Holstein-Primakoff representation
One of the very important aspects of quantum mechanics is the occurrence of—in general—non-commuting operators which represent observables, quantities that we can measure. A standard example of a set of such operators are the three components of the angular momentum operators, which are crucial in many quantum systems. These operators are complicated, and we would like to be able to find a simpler representation, which can be used to generate approximate calculational schemes.
The original Holstein-Primakoff transformation in quantum mechanics is a mapping from the angular momentum operators to boson creation and annihilation operators. As can be seen from a paper with about 1000 citations, this method has found widespread applicability and has been extended in many different directions. There is a close link to other methods of boson mapping of operator algebras; in particular the Dyson-Maleev technique, and to a lesser extent the Schwinger mapping. There is a close link to the theory of (generalized) coherent states in Lie algebras.

This is an excerpt from the article Holstein-Primakoff representation from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
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Holstein–Primakoff transformation - Wikipedia, the free encyclopedia
The original Holstein-Primakoff transformation in quantum mechanics is a mapping from the ... (i.e., we look at a single irreducible representation of SU(2)).
en.wikipedia.org/wiki/Holstein%E2%80%93Primakoff_transformation
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Holstein-Primakoff and Dyson-Maleev representation
Oct 23, 2012 ... In Holstein-Primakoff and Dyson-Maleev representation, spin operators are represented by bosonic operators. Roughly speaking, a state with ...
physics.stackexchange.com/questions/41485/holstein-primakoff-and-dyson-maleev-representation
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The classical limit for the Holstein-Primakoff representation in the ...
Soliton excitations in the anisotropic Heisenberg chain are studied in the classical limit by means of the Holstein-Primakoff boson representation, taking into ...
iopscience.iop.org/0953-8984/1/4/007
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Spin waves
Holstein-Primakoff approach, people often define m distinct flavors of boson, one on ... are often the same on each site, i.e. the spin waves can be represented in.
people.ccmr.cornell.edu/~clh/p654/5.5.pdf
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Lecture Notes - Rudolf Peierls Centre for Theoretical Physics
The second-quantised representation is. ˆA = ∑ pq ..... make approximations, and the Holstein-Primakoff transformation provides a convenient way to do so.
www-thphys.physics.ox.ac.uk/people/JohnChalker/qtcm/lecture-notes.pdf
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Boson Realization of the su(3)-Algebra. IV Holstein-Primakoff ...
On the basis of the Schwinger boson representation for the Elliott model developed in. (III), the Holstein-Primakoff representation for the su(3)-algebra is ...
ptp.ipap.jp/link?PTP/115/561/pdf
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HomeWork 2 : Representation of the spin 1 Natural representation of ...
of the spin known as the Holstein-Primakoff transformation. Within this ... operators. In this exercice, we show that a representation for spin 1/2 can be obtained in.
www.itp.uni-hannover.de/~flohr/lectures/stat/hw2.pdf
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Modification of the Conventional Holstein-Primakoff Boson ...
Abstract. In order to avoid unsatisfactory points of the conventional Holstein-Primakoff representation of the su(1,1)-algebra for the description of thermal effects ...
ptp.oxfordjournals.org/content/99/5/819.abstract
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HOLSTEIN-PRIMAKOFF REPRESENTATION FOR ... - Springer
HOLSTEIN-PRIMAKOFF. REPRESENTATION FOR STRONGLY. CORRELATED ELECTRON SYSTEMS. Siyavush Azakov. Institute of Physics, Azerbaijan ...
link.springer.com/content/pdf/10.1007%2F1-4020-2708-7_7.pdf
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PJH note
3.3.1 Holstein-Primakoff transformation . . . . . . 15. 3.3.2 Linear ..... representation forˆSz, which can be obtained by using the identity. (on a given site i). ˆ. S. 2.
www.phys.ufl.edu/~pjh/teaching/phz7427/7427notes/ch3.pdf
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Holstein-Primakoff representation in science
[PDF]Boson Realization of the su(3)-Algebra. IV Holstein-Primakoff ...
Holstein-Primakoff representation for the Elliott Model. Constança Providência, ... Faculty of Engineering, Kansai University, Suita 564-8680, Japan. (Received ...
Functional Schr\" odinger Representations of Holstein-Primakoff ...
Mar 10, 1999... Sung-Ho Suck Salk (Pohang University of Science and Technology, ... the functional Schr\"odinger representation of the Holstein-Primakoff ...
[PDF]Boson Realization of the su (3)-Algebra. II
Sep 30, 2005 ... Holstein-Primakoff representation for the Lipkin Model. Constança ... 2Physics Division, Faculty of Science, Kochi University, Kochi 780-8520,.
Boson Realization of the u(3)-Algebra. II --Holstein-Primakoff ...
