The behavior of ordered quantum Heisenberg antiferromagnets is analyzed from the nonlinear \ensuremath{\sigma} model in two and three dimensions. Many thermodynamic and dynamic properties are found to be universal at low temperatures and small magnetic fields. Finite-size effects are also investigated in detail; the results should be useful for analyzing numerical work on two-dimensional (2D) quantum antiferromagnets. The X-Y phase transition in 2D which is induced by a magnetic field is discussed. Applications to the ordered phase of solid $^{3}\mathrm{He}$ are also given.The behavior of ordered quantum Heisenberg antiferromagnets is analyzed from the nonlinear \ensuremath{\sigma} model in two and three dimensions. Many thermodynamic and dynamic properties are found to be universal at low temperatures and small magnetic fields. Finite-size effects are also investigated in detail; the results should be useful for analyzing numerical work on two-dimensional (2D) quantum antiferromagnets. The X-Y phase transition in 2D which is induced by a magnetic field is discussed. Applications to the ordered phase of solid $^{3}\mathrm{He}$ are also given.

Physical review. B, Condensed matterJun 1, 1989111 citations

The numerical value for a universal quantity of a two-dimensional dimerized quantum antiferromagnet

Fu-Jiun Jiang

The numerical value of a universal quantity associated with the quantum critical regime, namely χuc2/T, for a two-dimensional (2D) dimerized spin-1/2 antiferromagnet is calculated using the quantum Monte Carlo simulations (QMC). Here χu, c, and T are the uniform susceptibility, the spin-wave velocity, and the temperature, respectively. By simulating large lattices at moderately low temperatures, we find χuc2/T∼0.32. Our estimation of χuc2/T deviates from the related analytic prediction but agrees with recent numerical calculations of other 2D dimerized spin-1/2 antiferromagnets.The numerical value of a universal quantity associated with the quantum critical regime, namely χuc2/T, for a two-dimensional (2D) dimerized spin-1/2 antiferromagnet is calculated using the quantum Monte Carlo simulations (QMC). Here χu, c, and T are the uniform susceptibility, the spin-wave velocity, and the temperature, respectively. By simulating large lattices at moderately low temperatures, we find χuc2/T∼0.32. Our estimation of χuc2/T deviates from the related analytic prediction but agrees with recent numerical calculations of other 2D dimerized spin-1/2 antiferromagnets.

arXiv:2210.14471Results in PhysicsNov 26, 20220 citations

QUANTUM ANTIFERROMAGNETS IN TWO DIMENSIONS

Subir Sachdev A

Feb 1, 19956 citations

Spin Hartree-Fock approach to studying quantum Heisenberg antiferromagnets in low dimensions

A. Werth, Peter Kopietz, Oleksandr Tsyplyatyev

We construct a new mean-field theory for a quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition, in accord with the Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via a Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order $1/T$ expansions.We construct a new mean-field theory for a quantum (spin-1/2) Heisenberg antiferromagnet in one (1D) and two (2D) dimensions using a Hartree-Fock decoupling of the four-point correlation functions. We show that the solution to the self-consistency equations based on two-point correlation functions does not produce any unphysical finite-temperature phase transition, in accord with the Mermin-Wagner theorem, unlike the common approach based on the mean-field equation for the order parameter. The next-neighbor spin-spin correlation functions, calculated within this approach, reproduce closely the strong renormalization by quantum fluctuations obtained via a Bethe ansatz in 1D and a small renormalization of the classical antiferromagnetic state in 2D. The heat capacity approximates with reasonable accuracy the full Bethe ansatz result at all temperatures in 1D. In 2D, we obtain a reduction of the peak height in the heat capacity at a finite temperature that is accessible by high-order $1/T$ expansions.

arXiv:1802.07579Physical review. B./Physical review. BMay 8, 20187 citations

TWO-DIMENSIONAL QUANTUM ANTIFERROMAGNETS

Grégoire Misguich, C. Lhuillier

WORLD SCIENTIFIC eBooksMar 26, 20135 citations

^{3}\mathrm{He}

are also given.

1/T

expansions.