Motivated by
Mo3S7(dmit)
3, we investigate the Hubbard model on the triangular necklace lattice at two-thirds filling. We show, using second-order perturbation theory, that in the molecular limit, the ground state and the low-energy excitations of this model are identical to those of the spin-one Heisenberg chain. The latter model is known to be in the symmetry-protected topological Haldane phase. Away from this limit we show, on the basis of symmetry arguments and density matrix renormalization group (DMRG) calculations, that the low-energy physics of the Hubbard model on the triangular necklace lattice at two-thirds filling is captured by the ferromagnetic Hubbard-Kondo lattice chain at half-filling. This is consistent with and strengthens previous claims that both the half-filled ferromagnetic Kondo lattice model and the two-thirds filled Hubbard model on the triangular necklace lattice are also in the Haldane phase. A connection between Hund's rules and Nagaoka's theorem is also discussed.
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 Mo3S7(dmit)3.First, we propose a low energy Hamiltonian which is the Hubbard model on triangular lattice at two thirds filling to describe the low energy physics of the material Mo3S7(dmit)3 based on the experimental and numerical (DFT calculations) by Llusar et al. (Llusar et al. (2004)) investigations of this material. At the heart of this model lies a confluence of many interesting phenomena in strongly correlated system such as Kondo physics, symmetryprotected-topologically-ordered phase and spin liquids.We have also employed analytical techniques to show that the low energy physics of the model in the molecular limit is captured by the spin-one Heisenberg model and the ground state is in the Haldane phase. The model can be also mapped on to the Hubbard-Kondo lattice model with ferromagnetic interactions at half filling, whose ground state is believed to be in the Haldane phase. This mapping also helps us to understand the origin of insulating behaviour in this model.Matrix product states are one of the efficient numerical techniques to investigate onedimensional strongly correlated models. We have used the matrix product state formalism of DMRG to simulate the Hubbard model on the triangular necklace lattice at two-thirds filling. We have demarcated different phases exhibited by this model. From ourcalculations, we find that the model displays an unusual insulating phase away from half filling and the ground states of the model are found be in the Haldane phase. Properties such as the charge gap and the spin gap for the model have been calculated and compared with experiments.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 Mo3S7(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 Mo3S7(dmit)3
Using the triangular-lattice extended Hubbard model as a test system, we compare
GW+EDMFT results for the recently proposed self-consistency scheme with causal auxiliary fields to those obtained from the standard implementation which identifies the impurity Green's functions with the corresponding local lattice Green's functions. Both for short- and long-ranged interactions we find similar results, but the causal scheme yields slightly stronger correlation effects at half-filling. We use the two implementations of
GW+EDMFT to compute spectral functions and dynamically screened interactions in the parameter regime relevant for $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$. These simulations allow us to clarify if the sample used in a recent photoemission study [M. Ligges et al., Phys. Rev. Lett. 120, 166401 (2018)] was half-filled or hole doped.