University of Minnesota
School of Physics & Astronomy

Condensed Matter Seminar

Thursday, November 1st 2007
1:25 pm:
Condensed Matter Seminar in 210 Physics
Speaker: Raymond Bishop, Manchester
Subject: Quantum Phase Transitions in Spin-Lattice Systems With and Without Frustration

The coupled cluster method (CCM) has become one of the most pervasive and most powerful of all ab initio formulations of quantum many-body theory. It has yielded numerical results which are among the most accurate available for a wide range of both finite and extended physical systems defined on a spatial continuum. This widespread success has spurred recent applications to similar quantum-mechanical systems defined on an extended regular spatial lattice. In particular, we have shown how the systematic inclusion of multispin correlations for a wide variety of quantum spin-lattice problems can be very efficiently implemented with the CCM. The method is not restricted to bipartite lattices, to spin-half systems, or to non-frustrated systems, and can thus deal with problems where, for example, the quantum Monte Carlo (QMC) techniques would be faced with the infamous "minus-sign problem." In this talk I briefly review the CCM itself and then discuss an illustrative example from among many applications made to quantum spin-lattice systems, for a model with two types of interactions which exhibits competition between magnetic order and dimerization. As in all other cases the CCM may readily be implemented to high (LSUBm) orders using computer-algebraic techniques. Values for ground- and excited-state properties are obtained which are fully competitive with those from other state-of-the-art methods, including the much more computationally intensive QMC techniques, in the special cases where the latter can be applied. The raw LSUBm results are themselves generally excellent. They converge rapidly and can be extrapolated in the truncation index, m. The CCM can also provide valuable information on the quantum phase transitions, quantum order, and quantum criticality, as we show in our example. For such strongly correlated models of magnetism with competing interactions in two (or higher) dimensions, the CCM probably now represents the most powerful general method available, as I hope to show.

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