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

Biskup, Marek; Kotecký, Roman

doi:10.1088/1742-5468/2010/11/p11001

Cited by 6 publications

(13 citation statements)

References 41 publications

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“…The 90 • compass, where both ferro-and anti-ferromagnetic coupling appear across the two orthogonal diagonals here, has been proposed as a model to Mott insulators with orbital degrees of freedom and frustrated magnets [29]. Other compass-type models accessible through polariton graphs include the plaquette orbital model, where the ferromagnetic and anti-ferromagnetic coupling alternate along each direction [30] and the orbital compass model on a checkerboard lattice [31]. Fully random couplings in the square lattice describes the thermodynamic behaviour of several disordered systems, such as magnetic systems with random Dzyaloshinskii-Moriya interactions [32], disordered Josephson junction arrays [33], disordered substrates [34], and vortex glasses in high-T c cuprate superconductors [35].…”

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confidence: 99%

Realizing the classical XY Hamiltonian in polariton simulators

et al. 2017

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Several platforms are currently being explored for simulating physical systems whose complexity increases faster than polynomially with the number of particles or degrees of freedom in the system. Defects and vacancies in semiconductors or dielectric materials [1,2], magnetic impurities embedded in solid helium [3], atoms in optical lattices [4,5], photons [6], trapped ions [7,8] and superconducting q-bits [9] are among the candidates for predicting the behaviour of spin glasses, spin-liquids, and classical magnetism among other phenomena with practical technological applications. Here we investigate the potential of polariton graphs as an efficient simulator for finding the global minimum of the XY Hamiltonian. By imprinting polariton condensate lattices of bespoke geometries we show that we can simulate a large variety of systems undergoing the U(1) symmetry breaking transitions. We realise various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on unit cells of various lattices: square, triangular, linear and a disordered graph. Our results provide a route to study unconventional superfluids, spin-liquids, Berezinskii-KosterlitzThouless phase transition, classical magnetism among the many systems that are described by the XY Hamiltonian.Many properties of strongly correlated spin systems, such as spin liquids and unconventional superfluids are difficult to study as strong interactions between n particles become intractable for n as low as 30 [10]. Feynman envisioned that a quantum simulator -a special-purpose analogue processor -could be used to solve such problems [11]. It is expected that quantum simulators would lead to accurate modelling of the dynamics of chemical reactions, motion of electrons in materials, new chemical compounds and new materials that could not be obtained with classical computers using advanced numerical algorithms [12]. More generally, quantum simulators can be used to solve hard optimization problems that are at the heart of almost any multicomponent system: new materials for energy, pharmaceuticals, and photosynthesis, among others [13]. Many hard optimisation problems do not necessitate a quantum simulator as only recently realised through a network of optical parametric oscillators (OPOs) that simulated the Ising Hamiltonian of thousands of spins [14,15]. The Ising model corresponds to the n = 1 case of the n-vector model of classical unit vector spins s i with the Hamiltonian H I = − ij J ij s i · s j , where J ij is the coupling between the sites labelled i and j. For n = 2 the n-vector Hamiltonian becomes the XY Hamiltonian H XY = − ij J ij cos(θ i − θ j ), where we have parameterized unit planar vectors using the polar coordinates s i = (cos θ i , sin θ i ). Since H XY is invariant under rotation of all spins by the same angle θ i → θ i + φ the XY model is the simplest model that undergoes the U (1) symmetry-breaking transition. As such, it is used * correspondence address: pavlos.lagoudakis@soton.ac.uk to emulate Berezinskii-Kos...

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confidence: 99%

Realizing the classical XY Hamiltonian in polariton simulators

et al. 2017

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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: 60%

“…The interest in the 2D compass model is motivated by new opportunities it provides for quantum computing [26]. This motivated also plaquette orbital model (POM) introduced for a square lattice by Wenzel and Janke [40] which exhibits orientational long-range order in its classical version [41]. Here we will focus on the 1D quantum version of the POM and investigate the nature of the ground state and of low energy excitations.…”

Section: Introductionmentioning

confidence: 99%

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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“…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%