Quantum Dimer Model 2D — RVB Spin Liquid & Spinon Deconfinement

Quantum Fluctuations

Resonance rate t 3.0 Hz

Potential bias v/t 0.00

Animation speed 1.0×

Lattice

Spinon Pair

Live Readouts

Flippable plaquettes

Order parameter

0.00

Accepted flips/s

0.0

Spinon separation

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Horizontal valence bond

Vertical valence bond

Spinon (unpaired site)

How it works

Each lattice site holds one spin-1/2. A valence-bond (dimer) covering pairs every site into a singlet with exactly one neighbor — one term in the resonating-valence-bond (RVB) wavefunction |ψ⟩ = Σ_c |c⟩ over all dimer coverings c. This is the Rokhsar–Kivelson (RK) quantum dimer model:

H = -t Σ ( |⊐⊐⟩⟨⊏⊏| + h.c. )  +  v Σ ( |⊐⊐⟩⟨⊐⊐| + |⊏⊏⟩⟨⊏⊏| )

A 2×2 block covered by two parallel dimers is flippable: the resonance term t rotates it to the perpendicular pair — exactly the flips animated here. The potential term v rewards flippable blocks that stay put, so the flip-acceptance probability falls off as exp(−k·|v/t|) the further the bias sits from the RK point.

v/t ≈ 0 (the RK point) — flips are unbiased, dimers keep resonating between configurations with no static pattern: a quantum spin liquid, no long-range order even at zero temperature.
|v/t| large — one dimer pattern is energetically favored, flipping freezes out, and the lattice locks into a static columnar valence-bond crystal (order parameter → 1).
Break a bond — removing one dimer leaves two unpaired spins, spinons: fractional S=1/2 excitations. In an ordered antiferromagnet, separating two such defects stretches a string of misaligned spins whose energy grows with distance (confinement). Here each spinon instead hops by trading places with an adjacent dimer — no string forms, so the pair can wander arbitrarily far apart at (numerically) constant energy cost: deconfinement, the hallmark of a spin-liquid ground state.

The order parameter tracks |(horizontal dimers − vertical dimers)| / total, normalized to 0 (liquid) – 1 (fully columnar). Drag the lattice to pan and scroll/pinch to zoom; the strip chart below the lattice plots order parameter and flip rate over the last ~15 s.

Dimer covering (valence bonds) Spinons = deconfined defects

drag to pan · scroll to zoom

Order parameter Flips/s