2019
DOI: 10.1103/physrevb.100.134411
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Effective theories for quantum spin clusters: Geometric phases and state selection by singularity

Abstract: 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 r… Show more

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Cited by 9 publications
(5 citation statements)
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“…This is only the second known example, after the quantum XY quadrumer studied in Ref. 5. In Kitaev clusters, cartesian states are essentially a classical concept.…”
Section: Summary and Discussionmentioning
confidence: 99%
See 1 more Smart Citation

Order by singularity in Kitaev clusters

Srinivasan,
Khatua,
Baskaran
et al. 2019
Preprint
Self Cite
“…This is only the second known example, after the quantum XY quadrumer studied in Ref. 5. In Kitaev clusters, cartesian states are essentially a classical concept.…”
Section: Summary and Discussionmentioning
confidence: 99%
“…We briefly recapitulate its gist here; details can be found in Ref. 5. We start with a general principle that holds in the semi-classical large-S limit : the low energy physics of a cluster of quantum spins maps to that of a single particle moving on the classical ground state space (CGSS).…”
Section: Introductionmentioning
confidence: 99%

Order by singularity in Kitaev clusters

Srinivasan,
Khatua,
Baskaran
et al. 2019
Preprint
Self Cite
“…So the classical ground state space (CGSS) is made up of an exponential number of Cartesian states, as well as an exponentially large set of continuous families that interpolates between each x-and each y-Cartesian state. Due to the structure of the CGSS, the phenomenon of order by singularity [46,47] becomes relevant. The low-energy physics can be described by a particle moving on the CGSS, which has a non-manifold structure due to self-intersections at the Cartesian points [47].…”
Section: Classical and Semiclassical Limitsmentioning
confidence: 99%
“…The low-energy physics can be described by a particle moving on the CGSS, which has a non-manifold structure due to self-intersections at the Cartesian points [47]. Remarkably, the lowest energy states of this particle are localized near these singular points [46], representing a state selection mechanism completely distinct from the usual order by disorder (which also selects the Cartesian states [45]).…”
Section: Classical and Semiclassical Limitsmentioning
confidence: 99%
“…In such systems, interesting physics may emerge as, for example, in Cu 2 OSeO 3 , where the Cu 4 tetrahedra act as building blocks for several skyrmionic phases . In addition to large three-dimensionally shaped large molecule-like units like those found in polyoxometalate, for instance, giving rise to an S = 1 / 2 effective spin in the V 15 compound, most common examples and theoretical efforts rely on the trimerization or tetramerization of local spins, most often within trigonal layered topologies in real compounds, e.g., LiVO 2 and LiZn 2 Mo 3 O 8 . This leads to nonmagnetic, spin singlet, or low collective pseudospins with exotic behavior (see the so-called hybrid electrons in S = 1 / 2 in V 3 triangles of the recent-GaV 4 O 8 phase) .…”
Section: Introductionmentioning
confidence: 99%