Unlike that of SO(3) or SU(2), the Lie algebra for SO(2), which defines intermediate spin, comprises only $S_{z}$ and implies $S^{\pm}$ commute. In general, $S_{z}$ has a continuous spectrum. This intermediate spin scheme can realized for the low energy excitations of a wide class of large spin magnets. A magnetic field provides the necessary time reversal symmetry breaking and controls the effective value of the spin $\tilde S$ . Physical quantities are periodic in the equilibrium magnetization component induced by this field. In particular for one dimensional antiferromagnets there are periodic regions on the field axis for which the model is quantum critical while in two or three dimensions criticality is reduced to points.Unlike that of SO(3) or SU(2), the Lie algebra for SO(2), which defines intermediate spin, comprises only $S_{z}$ and implies $S^{\pm}$ commute. In general, $S_{z}$ has a continuous spectrum. This intermediate spin scheme can realized for the low energy excitations of a wide class of large spin magnets. A magnetic field provides the necessary time reversal symmetry breaking and controls the effective value of the spin $\tilde S$. Physical quantities are periodic in the equilibrium magnetization component induced by this field. In particular for one dimensional antiferromagnets there are periodic regions on the field axis for which the model is quantum critical while in two or three dimensions criticality is reduced to points.

arXiv:cond-mat/9901219Jan 21, 19990 citations

Quantum magnetism and strongly correlated electrons in low dimensions

Andreas Martin Läuchli

Jan 1, 20022 citations

Novel quantum magnetic states in low dimensions

Peng Li

Jan 1, 20060 citations

Quantum magnets: a brief overview

Indrani Bose

Quantum magnetism is one of the most active areas of research in condensed matter physics. There is significant research interest specially in low-dimensional quantum spin systems. Such systems have a large number of experimental realizations and exhibit a variety of phenomena the origin of which can be attributed to quantum effects and low dimensions. In this review, an overview of some aspects of quantum magnetism in low dimensions is given. The emphasis is on key concepts, theorems and rigorous results as well as models of spin chains, ladders and frustated magnetic systems.Quantum magnetism is one of the most active areas of research in condensed matter physics. There is significant research interest specially in low-dimensional quantum spin systems. Such systems have a large number of experimental realizations and exhibit a variety of phenomena the origin of which can be attributed to quantum effects and low dimensions. In this review, an overview of some aspects of quantum magnetism in low dimensions is given. The emphasis is on key concepts, theorems and rigorous results as well as models of spin chains, ladders and frustated magnetic systems.

arXiv:cond-mat/0107399Jul 19, 20015 citations

Field Theoretic Studies of Quantum Spin Systems in One Dimension

Diptiman Sen

We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and bosonization which are more useful for small values of spin such as spin-1/2, and the technique of low-energy effective Hamiltonians which can be useful if the system under consideration is perturbatively close to an exactly solvable model. We apply these techniques to similar spin models, such as spin chains with dimerization and frustration, and spin ladders in the presence of a magnetic field. This comparative study illustrates the relative strengths of the different methods.We describe some field theoretic methods for studying quantum spin systems in one dimension. These include the nonlinear sigma-model approach which is particularly useful for large values of the spin, the idea of Luttinger liquids and bosonization which are more useful for small values of spin such as spin-1/2, and the technique of low-energy effective Hamiltonians which can be useful if the system under consideration is perturbatively close to an exactly solvable model. We apply these techniques to similar spin models, such as spin chains with dimerization and frustration, and spin ladders in the presence of a magnetic field. This comparative study illustrates the relative strengths of the different methods.

arXiv:cond-mat/0107082Jul 4, 20010 citations

Magnetic Field Effects in Low-Dimensional Quantum Magnets

Adam Iaizzi

Springer thesesJan 1, 20186 citations

Unlike that of SO(3) or SU(2), the Lie algebra for SO(2), which defines intermediate spin, comprises only

S_{z}

and implies

S^{\pm}

commute. In general,

S_{z}

has a continuous spectrum. This intermediate spin scheme can realized for the low energy excitations of a wide class of large spin magnets. A magnetic field provides the necessary time reversal symmetry breaking and controls the effective value of the spin

\tilde S

. Physical quantities are periodic in the equilibrium magnetization component induced by this field. In particular for one dimensional antiferromagnets there are periodic regions on the field axis for which the model is quantum critical while in two or three dimensions criticality is reduced to points.