Generalised t-V model in one dimension

We use a strong coupling expansion [1] to solve the one-dimensional extended t V model of fermions [2,3]. The model is solved for a range of densities, including both commensurate – where a charge density wave is present – and incommensurate densities. The first set consists not only of a trivial case of half filling. The method allows us to trace the transition from a Luttinger liquid phase to a Mott insulating phase. This simple yet powerful method is not based on Bethe ansatz and it works for both integrable and non-integrable systems. References [1] C.J. Hamer, Phys. Lett. B, 1979, 82, 75-78. [2] G. Gómez-Santos, Phys. Rev. Lett., 1993, 70, 3780. [3] R.G. Dias, Phys. Rev. B, 2000, 62, 7791

Thermodynamics of localized magnetic moments in a Dirac conductor

We show that the magnetic susceptibility of a dilute ensemble of magnetic impurities in a conductor with a relativistic electronic spectrum is non-analytic in the inverse tempertature at $1/T\to 0$. We derive a general theory of this effect and construct the high-temperature expansion for the disorder averaged susceptibility to any order, convergent at all tempertaures down to a possible ordering transition. When applied to Ising impurities on a surface of a topological insulator, the proposed general theory agrees with Monte Carlo simulations, and it allows us to find the critical temperature of the ferromagnetic phase transition.Comment: 5 pages, 1 figure, 2 tables, RevTe

In situ single walled carbon nanotube growth using a Q500 TGA

Using the Q500 Thermogravimetric Analyzer (TGA) it is demonstrated that it is possible to monitor the real time growth of Single Walled Carbon Nanotubes (SWCNTs) by Chemical Vapour Deposition (CVD) on SiO 2 supported Ni catalyst. The catalyst is made by first dissolving Ni(NO 3)·6H 2 O and SiO 2 in acetone and then allowing the acetone to evaporate. The resulting powder is then thermally decomposed in the Q500 TGA under an inert atmosphere of Ar(g) to generate SiO 2 supported NiO. The CH 4 (g) carbon precursor is then introduced, reducing the NiO to Ni and initiating the CVD growth of Carbon Nanotubes (CNTs). Thus both the formation of the catalyst and the growth of SWCNTs are monitored in real time by this method. The CVD grown carbon is confirmed as containing SWCNTs by Raman Spectroscopy. We believe this to be the first example of SWCNTs grown by CVD in a TGA

Simulating graphene impurities

We study a model of magnetic impurities deposited onto a graphene lattice, interacting via exchange of conduction electrons. Our objective is to look for the long-range ordering of the impurities, which would lead to drastic changes in the transport properties of graphene. Numerical simulations are performed and we indeed observe the ordered phase. We also estimate the critical temperature of a transition between disordered and ordered phases

Numerical investigations of the Schwinger model and selected quantum spin models

Numerical investigations of the XY model, the Heisenberg model and the J-J' Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The low-lying energy levels are obtained and finite size scaling is performed to estimate the bulk limit values. The results are found to be consistent with the exact values. The DMRG results are found to be most promising. The Schwinger model is also studied using the exact diagonalisation and the strong coupling expansion. The massless, the massive model and the model with a background electric field are explored. Ground state energy, scalar and vector particle masses and order parameters are examined. The achieved values are observed to be consistent with previous results and theoretical predictions. Path to the future studies is outlined.Comment: 86 pages, 56 figures, Master's Thesi

Generalised t-V model in one dimension

We use a strong coupling expansion [1] to solve the one-dimensional extended t‑V model of fermions [2,3]. The model is solved for a range of densities, including both commensurate – where a charge density wave is present – and incommensurate densities. The first set consists not only of a trivial case of half filling. The method allows us to trace the transition from a Luttinger liquid phase to a Mott insulating phase. This simple yet powerful method is not based on Bethe ansatz and it works for both integrable and non-integrable systems.References:[1] C.J. Hamer, Phys. Lett. B, 82, 75-78 (1979).[2] G. Gómez-Santos, Phys. Rev. Lett., 70, 3780 (1993).[3] R.G. Dias, Phys. Rev. B, 62, 7791 (2000)