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Register a new userCompact quantum electrodynamics in 2+1 dimensions and spinon deconfinement: a renormalization group analysis
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We discuss compact (2+1)-dimensional Maxwell electrodynamics coupled to fermionic matter with N replica. For large enough N, the latter corresponds to an effective theory for the nearest neighbor SU(N) Heisenberg antiferromagnet, in which the fermions represent solitonic excitations known as spinons. Here we show that the spinons are deconfined for $N>N_c=36$, thus leading to an insulating state known as spin liquid. A previous analysis considerably underestimated the value of $N_c$. We show further that for $20<Nleq 36$ there can be either a confined or a deconfined phase, depending on the instanton density. For $Nleq 20$ only the confined phase exist. For the physically relevant value N=2 we argue that no paramagnetic phase can emerge, since chiral symmetry breaking would disrupt it. In such a case a spin liquid or any other nontrivial paramagnetic state (for instance, a valence-bond solid) is only possible if doping or frustrating interactions are included.
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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 Neel 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.
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