By Yuejin Z., Guodong X.
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W. Taylor, Y. Z. -W. Cheong, C. G. 2678 (2007) 47. P. T. Chalker, Phys. Rev. Lett. 102, 237106 (2009) Chapter 2 Introduction to Quantum Spin Liquids Claire Lhuillier and Grégoire Misguich Abstract In SU(2)-invariant spin models with frustrated interactions and low spin quantum number, long-ranged magnetic order and breaking of the SU(2) symmetry is not the most general situation, especially in low dimensions. Many such systems are, loosely speaking, “quantum paramagnets” down to zero temperature, states conveniently represented in terms of spins paired into rotationally invariant singlets, or “valence bonds” (VBs).
For large S we can treat this equation of motion classically. Within the harmonic approximation, obtained by linearising the right-hand side, the exchange field Hi is a superposition of contributions from finite frequency modes, which maintain phase coherence indefinitely, and therefore average to zero over long times. Anharmonic interactions have two consequences, which are distinct but turn out to be closely linked [9, 10]. One is to generate a lifetime for the finite frequency modes. The other is to introduce coupling between the ground state coordinates x and the coordinates y orthogonal to the ground state manifold.
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3D magnetic field computation of a permanent magnet disc-type generator using scalar potential method by Yuejin Z., Guodong X.