Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems

An interacting spin system is investigated within the scenario of the Feynman path integral representation of quantum mechanics. Short-time propagator algorithms and a discrete time formalism are used in combination with a basis set involving Grassmann variables coherent states to get a many-body an...

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Detalles Bibliográficos
Autores principales:	Anicich, P.G.O., Grinberg, H.
Formato:	JOUR
Materias:	Generating function Grassmann algebra Ising model Path integral Spin system Algebra Algorithms Functions Integral equations Magnetization Mathematical transformations Time domain analysis Generating functions Grassmann coherent states representation Jordan-Wigner transformations Spin systems Quantum theory
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00207608_v90_n6_p1562_Anicich
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_00207608_v90_n6_p1562_Anicich
record_format	dspace
spelling	todo:paper_00207608_v90_n6_p1562_Anicich2023-10-03T14:19:37Z Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems Anicich, P.G.O. Grinberg, H. Generating function Grassmann algebra Ising model Path integral Spin system Algebra Algorithms Functions Integral equations Magnetization Mathematical transformations Time domain analysis Generating functions Grassmann coherent states representation Ising model Jordan-Wigner transformations Path integral Spin systems Quantum theory An interacting spin system is investigated within the scenario of the Feynman path integral representation of quantum mechanics. Short-time propagator algorithms and a discrete time formalism are used in combination with a basis set involving Grassmann variables coherent states to get a many-body analytic propagator. The generating function thus obtained leads, after an adequate tracing over Grassmann variables in the imaginary time domain, to the partition function. A spin 1/2 Hamiltonian involving the whole set of interactions is considered. Fermion operators satisfying the standard anticommutation relations are constructed from the raising and lowering spin operators via the Jordan-Wigner transformation. The partition function obtained is more general than the partition function of the traditional Ising model involving only first-neighbor interactions. Computations were performed assuming that the coupling as a function of the distance can be reasonably well represented by an Airy function. Fil:Anicich, P.G.O. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Grinberg, H. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00207608_v90_n6_p1562_Anicich
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Generating function Grassmann algebra Ising model Path integral Spin system Algebra Algorithms Functions Integral equations Magnetization Mathematical transformations Time domain analysis Generating functions Grassmann coherent states representation Ising model Jordan-Wigner transformations Path integral Spin systems Quantum theory
spellingShingle	Generating function Grassmann algebra Ising model Path integral Spin system Algebra Algorithms Functions Integral equations Magnetization Mathematical transformations Time domain analysis Generating functions Grassmann coherent states representation Ising model Jordan-Wigner transformations Path integral Spin systems Quantum theory Anicich, P.G.O. Grinberg, H. Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems
topic_facet	Generating function Grassmann algebra Ising model Path integral Spin system Algebra Algorithms Functions Integral equations Magnetization Mathematical transformations Time domain analysis Generating functions Grassmann coherent states representation Ising model Jordan-Wigner transformations Path integral Spin systems Quantum theory
description	An interacting spin system is investigated within the scenario of the Feynman path integral representation of quantum mechanics. Short-time propagator algorithms and a discrete time formalism are used in combination with a basis set involving Grassmann variables coherent states to get a many-body analytic propagator. The generating function thus obtained leads, after an adequate tracing over Grassmann variables in the imaginary time domain, to the partition function. A spin 1/2 Hamiltonian involving the whole set of interactions is considered. Fermion operators satisfying the standard anticommutation relations are constructed from the raising and lowering spin operators via the Jordan-Wigner transformation. The partition function obtained is more general than the partition function of the traditional Ising model involving only first-neighbor interactions. Computations were performed assuming that the coupling as a function of the distance can be reasonably well represented by an Airy function.
format	JOUR
author	Anicich, P.G.O. Grinberg, H.
author_facet	Anicich, P.G.O. Grinberg, H.
author_sort	Anicich, P.G.O.
title	Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems
title_short	Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems
title_full	Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems
title_fullStr	Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems
title_full_unstemmed	Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems
title_sort	grassmann coherent states representation of the path integral: evaluation of the generating function for spin systems
url	http://hdl.handle.net/20.500.12110/paper_00207608_v90_n6_p1562_Anicich
work_keys_str_mv	AT anicichpgo grassmanncoherentstatesrepresentationofthepathintegralevaluationofthegeneratingfunctionforspinsystems AT grinbergh grassmanncoherentstatesrepresentationofthepathintegralevaluationofthegeneratingfunctionforspinsystems
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Grassmann coherent states representation of the path integral: Evaluation of the generating function for spin systems

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