Hornung, Manes (2021). The Vortex in the (2 + 1)dimensional O(2) Model and Effective LowEnergy Theory for Spin Chains in a Strong Magnetic Field. (Thesis). Universität Bern, Bern

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Abstract
Part I: The (2+1)dimensional O(2) model in the continuum limit at the WilsonFisher 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 integervalued link variables, we perform Monte Carlo simulations to calculate the mass of the vortex as a function of the finite and Cperiodic volume nonperturbatively. 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 WilsonFisher 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 twodefects sectors and the results are matched to an effective theory of nonrelativistic 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.
Item Type:  Thesis 

Dissertation Type:  Single 
Date of Defense:  2 July 2021 
Subjects:  500 Science > 530 Physics 
Institute / Center:  08 Faculty of Science > Institute of Theoretical Physics 10 Strategic Research Centers > Albert Einstein Center for Fundamental Physics (AEC) 
Depositing User:  Hammer Igor 
Date Deposited:  02 Dec 2021 16:09 
Last Modified:  02 Dec 2021 16:15 
URI:  https://boristheses.unibe.ch/id/eprint/3199 
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