Unified spin-wave theory for quantum spin systems with single-ion anisotropies

Zhou, Lei

doi:10.1088/0305-4470/32/38/307

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…In some cases more stringent exactness criteria have been applied, such as requiring that all non-physical matrix elements vanish [70]. This type of criteria can simplify formal quantum statistical treatments, since one does not have to be careful about excluding non-physical states in sums over states.…”

Section: E Commutator Properties and Exactness For The Improved Expan...mentioning

confidence: 99%

“…This is by no means an exhaustive list of spin representations -indeed, other representations can be be found in Refs. [65][66][67][68][69][70]. Since each of the available approaches has its own unique advantages and drawbacks, we will in this paper derive expressions for spin operators that i) involve only one boson species satisfying the canonical bosonic commutation relation, ii) preserve hermiticity, and iii) do not include square-roots or other non-polynomial functions of operators.…”

Section: Introductionmentioning

confidence: 99%

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Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots

Vogl,

Laurell,

Zhang

et al. 2020

Preprint

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Operator square-roots are ubiquitous in theoretical physics. They appear, for example, in the Holstein-Primakoff representation of spin operators and in the Klein-Gordon equation. Often the use of a perturbative expansion is the only recourse when dealing with them. In this work we show that under certain conditions differential equations can be derived which can be used to find perturbatively inaccessible approximations to operator square-roots. Specifically, for the number operator n = â † a we show that the square-root √ n near n = 0 can be approximated by a polynomial in n. This result is unexpected because a Taylor expansion fails. A polynomial expression in n is possible because n is an operator, and its constituents a and a † have a non-trivial commutator [a, a † ] = 1 and do not behave as scalars. We apply our approach to the zero mass Klein-Gordon Hamiltonian in a constant magnetic field, and as a main application, the Holstein-Primakoff representation of spin operators, where we are able to find new expressions that are polynomial in bosonic operators. We prove that these new expressions exactly reproduce spin operators. Our expressions are manifestly Hermitian, which offer an advantage over other methods, such as the Dyson-Maleev representation. I. NOTICE OF COPYRIGHTThis manuscript has been authored in part by UT-Battelle, LLC, under contract DE-AC05-00OR22725 with the US Department of Energy (DOE). The US government retains and the publisher, by accepting the article for publication, acknowledges that the US government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for US government purposes. DOE will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http: //energy.gov/downloads/doe-public-access-plan).

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Section: E Commutator Properties and Exactness For The Improved Expan...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots

Vogl,

Laurell,

Zhang

et al. 2020

Preprint

View full text Add to dashboard Cite

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Interacting spin-wave dispersion relations of ferrimagnetic Heisenberg chains with crystal-field anisotropy

Solano-Carrillo

Franco

Silva–Valencia

2010

Solid State Communications

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Quantum Phase Transition in Quasi-two-dimensional Heisenberg Antiferromagnet with Single-Ion Anisotropy

Ji¹

2007

Commun. Theor. Phys.

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In the present paper, we investigate the quantum phase transition in a spatially anisotropic antiferromagnetic Heisenberg model of S = 1 with single-ion energy anisotropy. By using the Schwinger boson representation, we calculate the Gaussian correction to the critical value J⊥c caused by quantum spin fluctuations. We find that, for the positive single-ion energy, a nonzero value of J⊥c is always needed to stabilize the antiferromagnetic long-range order in this model. It resolves a difference among literature and shows clearly that the effect of quantum fluctuations may qualitatively change a result obtained by the mean-field theories on lower-dimensional systems.

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Unified spin-wave theory for quantum spin systems with single-ion anisotropies

Cited by 5 publications

References 23 publications

Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots

Exact resummation of the Holstein-Primakoff expansion and differential equation approach to operator square-roots

Interacting spin-wave dispersion relations of ferrimagnetic Heisenberg chains with crystal-field anisotropy

Quantum Phase Transition in Quasi-two-dimensional Heisenberg Antiferromagnet with Single-Ion Anisotropy

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