Strongly correlated systems belong to a class of materials in which electron correlations play an important role. Correlated systems display many unconventional behaviours like high temperature superconductivity, fractionalised excitations, extremely fast non-linear optical responses and many more exotic properties. Thus strong correlated materials exhibit many interesting physics which have potential applications in a wide range of areas.In this Thesis, we explore the numerical simulation of a strongly correlated quasi one dimensional organic material Mo 3 S 7 (dmit) 3 . The Haldane phase is a symmetry-protected-topologically-ordered phase with edge states and a non-local string order. In our simulation using matrix products states, we see all these signatures, in addition to the double degeneracy in the entanglement spectrum that characterizes the Haldane phase. We find that the Haldane phase is robust despite the charge fluctuations in the model and the parity (inversion) symmetry protects the Haldane phase in fermionic models.The final part of the thesis deals with finding the tight-binding hopping integrals of Mo 3 S 7 (dmit) 3 using density functional theory. We make an unitary transformation of Kohn-Sham orbitals obtained using DFT to Wannier orbitals. Using the overlap of Wannier orbitals in the real space, we find the magnitude of tight-binding integrals. From these tight-binding integrals we arrive at low energy effective models that describe the material Mo 3 S 7 (dmit) 3 .ii
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