Publications
Quantum Monte Carlo calculations of energy gaps from first principles
R. J. Hunt, M. Szyniszewski, G. I. Prayogo, R. Maezono, N. D. Drummond
submitted to PRB
R. J. Hunt, M. Szyniszewski, G. I. Prayogo, R. Maezono, N. D. Drummond
submitted to PRB
We review the use of continuum quantum Monte Carlo (QMC) methods for the calculation of energy gaps from first principles, and present a broad set of excitedstate calculations carried out with the variational and fixednode diffusion QMC methods on atoms, molecules, and solids. We propose a finitesizeerror correction scheme for bulk energy gaps calculated in finite cells subject to periodic boundary conditions. We investigate the fixednode errors in diffusion Monte Carlo gaps evaluated with SlaterJastrow trial wave functions by examining the effects of backflow transformations, and also by considering the formation of restricted multideterminant expansions for excitedstate wave functions. For several molecules, we examine the importance of structural relaxation in the excited state in determining excitedstate energies. We study the feasibility of using variational Monte Carlo with backflow correlations to obtain accurate excitedstate energies at reduced computational cost, finding that this approach can be valid. We find that diffusion Monte Carlo gap calculations can be performed with much larger time steps than are typically required to converge the total energy, at significantly diminished computational expense, but that in order to alleviate fixednode errors in calculations on solids the inclusion of backflow correlations is sometimes necessary.
Diffusion quantum Monte Carlo study of excitonic complexes in twodimensional transitionmetal dichalcogenides
E. Mostaani, M. Szyniszewski, C. H. Price, R. Maezono, M. Danovich, R. J. Hunt, N. D. Drummond, V. I. Fal'ko
Phys. Rev. B 96(7), 075431 (2017)
E. Mostaani, M. Szyniszewski, C. H. Price, R. Maezono, M. Danovich, R. J. Hunt, N. D. Drummond, V. I. Fal'ko
Phys. Rev. B 96(7), 075431 (2017)
Excitonic effects play a particularly important role in the optoelectronic behavior of twodimensional semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide (i) statistically exact diffusion quantum Monte Carlo bindingenergy data for a MottWannier model of (donor/acceptorbound) excitons, trions, and biexcitons in twodimensional semiconductors in which charges interact via the Keldysh potential, (ii) contact pairdistribution functions to allow a perturbative description of contact interactions between charge carriers, and (iii) an analysis and classification of the different types of bright trion and biexciton that can be seen in singlelayer molybdenum and tungsten dichalcogenides. We investigate the stability of biexcitons in which two charge carriers are indistinguishable, finding that they are only bound when the indistinguishable particles are several times heavier than the distinguishable ones. Donor/acceptorbound biexcitons have similar binding energies to the experimentally measured biexciton binding energies. We predict the relative positions of all stable free and bound excitonic complexes of distinguishable charge carriers in the photoluminescence spectra of WSe₂ and MoSe₂.
Binding energies of trions and biexcitons in twodimensional semiconductors from diffusion quantum Monte Carlo calculations
M. Szyniszewski, E. Mostaani, N. D. Drummond, and V. I. Fal’ko
Phys. Rev. B 95(8), 081301 (Rapid Communication) (2017)
M. Szyniszewski, E. Mostaani, N. D. Drummond, and V. I. Fal’ko
Phys. Rev. B 95(8), 081301 (Rapid Communication) (2017)
Excitonic effects play a particularly important role in the optoelectronic behavior of twodimensional (2D) semiconductors. To facilitate the interpretation of experimental photoabsorption and photoluminescence spectra we provide statistically exact diffusion quantum Monte Carlo bindingenergy data for MottWannier models of excitons, trions, and biexcitons in 2D semiconductors. We also provide contact pair densities to allow a description of contact (exchange) interactions between charge carriers using firstorder perturbation theory. Our data indicate that the binding energy of a trion is generally larger than that of a biexciton in 2D semiconductors. We provide interpolation formulas giving the binding energy and contact density of 2D semiconductors as functions of the electron and hole effective masses and the inplane polarizability.
Chargedensitywave phases of the generalized tV model
M. Szyniszewski
to be published
M. Szyniszewski
to be published
The onedimensional extended tV model of fermions on a lattice is a model with repulsive interactions of finite range that exhibits a transition between a Luttinger liquid conducting phase and a Mott insulating phase. It is known that by tailoring the potential energy of the insulating system, one can force a phase transition into another insulating phase. We show how to construct all possible chargedensitywave phases of the system at low critical densities in the atomic limit. Higher critical densities are investigated by a bruteforce analysis of the possible finite unit cells of the Fock states.