... of the u(3)-Algebra. II --Holstein-Primakoff representation for the Lipkin Model ---. ... ABSTRACT On the basis of the Schwinger boson representation for the Lipkin model developed in (I), the ...... J. da Providência. University of Coimbra ...
Modification of the Conventional Holstein-Primakoff Boson ...
Modification of the Conventional Holstein-Primakoff Boson Representation for ... Kuriyama Atsushi KURIYAMA Atsushi; Faculty of Engineering, Kansai University.
Modification of the Conventional Holstein-Primakoff Boson ...
Modification of the Conventional Holstein-Primakoff Boson Representation for the su(1,1)-Algebra and Its Classical ... Oxford Journals Oxford University Press.
Boson Realization of the su(3)-Algebra. IV: Holstein-Primakoff ...
IV: Holstein-Primakoff representation for the Elliott Model ... 2Physics Division, Faculty of Science, Kochi University, Kochi 780-8520, Japan. 3Faculty of ...
Boson Realization of the su (3)-Algebra. IV: Holstein-Primakoff ...
Boson Realization of the su (3)-Algebra. IV: Holstein-Primakoff representation for the Elliott Model. Providência, Constança; da Providência, João; Tsue, ...
Holstein–Primakoff transformation - Wikipedia, the free encyclopedia
One of the very important aspects of quantum mechanics is the occurrence of—in general—non-commuting operators which represent observables, quantities ...
Holstein-Primakoff Representation for Strongly Correlated Electron ...
Holstein-Primakoff representation for Strongly Correlated Electron Systems. Siyavush Azakov … show ... University of Pennsylvania. Authors. Siyavush Azakov ...
Books on the term Holstein-Primakoff representation
Interacting Electrons and Quantum Magnetism
Interacting Electrons and Quantum Magnetism
Assa Auerbach, 1994
Spin. Representations. 7.1. Holstein-Primakoff. Bosons. The spin is a vector operator. In a broken symmetry phase, the expectation value of at least one of its component is nonzero. It is natural to describe the ordered phase in terms of small ...
Condensed Matter Physics
Condensed Matter Physics
Michael P. Marder, 2010
This Second Edition presents an updated review of the whole field of condensed matter physics. It consolidates new and classic topics from disparate sources, teaching not only about the effective masses of electrons in semiconductor crystals and band theory, but also about quasicrystals, dynamics of phase separation, why rubber is more floppy than ...
Physics of Spin in Solids: Materials, Methods and ...
Physics of Spin in Solids: Materials, Methods and ...
Samed Halilov, 2006
This is the standard way to develop the spin-wave technique for quantum spin systems, by introducing Holstein-Primakoff (HP) representation [8]. It is worthwhile to note, that when we speak about a specific model we assume a specific choice ...
Condensed Matter Field Theory
Condensed Matter Field Theory
Alexander Altland, 2010
Modern experimental developments in condensed matter and ultracold atom physics present formidable challenges to theorists. This book provides a pedagogical introduction to quantum field theory in many-particle physics, emphasizing the applicability of the formalism to concrete problems. This second edition contains two new chapters developing path...
Quantum Physics: Volume 1: From Basics to Symmetries and ...
Quantum Physics: Volume 1: From Basics to Symmetries and ...
Vladimir Zelevinsky, 2011
With the aid of these operators, explicitly construct states with given total angular momentum J and its projection M. Solution In the Holstein-Primakoff representation, Problem 16.8, we used the operators of spin deviations starting from the ...
Quantum Physics: Volume 1 - From Basics to Symmetries and Perturbations
Quantum Physics: Volume 1 - From Basics to Symmetries and Perturbations
2010
This two-volume set can be naturally divided into two semester courses, and contains a full modern graduate course in quantum physics. The idea is to teach graduate students how to practically use quantum physics and theory, presenting the fundamental knowledge, and gradually moving on to applications, including atomic, nuclear and solid state phys...
Condensed Matter Field Theory
Condensed Matter Field Theory
Alexander Altland, Ben D. Simons, 2010
Schwinger boson representation As with the Holstein—Primakoff representation, the Schwinger boson provides another representation of quantum mechanical spin. The aim of this problem is to confirm the validity of the representation.
Mathematical Optics: Classical, Quantum, and Computational ...
Mathematical Optics: Classical, Quantum, and Computational ...
Vasudevan Lakshminarayanan, María L. Calvo, Tatiana Alieva, 2012
The representation space is constructed in terms of quantum states with even photon numbers for k: 1/4 and with odd ... Furthermore, the SU(1,1) Lie generators in the Holstein—Primakoff representation are given by K, I ~/2k _1+ alaal, K, ...
Physics of Amorphous Metals
Physics of Amorphous Metals
2001
"...concentrates on the theoretical description, understanding, and derivation of the properties of glassy metals..." (SciTech Book News, Vol. 26, No. 2, June 2002)
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