Finite-temperature Néel ordering of fluctuations in a plaquette orbital model

Wenzel, Sandro Christian; Janke, Wolfhard

doi:10.1103/physrevb.80.054403

Cited by 13 publications

(27 citation statements)

References 36 publications

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“…We have shown that the local average values of these effective spins correspond with the average values of the bonds in the initial ladder so the long-range spin-spin correlations in the ground-subspace are the long-range bond-bond correlations in the Cx-Cz model. This resembles the Néel order of the plaquettes energies found in the two-dimensional plaquette orbital model [40], however it has been shown that this is an artifact of a deeper lying orientational order [41]. The polarized ground state configuration of the effective spins is slightly distorted by the quantum interaction terms that cause a two-sublattice modulation of the order such that the sublattices are related by the interchange of the x and z spin components.…”

Section: Discussionmentioning

confidence: 58%

Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model

Brzezicki

Oleś

2014

Phys. Rev. B

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We introduce a one-dimensional plaquette orbital model with a topology of a ladder and alternating interactions between x and z pseudospin components along both the ladder legs and on the rungs. We show that it is equivalent to an effective spin model in a magnetic field, with spin dimers that replace plaquettes and are coupled along the chain by three-spin interactions. Using perturbative treatment and mean field approaches with dimer correlations we study the ground state spin configuration and its defects in the lowest excited states. By the exact diagonalization approach we find that the quantum effects in the model are purely short-range and we get estimated values of the ground state energy and the gap in the thermodynamic limit from the system sizes up to L = 12 dimers. Finally, we study a class of excited states with classical-like defects accumulated in the central region of the chain to find that in this region the quantum entanglement measured by the mutual information of neighboring dimers is locally increased and coincides with disorder and frustration. Such islands of entanglement in otherwise rather classical system may be of interest in the context of quantum computing devices.

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Section: Discussionmentioning

confidence: 58%

Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model

Brzezicki

Oleś

2014

Phys. Rev. B

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“…It is not clear, though, whether this might lead to useful results for the study of this specific model. Another relevant model is the plaquette orbital model that was studied in [28,3]; interactions between neighbours x, y are of the form −S i x S i y , with i being equal to 1 or 3 depending on the edge.…”

Section: Setting and Resultsmentioning

confidence: 99%

Correlation Inequalities for Classical and Quantum XY Models

Benassi

Lees

Ueltschi

2017

Advances in Quantum Mechanics

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“…Recently, an interesting variant of the orbital compass model has been proposed and studied by Wenzel and Janke [37]. Their model, which they termed the plaquette orbital model (POM), is most naturally defined over the square lattice Z 2 , although generalizations to higher dimensions are straightforward.…”

Section: The Plaquette Orbital Modelmentioning

confidence: 99%

“…In [37] Wenzel and Janke studied the POM numerically both in its classical and quantum version. For an order parameter they chose the plaquette energy,…”

Section: The Plaquette Orbital Modelmentioning

confidence: 99%

True nature of long-range order in a plaquette orbital model

Biskup¹,

Kotecký²

2010

J. Stat. Mech.

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We analyze the classical version of a plaquette orbital model that was recently introduced and studied numerically by S. Wenzel and W. Janke. In this model, edges of the square lattice are partitioned into x and z-types that alternate along both coordinate directions and thus arrange into a checkerboard pattern of x and z-plaquettes; classical O(2)-spins are then coupled ferromagnetically via their first components over the x-edges and via their second components over the z-edges. We prove from first principles that, at sufficiently low temperatures, the model exhibits orientational long-range order (OLRO) in one of the two principal lattice directions. Magnetic order is precluded by the underlying symmetries. A similar set of results is inferred also for quantum systems with large spin although the spin-1 / 2 instance currently seems beyond the reach of rigorous methods. We point out that the Neél order in the plaquette energy distribution observed in numerical simulations is an artefact of the OLRO and a judicious choice of the plaquette energies. In particular, this order seems to disappear when the plaquette energies are adjusted to vanish at the ground-state level. We also discuss the specific role of the underlying symmetries in Wenzel and Janke's simulations and propose an enhanced method of numerical sampling that could in principle significantly increase the speed of convergence.

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Finite-temperature Néel ordering of fluctuations in a plaquette orbital model

Cited by 13 publications

References 36 publications

Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model

Locally tunable disorder and entanglement in the one-dimensional plaquette orbital model

Correlation Inequalities for Classical and Quantum XY Models

True nature of long-range order in a plaquette orbital model

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