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Field induced phase transition in one dimensional Heisenberg antiferromagnet model studied using density matrix renormalization group Gustainis, Peter


This thesis examines the Heisenberg antiferromagnetic spin chain in one dimension (1D) with a crystal field splitting term and applied magnetic field term. We use theoretical techniques from quantum field theory and conformal field theory (CFT) to make predictions about the excitation spectrum for our model. We then use Density Matrix Renormalization Group (DMRG) numerical techniques to simulate our spin chain and extract the energy spectrum as we vary our crystal field splitting and magnetic field terms. These results are compared and we examine where theoretical calculations accurately describe our system. This work is motivated by recent experimental work done on SrNi₂Vi₂O₈ by Bera et al. [1] which is a quasi-1D material with weakly coupled spin chains in the bulk. These 1D chains are expected to be described by the Hamiltonian we study in this thesis, and we neglect interchain coupling. We first consider our system where the crystal field splitting term is set to zero, which can be described theoretically using a mapping to the non linear sigma model (NLSM). Near the critical field, it undergoes a Bose condensation transition whose excitation spectrum can be mapped to non-interacting fermions in 1D. We then consider large negative crystal field splitting, and find that near small applied magnetic field we can describe some excited states using Landau-Ginsburg theory. Near critical field, we show that the transition is in the Ising universality, and use results from CFT to predict the spectrum for finite size systems. This allows us to make predictions about where the transition field would be for very large or infinite system size. Finally, we examine our crystal field splitting tuned to the value obtained in Ref. 1, which is a small, negative value. We observe qualitative elements in this spectrum from the spectra obtained at zero and large negative crystal field splitting.

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