.…”

Section: The Coupled Cluster Methodsmentioning

confidence: 99%

“…We have described in detail elsewhere (and see, e.g., Refs. [69,90,93] and references cited therein) how the otherwise infinite-order nested commutator expansion…”

Section: The Coupled Cluster Methodsmentioning

confidence: 99%

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High-order study of the quantum critical behavior of a frustrated spin- 12 antiferromagnet on a stacked honeycomb bilayer

Bishop

2017

Phys. Rev. B

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Numerical Simulations of Frustrated Systems

Läuchli

2010

Introduction to Frustrated Magnetism

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In many fields of science, computational approaches have become one of the central cornerstones alongside experimental and theoretical approaches. This is also the case in the field of frustrated magnetic systems, where theory, simulations, and experiments drive each other mutually, thus advancing our overall understanding. This chapter aims to provide an overview of the most common numerical techniques available for strongly correlated lattice models, with an emphasis on frustrated spin systems. While it is not possible to treat all methods in sufficient depth to provide a comprehensive introduction, here the key ideas are presented and special issues regarding their application to frustrated systems are discussed. The power of these techniques is illustrated by examples taken from the literature, 1 and specific references to appropriate detailed presentations are included where possible. Overview of MethodsIn this chapter, I present on a general level both classical and quantum Monte Carlo methods, series-expansion techniques, and the density-matrix renormalizationgroup approach, and illustrate their utility by selected applications. I then treat in rather more detail the exact-diagonalization technique, as this is not documented so extensively in the literature. I close by touching briefly on a small number of methods which are not so widespread and by providing some links to available source codes. Classical Monte CarloThe Monte Carlo technique is a probabilistic approach applicable to a large class of statistical physics problems. The method performs a stochastic evaluation of the expectation values of observables O, based for example on the canonical ensemble 1 The choice of examples here is subjective, and unfortunately cannot be exhaustive. 481

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The coupled cluster method applied to quantum magnetism

Cited by 62 publications

References 83 publications

The Magnetization Process of the Spin-One Triangular-Lattice Heisenberg Antiferromagnet

The Magnetization Process of the Spin-One Triangular-Lattice Heisenberg Antiferromagnet

High-order study of the quantum critical behavior of a frustrated spin- 12 antiferromagnet on a stacked honeycomb bilayer

Numerical Simulations of Frustrated Systems

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