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In this thesis we present contributions in the field of the applications of quantum field theories techniques to condensed matter models. In chapter 3 we investigate on the non covariant fermionic determinant and its connection to Luttinger…
The frustrated spin-one-half Heisenberg model on triangualr and Kagome Lattices is mapped onto a single specis of fermion carrying statistical flux. The corresponding Chern-Simons gauge theory is analyzed at the Gaussian level and found to…
The cradle of quantum spin liquids, triangular antiferromagnets show strong proclivity to magnetic order and require deliberate tuning to stabilize a spin-liquid state. In this brief review, we juxtapose recent theoretical developments that…
Employing large-scale quantum Monte Carlo simulations, we study the extended $XXZ$ model on the kagome lattice. A $\mathbb Z_2$ quantum spin liquid phase with effective even Ising gauge field structure emerges from the delicate balance…
The mechanism explaining the key role of AFM correlations in formation of the heavy fermion state is offered. It is shown that in the case of $(T^*-T_N)/T_N << 1$ the critical spin fluctuations transform the mean-field second-order…
Ultra-cold dipolar spinor fermions in zig-zag type optical lattices can mimic spin-orbital models relevant in solid-state systems, as transition-metal oxides with partially filled d-levels, with the interesting advantage of reviving the…
Motivated by the recent progress on the spin-orbit-coupled triangular lattice spin liquid candidate YbMgGaO4, we carry out a systematic projective symmetry group analysis and mean-field study of candidate U(1) spin liquid ground states. Due…
Motivated by the recent experimental progress on the strong spin-orbit-coupled rare earth triangular antiferromagnet, we analyze the highly anisotropic spin model that describes the interaction between the spin-orbit-entangled Kramers'…
The weak Mott insulating regime of the triangular lattice Hubbard model exhibits a rich magnetic phase diagram as a result of the ring exchange interaction in the spin Hamiltonian. These phases include the Kalmeyer-Laughlin type chiral spin…
Two-component dipolar fermions in zigzag optical lattices allow for the engineering of spin-orbital models. We show that dipolar lattice fermions permit the exploration of a regime typically unavailable in solid-state compounds that is…
We study the ground-state properties of the quantum spin liquid (QSL) phases of the spin-$1/2$ antiferromagnetic Heisenberg model on the triangular lattice with nearest- ($J_1$), next-nearest- ($J_2$), and third-neighbor ($J_3$)…
We study the strong coupling limit of the extended Hubbard model in two dimensions. The model consists of hopping, on-site interaction, nearest-neighbor interaction, spin-orbit coupling and Zeeman spin splitting. While the study of this…
We theoretically investigate the deflection-induced coupling of an electron spin to vibrational motion due to spin-orbit coupling in suspended carbon nanotube quantum dots. Our estimates indicate that, with current capabilities, a quantum…
Based on density matrix renormalization group method, we investigate the spin-orbit coupled Fermi gas with attractive interactions in one-dimensional optical lattice and present a complete phase diagram for a quarter-filling system with…
We investigate the superfluidity of attractive Fermi gas in a square optical lattice with spin-orbit coupling (SOC). We show that the system displays a variety of new filling-dependent features. At half filling, a quantum phase transition…
The essential role of synthetic spin-orbit coupling in discovering new topological matter phases with cold atoms is widely acknowledged. However, the engineering of spin-orbit coupling remains unclear for arbitrary-spin models due to the…
We study an exactly solvable model with bond-directional quadrupolar and octupolar interactions between spin-orbital entangled $j_{\mathrm{eff}} = \frac{3}{2}$ moments on the honeycomb lattice. We show that this model features a multipolar…
Recent numerical simulations find a possible chiral spin liquid state in the intermediate coupling regime of the triangular lattice Hubbard model. Here we provide a simple picture for its origin in terms of a Bosonic RVB description. More…
We argue for the existence of a liquid ground state in a class of square lattice models of orbitally degenerate insulators. Starting with the SU(4) symmetric Kugel-Khomskii model, we utilize a Majorana Fermion representation of spin-orbital…
Quantum spin-orbital liquids are elusive strongly correlated states of matter that emerge from quantum frustration between spin and orbital degrees of freedom. A promising route towards the observation of those states is the creation of…