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Using large-scale determinant quantum Monte Carlo simulations in combinationwith the stochastic analytical continuation, we study two-particle dynamicalcorrelation functions in the anisotropic square lattice of weakly coupledone-dimensional (1D) Hubbard chains at half-filling and in the presence of weakfrustration. The evolution of the static spin structure factor upon increasingthe interchain coupling is suggestive of the transition from the power-lawdecay of spin-spin correlations in the 1D limit to long-range antiferromagneticorder in the quasi-1D regime and at $T=0$. In the numerically accessible regimeof interchain couplings, the charge sector remains gapped. The low-energymomentum dependence of the spin excitations is well described by the linearspin-wave theory with the largest intensity located around theantiferromagnetic wave vector. This magnon mode corresponds to a bound state oftwo spinons. At higher energies the spinons deconfine and we observe signaturesof the two-spinon continuum which progressively fade away as a function ofinterchain hopping.

Spinon confinement: dynamics of weakly coupled Hubbard chains