Transições de Fase Quânticas em Sistemas Correlacionados

In this work we have studied quantum phase transitions in strongly correlated systems using a bond-operator method within a Gaussian approximation. Specifically, we have studied the Kondo necklace model with an Ising-like anisotropy characterized by a parameter, and a magnetic field applied H in the z-direction. This model, at half-filling, is relevant to describe a class of heavy fermions, the so-called Kondo insulators. Firstly, the Ising-like anisotropy parameter in the Kondo necklace model is analyzed at zero and finite temperatures for arbitrary "d" dimensions. At zero temperature and in the paramagnetic phase, we have determined the spin gap exponent approximately 0.5, in three dimensions. This is independent of the anisotropy between 0 and 1 and is consistent with the dynamic exponent assuming the value z = 1, taking into account the Gaussian character of the approximation used in the bond-operator treatment. At low but finite temperatures, in the antiferromagnetic phase, the line of Neel transitions is calculated for . For d > 2 it is only re-normalized by the anisotropy parameter and varies with the distance to the quantum critical point |g| as T_N = |g|^\psi where, the shift exponent \psi= 1/(d - 1). Nevertheless, in two dimensions, a long range magnetic order occurs only at T = 0. In the paramagnetic phase, we find a power law temperature dependence on the specific heat at the quantum critical trajectory J/t = (J/t)c, T-> 0. It behaves as C_V= T^d, in concordance with the scaling theory for z = 1. We also have studied the magnetic field effects in the Kondo necklace model. This field is applied in the spin liquid state and induces an antiferromagnetic phase above a critical field H_{c1}. This ordered phase survives until a second critical field H_{c2}, called of saturation field. For fields larger than H_{c2}, the ground state is a saturated paramagnetic phase, with all the spins pointing in the field direction. Subsequently, dimensional crossover in the Kondo necklace model is analyzed at zero and finite temperatures. Explicit relations describing quasi-two-dimensional properties are obtained by asymptotically solving the resulting equations. The crossover from two dimensions (2d) to three dimensions (3d) is investigated, turning on the electronic hopping (t_{\perp}) of conduction electrons between different planes. In addition, the cases of quasi-three-dimensional (q3d) and quasi-one-dimensional (q1d) system, were also investigated. The phase diagram as a function of temperature T and t_{\perp}/t_{\parallel}, where t_{\parallel} is the hopping within the planes, is calculated. Unusual reentrant behavior in the temperature-dependent antiferromagnetic critical line is found close to two dimensions. Near the isotropic three-dimensional quantum critical point, the critical line is described by a standard power law with a square root dependence on the distance to the quantum critical point. Finally, we have studied the quantum phase transition in anisotropic antiferromagnets as the field is reduced below the saturation field H_{c2} and the system enters an XY-antiferromagnetic phase. At zero temperature and strong applied magnetic fields, the ground state of an anisotropic antiferromagnet is a saturated paramagnet with fully aligned spins. Using a bond operator representation we consider a model spin-1 Heisenberg antiferromagnetic with single-ion anisotropy in hyper-cubic lattices under strong magnetic fields. We have showed that the transition at H_{c2} can be interpreted as a Bose-Einstein condensation of magnons. These theoretical results were used to analyze the magnetization versus field data in the organic compound NiCl_{2}-4SC(NH_{2})_{2} (DTN) at very low temperatures. This is an ideal system to study Bose-Einstein condensation since H_{c2} is sufficiently low to be reached with static magnetic fields as opposed to pulsed fields. The scaling of the magnetization as a function of field and temperature close to H_{c2} has shown excellent agreement with the theoretical predictions and allowed us to obtain the quantum critical exponents and confirm the Bose-Einstein condensation nature of the transition at H_{c2}.