The vortex in the (2 + 1)-dimensional O(2) model and effective low-energy theory for spin chains in a strong magnetic field

Part I: The (2+1)-dimensional O(2) model in the continuum limit at the Wilson-Fisher fixed point approached from the broken phase contains massless Goldstone bosons and vortices. The latter are infraparticles and therefore have a mass that is expected to diverge logarithmically with the volume due to the infinite cloud of massless Goldstone bosons that surrounds them. Making use of the exact duality that relates the O(2) model on the lattice to a gauge theory with integer-valued link variables, we perform Monte Carlo simulations to calculate the mass of the vortex as a function of the finite and C-periodic volume non-perturbatively. We confirm the logarithmic divergence of the vortex mass numerically, and calculate the strength of the divergence that is related to the vortex charge, to be b = 3:55(9). This constitutes a universal amplitude ratio associated with the Wilson-Fisher fixed point.

Part II: In a large external magnetic field, spin chains saturate. We study defects in the saturated state for the XXZ Heisenberg spin chain as well as for a SU(3) spin chain that is related to a regularization of the CP(2) model suitable for quantum simulation. The Hamiltonian is diagonalized in the one- and two-defects sectors and the results are matched to an effective theory of non-relativistic point particles with a contact interaction. We find that the defects in the saturated state of the SU(3) spin chain are equivalent to the ones in an antiferromagnetic, anisotropic XXZ Heisenberg spin chain, and that they interact repulsively.

2021

dissertation

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