Lattice Hamiltonian approach to the Schwinger model: further results from the strong coupling expansion
M. Szyniszewski, K. Cichy, A. KujawaCichy
Proceedings of Science (Lattice 2014) 314 (2015)
M. Szyniszewski, K. Cichy, A. KujawaCichy
Proceedings of Science (Lattice 2014) 314 (2015)
We employ exact diagonalization with strong coupling expansion to the massless and massive Schwinger model. New results are presented for the ground state energy and scalar mass gap in the massless model, which improve the precision to nearly 10⁻⁹ %. We also investigate the chiral condensate and compare our calculations to previous results available in the literature. Oscillations of the chiral condensate which are present while increasing the expansion order are also studied and are shown to be directly linked to the presence of flux loops in the system.
The generalized tV model in one dimension
M. Szyniszewski, E. Burovski
J. Phys.: Conf. Ser. 592 (SCES2014), 012057 (2015)
M. Szyniszewski, E. Burovski
J. Phys.: Conf. Ser. 592 (SCES2014), 012057 (2015)
We develop a systematic strong coupling approach for studying an extended tV model with interactions of a finite range. Our technique is not based on the Bethe ansatz and is applicable to both integrable and nonintegrable models. We illustrate our technique by presenting analytic results for the ground state energy (up to order 7 in t/V), the current density and densitydensity correlations for integrable and nonintegrable models with commensurate filling factors. We further present preliminary numerical results for incommensurate nonintegrable models.
In situ Single Walled Carbon Nanotube growth using a Q500 TGA
C. Oakland, A. Rooney, M. Szyniszewski, A. F. Verre, S. Worrall
TA Instruments Applications Library TA372 (2014)
1st prize in Student Application Award Program in category Thermal Analysis
C. Oakland, A. Rooney, M. Szyniszewski, A. F. Verre, S. Worrall
TA Instruments Applications Library TA372 (2014)
1st prize in Student Application Award Program in category Thermal Analysis
Using the Q500 Thermogravimetric Analyzer (TGA) we demonstrate that it is possible to monitor the real time growth of Single Walled Carbon Nanotubes (SWCNTs) by Chemical Vapour Deposition (CVD) on SiO2 supported Ni catalyst. The catalyst is made by first dissolving Ni(NO3)·6H2O and SiO2 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 a SiO2 supported NiO. The CH4(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.
Lattice Hamiltonian approach to the massless Schwinger model: precise extraction of the mass gap
K. Cichy, A. KujawaCichy, M. Szyniszewski
Comp. Phys. Comm. 184(7), 16661672 (2013)
K. Cichy, A. KujawaCichy, M. Szyniszewski
Comp. Phys. Comm. 184(7), 16661672 (2013)
We present results of applying the Hamiltonian approach to the massless Schwinger model. A finite basis is constructed using the strong coupling expansion to a very high order. Using exact diagonalization, the continuum limit can be reliably approached. This allows to reproduce the analytical results for the ground state energy, as well as the vector and scalar mass gaps to an outstanding precision better than 10⁻⁶ %.
Thermodynamics of localized magnetic moments in a Dirac conductor
V. Cheianov, M. Szyniszewski, E. Burovski, Yu. Sherkunov, V. Fal'ko
Phys. Rev. B 86(5), 054424 (2012)
V. Cheianov, M. Szyniszewski, E. Burovski, Yu. Sherkunov, V. Fal'ko
Phys. Rev. B 86(5), 054424 (2012)
We show that the magnetic susceptibility of a dilute ensemble of magnetic impurities in a conductor with a relativistic electronic spectrum is nonanalytic in the inverse temperature at 1/T→0. We derive a general theory of this effect and construct the hightemperature expansion for the disorder averaged susceptibility to any order, convergent at all temperatures 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.
Output

Numerical investigations of the Schwinger model and selected quantum spin models
Master's Thesis, Poznań 2012 Numerical investigations of the XY model, the Heisenberg model and the JJ' Heisenberg model are conducted, using the exact diagonalisation, the numerical renormalisation and the density matrix renormalisation group approach. The lowlying 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. 

Simulating graphene impurities using the worm algorithm
MPhys Project, Lancaster 2011 Using computer simulation with one of the Monte Carlo algorithms, worm algorithm, we study the twodimensional Ising model. The critical temperature Tc of the phase transition is calculated by the usage of the critical exponents and the results are compared to the analytical result, giving outstanding accuracy.
We also show that the magnetic ordering of impurities distributed on graphene is possible by simulating the properly constructed model with the same algorithm. The value of Tc is estimated. Furthermore, dependence of Tc on the interaction constants is explored. We outline how one can proceed in investigating this relation in the future. 
© Marcin Szyniszewski 20122015