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Effects of a strict site-occupation constraint in the description of quantum spin systems at finite temperature

Raoul Dillenschneider

Published Sep 8, 2006• 0 citations
OpenAlex

Abstract

We study quantum spin systems described by Heisenberg-like models at finite temperature with a strict site-occupation constraint imposed by a procedure originally proposed by V. N. Popov and S. A. Fedotov. We show that the strict site-occupation constraint modifies quantitatively the behaviour of physical quantities when compared to the case for which this constraint is fixed in the average by means of a Lagrange multiplier method. The relevance of the Neel state with the strict site-occupation contraint of the spin lattice is studied. With an exact site-occupation the transition temperature of the antiferromagnetic Neel and spin liquid order parameters are twice as large as the critical temperature one gets with an average Lagrange multiplier method. We consider also a mapping of the low-energy spin Hamiltonian into a QED3 Lagrangian of spinons. In this framework we compare the dynamically generated mass to the one obtained by means of an average site-occupation constraint.

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Effects of a strict site-occupation constraint in the description of quantum spin systems at finite temperature

Raoul Dillenschneider

We study quantum spin systems described by Heisenberg-like models at finite temperature with a strict site-occupation constraint imposed by a procedure originally proposed by V. N. Popov and S. A. Fedotov \cite{Popov-88}. We show that the strict site-occupation constraint modifies quantitatively the behaviour of physical quantities when compared to the case for which this constraint is fixed in the average by means of a Lagrange multiplier method. The relevance of the Néel state with the strict site-occupation contraint of the spin lattice is studied. With an exact site-occupation the transition temperature of the antiferromagnetic Néel and spin liquid order parameters are twice as large as the critical temperature one gets with an average Lagrange multiplier method. We consider also a mapping of the low-energy spin Hamiltonian into a $QED_3$ Lagrangian of spinons. In this framework we compare the dynamically generated mass to the one obtained by means of an average site-occupation constraint.

arXiv:cond-mat/0609239•Sep 11, 2006•0 citations

Strict site-occupation constraint in two-dimensional Heisenberg models and dynamical mass generation in QED3 at finite temperature

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FINITE TEMPERATURE RESULTS FROM CONSTRAINED FERMIONIZATION IN THE 2-D SPIN 1/2 HEISENBERG ANTIFERROMAGNET I: THE NÉEL PHASE

Mario Di Stasio, A. Tagliacozzo, Elisa Ercolessi +1 more

The antiferromagnetic saddle point is studied up to one-loop corrections, including, within the same approximation, the constraint of single site occupancy in the fermionization procedure, at all temperatures. The resulting spin wave spectrum and zero point fluctuations are the same as those of the spin wave theory. The effect of the constraint on the temperature dependence of the specific heat is discussed.

International Journal of Modern Physics B•Mar 15, 1994•4 citations
We study quantum spin systems described by Heisenberg-like models at finite temperature with a strict site-occupation constraint imposed by a procedure originally proposed by V. N. Popov and S. A. Fedotov. We show that the strict site-occupation constraint modifies quantitatively the behaviour of physical quantities when compared to the case for which this constraint is fixed in the average by means of a Lagrange multiplier method. The relevance of the Neel state with the strict site-occupation contraint of the spin lattice is studied. With an exact site-occupation the transition temperature of the antiferromagnetic Neel and spin liquid order parameters are twice as large as the critical temperature one gets with an average Lagrange multiplier method. We consider also a mapping of the low-energy spin Hamiltonian into a QED3 Lagrangian of spinons. In this framework we compare the dynamically generated mass to the one obtained by means of an average site-occupation constraint.
We study quantum spin systems described by Heisenberg-like models at finite temperature with a strict site-occupation constraint imposed by a procedure originally proposed by V. N. Popov and S. A. Fedotov \cite{Popov-88}. We show that the strict site-occupation constraint modifies quantitatively the behaviour of physical quantities when compared to the case for which this constraint is fixed in the average by means of a Lagrange multiplier method. The relevance of the Néel state with the strict site-occupation contraint of the spin lattice is studied. With an exact site-occupation the transition temperature of the antiferromagnetic Néel and spin liquid order parameters are twice as large as the critical temperature one gets with an average Lagrange multiplier method. We consider also a mapping of the low-energy spin Hamiltonian into a QED3QED_3QED3​ Lagrangian of spinons. In this framework we compare the dynamically generated mass to the one obtained by means of an average site-occupation constraint.
We study the effect of site occupation in two-dimensional quantum spin systems at finite temperature in a $\ensuremath{\pi}$-flux state description at the mean-field level. We impose each lattice site to be occupied by a single SU(2)SU(2)SU(2) spin. This is realized by means of a specific prescription. We consider the low-energy Hamiltonian which is mapped into a QED3{\mathrm{QED}}_{3}QED3​ Lagrangian of spinons. We compare the dynamically generated mass to the one obtained by means of an average site occupation constraint.
We study the effect of site occupation on the description of quantum spin systems at finite temperature and mean-field level. We impose each lattice site to be occupied by a single electron. This is realized by means of a specific prescription. The outcome of the prescription is compared to the result obtained by means of a projection procedure that fixes the site occupation to one particle per site, on average. The comparison is performed for different representations of the Hamiltonian in Fock space leading to different types of mean-field solutions. The behavior of order parameters is analyzed for each choice of the mean-field and constraint that fixes the occupation rate at each site. Sizable quantitative differences between the outcomes obtained with the two different constraints are observed.
We implement a Chern-Simons (CS) contribution into the compact QED3 description of the antiferromagnetic Heisenberg model in two dimensions at zero temperature. The CS term allows for the conservation of the SU(2) symmetry of the quantum spin system and fixes the flux through a plaquette to be a multiple of pi as was shown by Marston. We work out the string tension of the confining potential which acts between the spinons and show that the CS term induces a screening effect on the magnetic field only. The confining potential between spinons is not affected by the CS flux. The strict site-occupation by a single spin-1/2 is enforced by the introduction of an imaginary chemical potential constraint.
We present diagrammatic approximations to the spin dynamics of the 2d Heisenberg antiferromagnet for all temperatures, employing an auxiliary-fermion representation. The projection onto the physical subspace is effected by introducing an imaginary-valued chemical potential as proposed by Popov and Fedotov. The method requires that the fermion number at any lattice site is strictly conserved. We compare results obtained within a self-consistent approximation using two different auxiliary-particle projection schemes, (1) exact and (2) on average. Significant differences between the two are found at higher temperatures, whereas in the limit of zero temperature (approaching the magnetically ordered ground state) identical results emerge from (1) and (2), providing the qualitatively correct dynamical scaling behavior. An interpretation of these findings is given. We also present in some detail the derivation of the approximation, which goes far beyond mean-field theory and is formulated in terms of complex-valued spectral functions of auxiliary fermions.