E. V. Correa Silva

Unidimensional generalized Hubbard model in the high temperature limit

We explore the properties of the non-commutative Grassmann algebra to study the unidimensional Generalized Hubbard model, obtaining the analytical expressions for the first three terms in the high temperature expansion of its grand canonical partition function, with no restrictions to the constant parameters of the model. We obtain corrections to known results, in the case of half-filled band with hopping constants t=0 and X=0.

Application of non-commutative algebra to a soluble fermionic model

We explore the properties of the non-commutative Grassmann algebra to obtain the high-temperature expansion of the grand canonical partition function for self-interacting fermionic systems. As an application, we consider the anharmonic fermionic oscillator, the simplest model in Quantum Mechanics with self-interacting fermions that is exactly soluble. The knowledge of the exact expression for its grand canonical partition function enables us to check the β-expansion obtained using our Grassmann-algebra-based technique.

The thermodynamics of the anisotropic spin-S XXZ chain in the high-temperature region

We report analytical calculations of the Helmholtz free energy of non-integrable anisotropic quantum XXZ chains in the high-temperature regime for several values of the spin S. Single-ion anisotropy and interaction with an external magnetic field are taken into account. The seven lowest-order terms in the high-temperature expansion of Helmholtz free energy are obtained. Our results contribute to the existing literature on high-temperature expansions and numerical studies of those models by discussing the effects of anisotropy upon their high-temperature thermodynamic properties, such as the average energy per site, the specific heat and magnetic susceptibility.

Multivariable Grassmann integrals and the high temperature expansion of interacting fermionic models

Using the noncommuting nature of fermionic fields we obtain a nonperturbative method to calculate the high temperature limit of the grand canonical partition function of interacting fermionic models. This nonperturbative approach is applied to the Hubbard model in d=2(1+1) and we recover the known results in the limit T → ∞.

Electromagnetic response of charged bosons coupled to a Chern-Simons gauge field: A path-integral approach

We analyze the electromagnetic response of a system of charged bosons coupled to a Chern-Simons (CS) gauge field. Path-integral techniques are used to obtain an effective action for the particle density of the system dressed with quantum fluctuations of the CS gauge field. From the action thus obtained we compute the U(1) current of the theory for an arbitrary electromagnetic external field. For the particular case of a homogeneous external magnetic field, we show, neglecting the back reaction of density-current to electromagnetic fields, the quantization of the transverse conductivity, even in the presence of an arbitrary impurity distribution. The relevance of edge states in this context is analyzed. The propagator of density fluctuations is computed, and an effective action for the matter density in the presence of a vortex excitation is suggested.

Thermodynamics of the spin ladder as a composite chain model

A special class of S=1 spin ladder Hamiltonians, with second-neighbor exchange interactions and with anisotropies in the z-direction, can be mapped onto one-dimensional composite S=2 (tetrahedral S=1) models. We calculate the high temperature expansion of the Helmoltz free energy for the latter class of models, and show that their magnetization behaves closely to that of standard XXZ models with a suitable effective spin Seff, such that Seff(1+Seff)=〈S⇒i2〉, where Si refers to the components of spin in the composite model. It is also shown that the specific heat per site of the composite model, on the other hand, can be very different from that of the effective spin model, depending on the parameters of the Hamiltonian.