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arXiv:2512.02962

Spinons and Spin-Charge Separation at the Deconfined Quantum Critical Point

Sibin Yang, Anders W. Sandvik

Published Dec 2, 2025• 0 citations
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Abstract

Using quantum Monte Carlo and numerical analytic continuation methods, we study the dynamic spin structure factor and the single-hole spectral function of a two-dimensional quantum magnet ($J$-$Q$ model) at its quantum phase transition separating Néel antiferromagnetic and spontaneously dimerized ground states. At this putative deconfined quantum-critical point, we find a broad continuum of spinon excitations that can be accounted for by the fermionic $π$-flux state; a known mean-field model for deconfined quantum criticality. We find that the best description of the two-spinon continuum is with a version of the model with a $2\times 2$ unit cell, reflecting non-trivial mutual statistics of spinons and anti-spinons. The single-hole spectral function can be described by the same spinon dispersion relation and an independently propagating holon. Thus, the system exhibits spin-charge separation and will likely evolve into an extended holon metal phase at finite doping.

DOI
10.48550/arxiv.2512.02962

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We study the level structure of excitations at the ``deconfined'' critical point separating antiferromagnetic and valence-bond-solid phases in two-dimensional quantum spin systems using the $J\text{\ensuremath{-}}Q$ model as an example. Energy gaps in different spin (S)(S)(S) and momentum (k)(\mathbf{k})(k) sectors are extracted from imaginary-time correlation functions obtained in quantum Monte Carlo simulations. We find strong quantitative evidence for deconfined linearly dispersing spinons with gapless points at $\mathbf{k}=(0,0),(\ensuremath{\pi},0),(0,\ensuremath{\pi})$, and $(\ensuremath{\pi},\ensuremath{\pi})$, as inferred from two-spinon excitations (S=0S=0S=0 and S=1S=1S=1 states) around these points. We also observe a duality between singlet and triplet excitations at the critical point and inside the ordered phases, in support of an enhanced symmetry, possibly SO(5).
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We use Monte Carlo methods to study spinons in two-dimensional quantum spin systems, characterizing their intrinsic size $\ensuremath{\lambda}$ and confinement length $\ensuremath{\Lambda}$. We confirm that spinons are deconfined, $\ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty}$ and $\ensuremath{\lambda}$ finite, in a resonating valence-bond spin-liquid state. In a valence-bond solid, we find finite $\ensuremath{\lambda}$ and $\ensuremath{\Lambda}$, with $\ensuremath{\lambda}$ of a single spinon significantly larger than the bound state---the spinon is soft and shrinks as the bound state is formed. Both $\ensuremath{\lambda}$ and $\ensuremath{\Lambda}$ diverge upon approaching the critical point separating valence-bond solid and N\'eel 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.
We investigate the continuous quantum phase transition from an antiferromagnetic metal to a heavy-fermion liquid based on the Kondo lattice model in two dimensions. We propose that antiferromagnetic spin fluctuations and conduction electrons fractionalize into neutral bosonic spinons and charged spinless fermions at the quantum critical point. This deconfined quantum criticality leads us to establish a critical field theory in terms of the fractionalized fields interacting via emergent U(1) gauge fields. The critical field theory not only predicts non-Fermi liquid physics near the quantum critical point but also recovers Fermi liquid physics away from the quantum critical point.
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