Quantum spin quadrumer

Khatua, Subhankar; Shankar, Ravi; Ganesh, R.

doi:10.1103/physrevb.97.054403

Cited by 4 publications

(4 citation statements)

References 58 publications

(60 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Our analysis of the XY quadrumer resonates strongly with the problem of the Heisenberg quadrumer. Two of the current authors have shown that the Heisenberg quadrumer possesses a non-manifold ground state space 17 . It is generically five-dimensional.…”

Section: Summary and Discussionmentioning

confidence: 88%

“…In fact, the XY CGSS is a slice of the Heisenberg ground state space. Remarkably, in the Heisenberg problem, the low-energy states do not consist of bound states, and a good effective description is obtained by neglecting singularities 17 . This suggests that not all non-manifolds can induce bound states.…”

Section: Summary and Discussionmentioning

confidence: 99%

“…The trimer maps to a rigid rotor, i.e., a particle in SO(3) space [8][9][10]16 . The quadrumer maps to a particle in a five-dimensional space with singular subspaces; this can be approximated as a rigid rotor and an emergent free spin 17 .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

2019

Self Cite

View full text Add to dashboard Cite

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 ⊗ Z2). It has an additional subtlety for half-integer S values, wherein both rings must be threaded by π-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 non-manifold 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 π-flux tubes that reside in the space between the tori. The non-manifold 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.

show abstract

Section: Summary and Discussionmentioning

confidence: 88%

Section: Summary and Discussionmentioning

confidence: 99%

See 1 more Smart Citation

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

2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…It is minimized in configurations where the sum of four spins vanishes. The set of all such states has been shown to form a non-manifold space that is generically five-dimensional 33 . Here, as seen from Tab.…”

Section: Summary and Discussionmentioning

confidence: 99%

Order by singularity in Kitaev clusters

Srinivasan,

Khatua,

Baskaran

et al. 2019

Preprint

Self Cite

View full text Add to dashboard Cite

The Kitaev model is a beautiful example of frustrated interactions giving rise to novel and unexpected physics. In particular, its classical version has remarkable properties stemming from exponentially large ground state degeneracy. Here, we present a study of magnetic clusters with spin-S moments coupled by Kitaev interactions. We focus on two cluster geometries -the Kitaev square and the Kitaev tetrahedron -that allow us to explicitly enumerate all classical ground states. In both cases, the space of ground states is large and self-intersecting, with non-manifold character. In the semi-classical large-S limit, we argue for effective low energy descriptions in terms of a single particle moving on non-manifold spaces. Remarkably, at low energies, the particle is tied down in bound states formed around singularities at self-intersection points. In the language of spins, the low energy physics is determined by a distinct set of states that lies well below other eigenstates. This set consists of admixtures of classical 'cartesian' states, with one state for each cartesian state in the classical ground state space. This brings out a strong role for cartesian states, a special class of classical ground states that are derived from dimer covers of the underlying lattice. This constitutes an example of order by singularity -where certain states from the classical ground state space are selected, not by fluctuations, but rather by singularities in the space.

show abstract

Bound states without potentials: Localization at singularities

Ganesh

2023

Phys. Rev. A

View full text Add to dashboard Cite

Quantum spin quadrumer

Cited by 4 publications

References 58 publications

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

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

Order by singularity in Kitaev clusters

Bound states without potentials: Localization at singularities

Contact Info

Product

Resources

About