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|Title:||A Density-Matrix Renormalization Group Study of Quantum Spin Models with Ring Exchange|
|Department:||Physics and Astronomy|
|Keywords:||density-matrix renormalization group;dmrg;heisenberg model;logarithmic corrections;two-leg ladders;four-spin ring-exchange;Condensed Matter Physics;Condensed Matter Physics|
|Abstract:||<p>In this thesis we discuss in detail the density-matrix renormalization group (DMRG) for simulating low-energy properties of quantum spin models. We implement an original DMRG routine on the S=1/2 antiferromagnetic Heisenberg chain and benchmark its efficiency against exact results (energies, correlation functions, etc.) as well as conformal field-theoretical calculations due to finite-size scaling (ground-state energy and spin gap logarithmic corrections). Moreover, we apply the DMRG to a two-leg square ladder system, where in addition to bilinear exchange terms, we also consider an additional cyclic four-spin ring-exchange. The transposition of four spins gives rise to biquadratic exchange terms which are non-trivial to implement in the DMRG. Intermediate results of the ring-exchange are presented along with the difficulties presently encountered.</p>|
|Appears in Collections:||Open Access Dissertations and Theses|
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