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Effective theories for quantum spin clusters: Geometric phases and state selection by singularity

Khatua, Subhankar and Sen, Diptiman and Ganesh, R (2019) Effective theories for quantum spin clusters: Geometric phases and state selection by singularity. In: PHYSICAL REVIEW B, 100 (13).

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Official URL: https://dx.doi.org/10.1103/PhysRevB.100.134411


Magnetic systems with frustration often have large classical degeneracy. We show that their low-energy physics can be understood as dynamics within the space of classical ground states. We demonstrate this mapping in a family of quantum spin clusters where every pair of spins is connected by an XY antiferromagnetic bond. The dimer with two spin-S spins provides the simplest example-it maps to a quantum particle on a ring (S-1). The trimer is more complex, equivalent to a particle that lives on two disjoint rings (S-1 circle times Z(2)). It has an additional subtlety for half-integer S values, wherein both rings must be threaded by pi fluxes to obtain a satisfactory mapping. This is a consequence of the geometric phase incurred by spins. For both the dimer and the trimer, the validity of the effective theory can be seen from a path-integral-based derivation. This approach cannot be extended to the quadrumer which has a nonmanifold ground-state space, consisting of three tori that touch pairwise along lines. In order to understand the dynamics of a particle in this space, we develop a tight-binding model with this connectivity. Remarkably, this successfully reproduces the low-energy spectrum of the quadrumer. For half-integer spins, a geometric phase emerges which can be mapped to two pi-flux tubes that reside in the space between the tori. The nonmanifold character of the space leads to a remarkable effect-the dynamics at low energies is not ergodic as the particle is localized around singular lines of the ground-state space. The low-energy spectrum consists of an extensive number of bound states formed around singularities. Physically, this manifests as an order-by-disorder-like preference for collinear ground states. However, unlike order-by-disorder, this ``order by singularity'' persists even in the classical limit. We discuss consequences for field theoretic studies of magnets.

Item Type: Journal Article
Additional Information: Copyright of this article belongs to AMER PHYSICAL SOC
Department/Centre: Division of Physical & Mathematical Sciences > Centre for High Energy Physics
Depositing User: Id for Latest eprints
Date Deposited: 28 Nov 2019 09:54
Last Modified: 28 Nov 2019 09:54
URI: http://eprints.iisc.ac.in/id/eprint/63830

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