arXiv:cond-mat/0602487 · Physical Review B

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

Raoul Dillenschneider, J. Richert

Published Jun 30, 2006• 11 citations

Abstract

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 $SU(2)$ spin. This is realized by means of a specific prescription. We consider the low-energy Hamiltonian which is mapped into a ${\mathrm{QED}}_{3}$ Lagrangian of spinons. We compare the dynamically generated mass to the one obtained by means of an average site occupation constraint.

DOI: 10.1103/physrevb.73.224443

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arXiv:cond-mat/0602487 · Physical Review B

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

Raoul Dillenschneider, J. Richert

Published Jun 30, 2006• 11 citations

arXiv HTML PDF

Abstract

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)

spin. This is realized by means of a specific prescription. We consider the low-energy Hamiltonian which is mapped into a

{\mathrm{QED}}_{3}

Lagrangian of spinons. We compare the dynamically generated mass to the one obtained by means of an average site occupation constraint.

DOI: 10.1103/physrevb.73.224443

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Raoul Dillenschneider, J. Richert

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 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.

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arXiv:cond-mat/0405438Physical Review BNov 1, 20047 citations

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)

spin. This is realized by means of a specific prescription. We consider the low-energy Hamiltonian which is mapped into a

{\mathrm{QED}}_{3}

Lagrangian of spinons. We compare the dynamically generated mass to the one obtained by means of an average site occupation constraint.

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.

The nearest-neighbor quantum antiferromagnetic (AF) Heisenberg model for spin-

1∕2

on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge

{Q}_{i}=1

on each lattice site

i

, which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length, $\ensuremath{\xi}(T)\ensuremath{\propto}\mathrm{exp}(aJ∕T)$, come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low

T

. This drawback, which is caused by overdamping, is overcome in a ``minimal self-consistent approximation'' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths $\ensuremath{\lambda}>\ensuremath{\xi}$ and in the short-range-order regime at $\ensuremath{\lambda}<\ensuremath{\xi}$. We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.