Research OverviewAnalytical and numerical solutions for manybody quantum systems. Dynamics of systems out of equilibrium. Quantum phase transitions. Investigating the massless and massive Schwinger model using various approaches.

Current project
My current project is titled "Effects of strain in graphene/hexagonalboronnitride heterostructures"  M. Szyniszewski, E. Mostaani, N.D. Drummond, V.I. Fal'ko
We investigate the effects of strain in 2D heterostructures with lattice mismatches, such as graphene/hexagonalboronnitride (hBN) bilayers. One interesting and practically important issue here is the question of why there are physical differences between exfoliated graphene transferred onto a hBN substrate and graphene grown directly on hBN [1]. To describe possible metastable states in these systems [2], we use a combination of theoretical and numerical modelling. Density functional theory and quantum Monte Carlo methods can be used to evaluate binding energies as functions of local lattice mismatch from first principles; the results are used to find an approximate expression for the energy as a functional of strain in the layers [3]. One can then search for strain fields that minimise the energy to determine locally stable configurations.
References:
[1] Meng, et al., Nanoscale 7, 1604616053 (2015); Yang, et al., Nat. Mater. 12, 792–797 (2013).
[2] Yankowitz, et al., arXiv:1603.03244, accepted in Nat. Commun.
[3] SanJose, et al., Phys. Rev. B 90, 075428 (2014); Aitken and Huang, J. Appl. Phys. 107, 123531 (2010).
[2] Yankowitz, et al., arXiv:1603.03244, accepted in Nat. Commun.
[3] SanJose, et al., Phys. Rev. B 90, 075428 (2014); Aitken and Huang, J. Appl. Phys. 107, 123531 (2010).
PhD Thesis Title
Lowdimensional quantum systems
PhD Thesis Outline
We study lowdimensional quantum systems with analytical and computational methods. Firstly, the onedimensional extended tV model of fermions with interactions of finite range is investigated. The model exhibits a phase transition between liquid and insulating regimes. We use various analytical approaches to generalise previous theoretical studies. We devise a strong coupling expansion to go beyond firstorder perturbation theory. The method is insensitive to the presence or the lack of integrability of the system. We extract the ground state energy and critical parameters of the model near the Mott insulating commensurate density. A summary of the methods used is provided to give a broader view of their advantages and disadvantages.
We also study the possible chargedensitywave phases that exist when the model is at the critical density. A complete description of phase diagrams of the model is provided: at low critical densities the phases are defined analytically, and at higher critical densities we tackle this problem computationally. We also provide a future outlook for determining the phases that occur at nonzero temperature.
Secondly, we investigate MottWannier complexes of two (excitons), three (trions) and four (biexcitons) charge carriers in twodimensional semiconductors. The fermions interact through an effective interaction of a form introduced by Keldysh. Our study also includes impuritybound complexes. We provide a classification of trions and biexcitons in transitionmetal dichalcogenides, which incorporates the difference of spin polarisation between molybdenum and tungstenbased materials. Using the diffusion Monte Carlo method, which is statistically exact for these systems, we extract binding energies of the complexes for a complete set of parameters of the model. Our results are compared with theoretical and experimental work on transitionmetal dichalcogenides. Agreement is found for excitonic and trionic results, but we also observe a large discrepancy in the theoretical biexcitonic binding energies as compared to the experimental values. Possible reasons for this are outlined. Simple interpolation formulas for binding energies are provided, that can be used to easily determine the values within the accuracy of 5% for any twodimensional semiconductor. We also calculate contact pair densities, which in the future can be used in the determination of the contact interaction.
Research Grants
Marcin Szyniszewski was funded by EPSRC NoWNano DTC grant number EP/G03737X/1 during his PhD.
His participation in SCES2014 conference was possible due to Lancaster University Graduate School Travel Grant GSTG1426.
His participation in Tensor Network Summer School 2015 was possible due to Lancaster University Graduate School Travel Grant GSTG1576.
His participation in 34th International Symposium on Lattice Field Theory (Lattice 2015) was possible due to Lancaster University Graduate School Travel Grant GSTG1685.
He was awarded IOP Research Student Conference Fund by IOP Computational Physics Group for the Psik 2015 Conference.
His participation in SCES2014 conference was possible due to Lancaster University Graduate School Travel Grant GSTG1426.
His participation in Tensor Network Summer School 2015 was possible due to Lancaster University Graduate School Travel Grant GSTG1576.
His participation in 34th International Symposium on Lattice Field Theory (Lattice 2015) was possible due to Lancaster University Graduate School Travel Grant GSTG1685.
He was awarded IOP Research Student Conference Fund by IOP Computational Physics Group for the Psik 2015 Conference.