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Title: Quantized lattice dynamic effects on the Peierls transition
Author: Pearson, Christopher John
Awarding Body: Oxford University
Current Institution: University of Oxford
Date of Award: 2011
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The prevailing physics of one-dimensional (10) quantum many-body systems is reviewed, noting the emergence of the Luttinger model from the breakdown of Fermi-liquid theory. The possibility of a transition to a ground state phase supporting a spectral gap is rationalized and the well-known Peierls instability is introduced. To investigate the role of quantum fluctuations in 10 dimerization, we introduce the gapped, dispersionless (Einstein) and gapless, dispersive (Debye) phonon regimes, motivating a multiphonon treatment of the underlying lattice. Phonon-mediated renormalization of the fermion subspace leads to a modified Berezinskii-Kosterlitz- Thouless (BKT) transition in both the electronic- and spin-Peierls systems. The computational problem is correspondingly involved and we introduce the density-matrix renormalization group (OMRG) - a numerical method for studying quantum many-body systems - and adapt it for quantum phonons. We subsequently consider phase transitions at T = 0, proposing a series of critical-point characterizations: energy gap crossing, finite-size scaling, bond order auto-correlation functions, quantum bipartite entanglement, and conformal invariance. The optimal-phonon OMRG is used to investigate the spin-Peierls transition for qubit lattices. We use a phonon spectrum that interpolates between the dispersionless and disper sive regimes, observing a BKT transition at non-zero spin-phonon coupling, gc. Extrapo- lation from the Einstein- to the Debye-limit is accompanied by an increase in gc for fixed optical (q = π) phonon gap. We therefore conclude that the dimerized state is more unstable with respect to Debye phonons, which renormalize the effective spin-lattice coupling for the Peierls-active mode. Analogous conclusions are obtained for the extended Hubbard Peierls model. Varying the Coulomb interaction, U, a generalized Peierls transition is observed, intermediate to the uncorrelated (U = 0) and spin-Peierls (U-> infinity) limits. The non-monotonicity of the spin gap with respect to U is discussed in terms of valence-bond theory and the Gutzwiller approximation. Then, using the extended Hubbard model with Debye phonons, we show the dimerization of trans-polyacetylene to be close to the critical regime. We conclude by rationalizing the differential destabilization of the Peierls phase under Einstein and Oebye phonons, presenting the electronic- and spin-Peierls transitions within a unified framework.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available