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Bose expansion and investigation of the critical behaviour of quantum Heisenberg models

Isaac Goldhirsch

Annals of the Israel Physical SocietyJan 1, 19780 citations

Super-Heisenberg behaviour at quantum criticality and its ultra-cold bosons implementation

Marek M. Rams, Piotr Sierant, Omjyoti Dutta +2 more

Feb 18, 20170 citations

A new approach to critical behaviour in the heisenberg model?

Vinod Mubayi

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoJun 1, 19701 citation

Critical Behavior of Quantum Heisenberg Chains

P. Schlottmann, Kong-Ju-Bock Lee

Springer proceedings in physicsJan 1, 19901 citation

Critical behaviour of structure factors at a quantum phase transition

Chris J. Hamer

We review the theoretical behaviour of the total and one-particle structure factors at a quantum phase transition for temperature T = 0. The predictions are compared with exact or numerical results for the transverse Ising model, the alternating Heisenberg chain, and the bilayer Heisenberg model. At the critical wavevector, the results are generally in accord with theoretical expectations. Away from the critical wavevector, however, different models display quite different behaviours for the one-particle residues and structure factors.We review the theoretical behaviour of the total and one-particle structure factors at a quantum phase transition for temperature T = 0. The predictions are compared with exact or numerical results for the transverse Ising model, the alternating Heisenberg chain, and the bilayer Heisenberg model. At the critical wavevector, the results are generally in accord with theoretical expectations. Away from the critical wavevector, however, different models display quite different behaviours for the one-particle residues and structure factors.

arXiv:0809.2857Journal of Physics Condensed MatterFeb 25, 20091 citation

Critical Behaviour of Mixed Heisenberg Chains

F. C. Alcaraz, A. L. Malvezzi

The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S ′) SU(2) operator interacting with a XXZ like interaction (anisotropy ∆). Our results indicate universal properties for all these chains. The whole phase, 1> ∆> −1, where the models change from ferromagnetic ( ∆ = 1) to ferrimagnetic ( ∆ = −1) behaviour is critical. Along this phase the critical fluctuations are ruled by a c = 1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions. 1The critical behaviour of anisotropic Heisenberg models with two kinds of antiferromagnetically exchange-coupled centers are studied numerically by using finite-size calculations and conformal invariance. These models exhibit the interesting property of ferrimagnetism instead of antiferromagnetism. Most of our results are centered in the mixed Heisenberg chain where we have at even (odd) sites a spin-S (S ′) SU(2) operator interacting with a XXZ like interaction (anisotropy ∆). Our results indicate universal properties for all these chains. The whole phase, 1> ∆> −1, where the models change from ferromagnetic ( ∆ = 1) to ferrimagnetic ( ∆ = −1) behaviour is critical. Along this phase the critical fluctuations are ruled by a c = 1 conformal field theory of Gaussian type. The conformal dimensions and critical exponents, along this phase, are calculated by studying these models with several boundary conditions. 1

Jan 1, 199628 citations

Bosonization of quantum Heisenberg models and investigation of their critical behaviour

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