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We study the 2D Ising model on a square lattice with additional non-equal diagonal next-nearest neighbor interactions. The cases of classical and quantum (transverse) models are considered. Possible phases and their locations in the space…
The phase diagram of a frustrated spin-$S$ zig-zag ladder is studied through different numerical and analytical methods. We show that for arbitrary $S$, there is a family of Hamiltonians for which a fully-dimerized state is an exact ground…
Using the coupled cluster method (CCM) we study the full (zero-temperature) ground-state (GS) phase diagram of a spin-half ($s=1/2$) $J_{1}$-$J_{2}$ Heisenberg model on a cross-striped square lattice. Each site of the square lattice has 4…
We investigate frustrated antiferromagnetic Heisenberg quantum spin chains at T=0 for S=3/2 and S=2 using the DMRG method. We localize disorder and Lifshitz points, confirming that quantum disorder points can be seen as quantum remnants of…
The ground state phase diagram of the spin-1/2 Heisenberg frustrated $\Delta$-chain with a ferromagnetic main chain is investigated. In addition to the ferromagnetic phase, various nonmagnetic ground states are found. If the ferromagnetic…
We present an antiferromagnetic quantum spin-1/2 model on honeycomb lattice. It has two parts, one of which is the usual nearest-neighbor Heisenberg model. The other part is a certain multiple spin interaction term, introduced by us, which…
We study the phase diagram of a system of $2\times2\times2$ hard cubes on a three dimensional cubic lattice. Using Monte Carlo simulations, we show that the system exhibits four different phases as the density of cubes is increased:…
We design a (2+1))-dimensional [(2+1)D] quantum spin model in which spin-1/2 ladders are coupled through antiferromagnetic Ising interactions. The model hosts a quantum phase transition in the (2+1)D $Z_2$ universality class from the…
We study the ground-state phase diagram of a Heisenberg model with spin $S=\frac{1}{2}$ on a diamond-like decorated square lattice. A diamond unit has two types of antiferromagnetic exchange interactions, and the ratio $\lambda$ between the…
The phase transition of the quantum spin-1/2 frustrated Heisenberg antiferroferromagnet on an anisotropic square lattice is studied by using a variational treatment. The model is described by the Heisenberg Hamiltonian with two…
Using modified spin wave (MSW) method, we study the $J_1-J_2$ Heisenberg model with first and second neighbor antiferromagnetic exchange interactions. For symmetric $S=1/2$ model, with the same couplings for all the equivalent neighbors, we…
Critical behavior of three-dimensional classical frustrated antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state is studied. We consider two lattice models, whose continuous limit…
Making use of infinite projected entangled pair states, we investigate the ground state phase diagram of the nearest-neighbor spin-1 bilinear-biquadratic Heisenberg model on the triangular lattice. In agreement with previous studies, we…
We study the spin S=1 antiferromagnetic Heisenberg model on the square lattice with, in addition to the nearest-neighbor interaction, a three-site interaction of the form (S_i S_j)*(S_j S_k) + h.c.. This interaction appears naturally in a…
In this thesis, I study a two-dimensional extended Hubbard model in the weak coupling limit. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons. However in the special case of a…
Aiming to describe frustrated quantum magnets with non-magnetic singlet ground states, we have extended the Rokhsar-Kivelson (RK) loop-expansion to derive a generalized Quantum Dimer Model containing only connected terms up to arbitrary…
Using stochastic series expansion quantum Monte Carlo and density matrix renormalization group methods, we investigate the ground-state phase diagram of the $S=1/2$ Heisenberg model on the two-dimensional square-hexagon-octagon (SHO)…
We develop the density matrix renormalization group approach to systematically identify the topological order of the quantum spin liquid (QSL) through adiabatically obtaining different topological sectors of the QSL on an infinite cylinder.…
We investigate the quantum spin-1/2 zigzag chain with frustrated $J_1$-$J_2$ Heisenberg interactions, incorporating additional off-diagonal exchange interactions known as the $\Gamma$ term, both with and without an applied magnetic field.…
This article reviews recent studies of mean-field and one dimensional quantum disordered spin systems coupled to different types of dissipative environments. The main issues discussed are: (i) The real-time dynamics in the glassy phase and…