Related papers: Semiclassical representation of the Hubbard model
We relate the quantum dynamics of the Bose-Hubbard model (BHM) to the semiclassical nonlinear equations that describe an array of interacting Bose condensates by implementing a standard variational procedure based on the coherent state…
I introduce several simplified schemes for the approximation of the self-consistency condition of the dynamical cluster approximation. The applicability of the schemes is tested numerically using the fluctuation-exchange approximation as a…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
In this work the two site Bose-Hubbard model is studied analytically in the limit of weak coupling u and large number of particles N . The semiclassical approximation where \frac{1}{N} plays the role of Planck's constant was used and…
The semiclassical approximation to the coherent state propagator requires complex classical trajectories in order to satisfy the associated boundary conditions, but finding these trajectories in practice is a difficult task that may…
We consider a quantum system of non-interacting fermions at temperature T, in the framework of linear response theory. We show that semiclassical theory is an appropriate framework to describe some of their thermodynamic properties, in…
By using a modulated magnetic field in a Feshbach resonance for ultracold fermionic atoms in optical lattices, we show that it is possible to engineer a class of models usually referred to as correlated-hopping models. These models differ…
A closed (in terms of classical data) expression for a transition amplitude between two generalized coherent states associated with a semisimple Lee algebra underlying the system is derived for large values of the representation highest…
Understanding the behavior of interacting fermions is of fundamental interest in many fields ranging from condensed matter to high energy physics. Developing numerically efficient and accurate simulation methods is an indispensable part of…
In the Hilbert space of a quantum particle the standard coherent-state resolution of unity is written in terms of a phase-space integration of the outer product $|z\rangle \langle z|$. Because no pair of coherent states is orthogonal, one…
We investigate a specific limit of the one-dimensional non-Hermitian Hubbard Hamiltonian with complex interactions. In this framework, fermions with different spin quantum numbers are mapped onto two distinct spin species, resulting in two…
In this thesis, I present a non-perturbative approach to the single-band attractive Hubard model which is an extension of previous work by Vilk and Tremblay on the repulsive model. Exact results are derived in the general context of…
We propose a scheme for investigating the quantum dynamics of interacting electron models by means of time-dependent variational principle and spin coherent states of space lattice operators. We apply such a scheme to the one-dimensional…
Analytical results on the correlation functions of strongly correlated many-body systems are rare in the literature and their importance cannot be overstated. We present determinant representations for the space-, time-, and…
We study a general bipartite quantum system consisting of a spin interacting with a bosonic field, with the initial state prepared as the product of a spin coherent state and a canonical coherent state. Our goal is to develop a…
We study coherent states for Bianchi type I cosmological models, as examples of semiclassical states for time-reparametrization invariant systems. This simple model allows us to study explicitly the relationship between exact semiclassical…
The notion of semi-classical states is first sharpened by clarifying two issues that appear to have been overlooked in the literature. Systems with linear and quadratic constraints are then considered and the group averaging procedure is…
We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the…
The internal structure of stripes in the two dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes, consistent with experimental observations, are stabilized by quantum fluctuations,…
Semiclassical methods are extremely important in the subjects of wave packet and coherent state dynamics. Unfortunately, these essentially saddle point approximations are considered nearly impossible to carry out in detail for systems with…