Three-dimensional antiferromagnetic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mtext>CP</mml:mtext><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:math>models

Delfino, Francesco; Pelissetto, Andrea; Vicari, Ettore

doi:10.1103/physreve.91.052109

Cited by 32 publications

(45 citation statements)

References 48 publications

(85 reference statements)

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“…If statistical fluctuations are small-this is the basic assumption-the transition is of first order also in three dimensions. In this approach, continuous transitions may still occur, but they require a fine tuning of the microscopic parameters, leading to the effective cancellation of the cubic term [56].…”

Section: The Gauge-invariant Lgw Frameworkmentioning

confidence: 99%

Lattice Abelian-Higgs model with noncompact gauge fields

2021

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Higgs model with noncompact gauge fields. For any N 2, the phase diagram shows three phases differing for the behavior of the scalar-field and gauge-field correlations: The Coulomb phase (short-ranged scalar and long-ranged gauge correlations), the Higgs phase (condensed scalarfield and gapped gauge correlations), and the molecular phase (condensed scalar-field and long-ranged gauge correlations). They are separated by three transition lines meeting at a multicritical point. Their nature depends on the phases they separate, and on the number N of components of the scalar field. In particular, the Coulombto-molecular transition line (where gauge correlations are irrelevant) is associated with the Landau-Ginzburg-Wilson 4 theory sharing the same SU(N) global symmetry but without explicit gauge fields. On the other hand, the Coulomb-to-Higgs transition line (where gauge correlations are relevant) turns out to be described by the continuum Abelian-Higgs field theory with explicit gauge fields. Our numerical study is based on finite-size scaling analyses of Monte Carlo simulations with C * boundary conditions (appropriate for lattice systems with noncompact gauge variables, unlike periodic boundary conditions), for several values of N, i.e., N = 2, 4, 10, 15, and 25. The numerical results agree with the renormalization-group predictions of the continuum field theories. In particular, the Coulomb-to-Higgs transitions are continuous for N 10, in agreement with the predictions of the Abelian-Higgs field theory.

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Section: The Gauge-invariant Lgw Frameworkmentioning

confidence: 99%

Lattice Abelian-Higgs model with noncompact gauge fields

2021

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“…They are obtained from the results reported in Refs. [58,[68][69][70][71]. The RG analysis of the continuum AH field theory, see, e.g., Refs.…”

Section: Phase Diagram Along the κ = ∞ Linementioning

confidence: 99%

Higher-charge three-dimensional compact lattice Abelian-Higgs models

2020

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We consider three-dimensional higher-charge multicomponent lattice Abelian-Higgs (AH) models, in which a compact U(1) gauge field is coupled to an N-component complex scalar field with integer charge q, so that they have local U(1) and global SU(N) symmetries. We discuss the dependence of the phase diagram, and the nature of the phase transitions, on the charge q of the scalar field and the number N 2 of components. We argue that the phase diagram of higher-charge models presents three different phases, related to the condensation of gaugeinvariant bilinear scalar fields breaking the global SU(N) symmetry, and to the confinement and deconfinement of external charge-one particles. The transition lines separating the different phases show different features, which also depend on the number N of components. Therefore, the phase diagram of higher-charge models substantially differs from that of unit-charge models, which undergo only transitions driven by the breaking of the global SU(N) symmetry, while the gauge correlations do not play any relevant role. We support the conjectured scenario with numerical results, based on finite-size scaling analyses of Monte Carlo simuations for doubly charged unit-length scalar fields with small and large number of components, i.e., N = 2 and N = 25.

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“…The physics of AFM low-energy excitations is most transparent upon a mapping onto two sub-lattices [32][33][34][35][36] denoted A and B with antiparallel spins (cf. Fig.…”

Section: Afm Magnonic Dirac Dynamicsmentioning

confidence: 99%

“…The ordering in each sublattice is FM but a translation by a lattice vector transforms S(r + a) → − S(r), meaning that the translational invariance is broken. Thus, the AFM Heisenberg system is mappable onto an antiferromagnetic (AFM) CP 1 model 36 . Note, the AFM Hamiltonian is still invariant under the combined time-reversal (T ) and sub-lattice exchange (I ), a fact underlying the degeneracy of the two chiral magnon modes.…”

Section: Afm Magnonic Dirac Dynamicsmentioning

confidence: 99%

“…Equation (1) is, in addition, invariant under global spin rotation around the z-axis, and thus the z-component of the total spin is a good quantum number. For a further insight, let us follow Haldane 32 (see also 33,35,36 ) and consider small sublatticedependent fluctuations around the one-dimensional Néel ground state 32 . To do so, one introduces…”

Section: Afm Magnonic Dirac Dynamicsmentioning

confidence: 99%

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Chiral logic computing with twisted antiferromagnetic magnon modes

et al. 2021

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Antiferromagnetic (AFM) materials offer an exciting platform for ultrafast information handling with low cross-talks and compatibility with existing technology. Particularly interesting for low-energy cost computing is the spin wave-based realization of logic gates, which has been demonstrated experimentally for ferromagnetic waveguides. Here, we predict chiral magnonic eigenmodes with a finite intrinsic, magnonic orbital angular momentum ℓ in AFM waveguides. ℓ is an unbounded integer determined by the spatial topology of the mode. We show how these chiral modes can serve for multiplex AFM magnonic computing by demonstrating the operation of several symmetry- and topology-protected logic gates. A Dzyaloshinskii–Moriya interaction may arise at the waveguide boundaries, allowing coupling to external electric fields and resulting in a Faraday effect. The uncovered aspects highlight the potential of AFM spintronics for swift data communication and handling with high fidelity and at a low-energy cost.

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Three-dimensional antiferromagneticCPN−1models

Cited by 32 publications

References 48 publications

Lattice Abelian-Higgs model with noncompact gauge fields

Lattice Abelian-Higgs model with noncompact gauge fields

Higher-charge three-dimensional compact lattice Abelian-Higgs models

Chiral logic computing with twisted antiferromagnetic magnon modes

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