Confinement and Deconfinement of Spinons in Two Dimensions

Abstract

We use Monte Carlo methods to study spinons in two-dimensional quantum spin systems, characterizing their intrinsic size $\lambda$ and confinement length $\Lambda$. We confirm that spinons are deconfined, $\Lambda \to \infty$ and $\lambda$ finite, in a resonating valence-bond spin-liquid state. In a valence-bond solid, we find finite $\lambda$ and $\Lambda$, with $\lambda$ of a single spinon significantly larger than the bound-state---the spinon is soft and shrinks as the bound state is formed. Both $\lambda$ and $\Lambda$ diverge upon approaching the critical point separating valence-bond solid and Néel ground states. We conclude that the spinon deconfinement is marginal in the lowest-energy state in the spin-1 sector, due to weak attractive spinon interactions. Deconfinement in the vicinity of the critical point should occur at higher energies.

5 pages, 5 figures

References in corpus (14)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• From an Antiferromagnet to a Valence Bond Solid: Evidence for a First Order Phase Transition
• Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Spinon Phonon Interaction and Ultrasonic Attenuation in Quantum Spin Liquids
• Large-N estimates of universal amplitudes of the CP^{N-1} theory and comparison with the JQ model
• Spinon deconfinement in doped frustrated quantum antiferromagnets
• Thermodynamics of a gas of deconfined bosonic spinons in two dimensions
• Generalization of the singlet sector valence bond loop algorithm to antiferromagnetic ground states with total spin $S_{tot}=1/2$
• Quantum magnets with weakly confined spinons: Multiple length scales and quantum impurities
• Correlated valence-bond states

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• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Dynamical Signature of Fractionalization at the Deconfined Quantum Critical Point
• Confinement in the bulk, deconfinement on the wall: infrared equivalence between compactified QCD and quantum magnets
• Global symmetries, volume independence and continuity
• Roton minimum as fingerprint of magnon-Higgs scattering in ordered quantum antiferromagnets
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• The (2+1)-d U(1) Quantum Link Model Masquerading as Deconfined Criticality
• Level spectroscopy in a two-dimensional quantum magnet: Linearly dispersing spinons at the deconfined quantum critical point
• Nature of strong hole pairing in doped Mott antiferromagnets
• Quantum Monte Carlo studies of spinons in one-dimensional spin systems
• Emergent O(4) symmetry at the phase transition from plaquette-singlet to antiferromagnetic order in quasi-two-dimensional quantum magnets
• Deconfined quantum criticality in spin-1/2 chains with long-range interactions
• Fractional spin excitations in the infinite-layer cuprate CaCuO${}_2$
• Ferromagnetism and spin excitations in topological Hubbard models with a flatband
• Nonequilibrium dynamics in deconfined quantum critical point revealed by imaginary-time evolution
• Field-driven quantum phase transitions in $S=1/2$ spin chains
• Modern Physics of the Condensed State: Strong Correlations and Quantum Topology
• Metamagnetism and zero-scale-factor universality in the two-dimensional $J$-$Q$ model
• Equilibration of Topological Defects Near the Deconfined Quantum Multicritical Point
• Dual dynamic scaling in deconfined quantum criticality
• Valence bond distribution and correlation in bipartite Heisenberg antiferromagnets
• Quantitative Determination of the Confinement and Deconfinement of spinons in the anomalous spectra of Antiferromagnets via the Entanglement Entropy
• Low-energy singlet excitations in spin- 1/2 Heisenberg antiferromagnet on square lattice
• Exact results for the Hubbard model on bipartite lattices in spatial dimensions $d>1$: Seven theorems from the full [SU(2)$\times$SU(2)$\times$U(1)]/${\mathbb{Z}}_2^2$ symmetry
• Single-hole spectral functions in one-dimensional quantum magnets with different ground states
• Preparation of the single-spinon wave function on a quantum computer
• Roundtable: What can we learn about confinement and anomalous effects in QCD using analog systems?