Large scale computer-simulations of many-body Bose and Fermi systems at low temperature

Abstract

of thesis entitled LARGE SCALE COMPUTER-SIMULATIONS OF MANY-BODY BOSE AND FERMI SYSTEMS AT LOW TEMPERATURE Submitted by Siegfried Guertler for the Degree of Doctor of Philosophy at The University of Hong Kong in July 2008 Many-body systems are of great interest for condensed matter physics. There are several reasons for this: First, it is highly relevant to material science and therefore engineering. Some of the novel materials partly already in use by engineers are not understood. The most prominent case is high-temperature superconductors. Therefore if we are able to understand “how they work” we are probably able to help engineers to create even smarter and more useful materials, which can then find its applications to civiland mechanical-engineering, medicine and space-exploration. Second, the physics involved is very interesting, challenging and competitive. Again high-temperature superconductivity is a good example. Found already in the eighties, there is still no general consensus in the community about the underlying mechanism. Another more recent example is the “supersolid”. A supersolid is a material which has superfluid properties, but keeps its crystal ordering. This leads to the amazing property of a reduced (“non-classical”) rotational momentum, which was found by Kim and Chan in 2004 in solid helium-4. In this thesis we investigate two model-systems numerically. The first one is initially motivated by the recently found supersolid. Based on the original experiments we performed quantum Monte-Carlo, here we consider it a bulk equilibrium state. The model considers the movement and interaction of two types of defects: vacancies and interstitials, both of which are bosons doped into an ideal crystal. These defects are considered within a bosonic Hubbard model with an attractive interaction between them. We compare our results with previous mean-field theories for the same model, and extent the work in terms of finite-temperature investigation. We find our results in qualitative agreement with previous works, and find an extended region for the supersolid state. We could classify the phase-transitions to be all of Kosterlitz-Thouless type, and our finite temperature investigation showed separate Bose-condensation of the two types of bosons at different temperatures. Our second model system is concerned on an investigation of the form of superconductivity occurring in organic materials such as (TMTSF)2PF6. The mechanism for this form of superconductivity seems to be different from both the traditional low-temperature superconductivity found by H. K. Onnes (1913) and different from the high-temperature superconductivity found by K. A. Mueller (1986). This form was dubbed ”gossamer superconductivity” due to its small value for the superfluid density which Robert Laughlin called the first theoretical ideas on a microscopic level. The theory considers a wave-function which partially Gutzwiller projects double occupied states out. We perform variational Monte-Carlo for a previously proposed fermion Hubbard model. The Hamiltonian contains an additional antiferromagnetic coupling term, to describe virtual hopping at intermediate on-site strengh U . We consider a lattice structure matching to κ-(BEDT-TTF)2X. We could successfully identify the three phases metallic, superconducting and anti-ferromagnetic. These are in qualitative agreement with analytical varitional calculations. We could further find a region with a particularly high value of the superconducting order parameter. LARGE SCALE COMPUTER-SIMULATIONS OF MANY-BODY BOSE AND FERMI SYSTEMS AT LOW TEMPERATURE by Siegfried Guertler Dipl.-Ing., Graz University of Technology, Austria A thesis submitted in partial fulfilment of the requirements for the Degree of Doctor of Philosophy at The University of Hong Kong.