Sharif Digital Repository

The Hubbard model is one of the simplest interacting models in theoretical physics, especially condensed matter physics which despite its simplicity, its solutions are highly nontrivial and intractable. After 5 decades since its introduction, its phase diagram is not fully understood and whether or not, it has a high-temperature superconducting phase. In this thesis, we aim to employ the recent advances in machine learning and GPU programming to accelerate the QMC method. By accelerated QMC methods, we can explore the Hubbard model's phase diagram more efficiently. Using massive parallelization of the GPUs can speed up the measuring process by several times. The self-learning quantum... 

The Hamiltonian of the Hubbard model was introduced by Hubbard in 1963 to model electron correlations in narrow energy bands and it provided an approximate description of electrons in solids.This model provides a simple description of materials, but its exact solution is possible only in one dimension.In the physical examining of this model in quasi two-dimensional systems, the Density Matrix Renormalization Group(DMRG) is used, which is one of the most powerful numerical methods in studying quantum systems. The quantity that is important to solve the systems is the density matrix, which by knowing, many of the observable quantities of the systems can be obtained. Calculating the density... 

Recent advances in numerical computations in the field of strongly correlated systems have provided us to calculate the entanglement spectrum and the entanglement entropy for interacting systems. Calculating the explicit form of the entanglement Hamiltonian (a.k.a. the modular Hamiltonian) is considered as a difficult problem.In this dissertation, we intend to introduce a method and by means of the d ensity-matrix-renormalization-group algorithm to obtain for the first time the second quantization form of the entanglement Hamiltonian of interacting systems at zero temperature. We implement our method for one-dimensional Heisenberg spin chain and also Heisenberg model on a square lattice... 

After the introduction of the framework of quantum mechanics and its experimental success, it was assumed that any physical phenomenon could be analyzed and understood accurately using quantum mechanics. But very soon we found out that in most cases, it is too hard or sometimes impossible to solve the Schrödinger equation exactly even for few-body systems. The reason is that the dimension of the Hilbert space increases exponentially with the number of particles, in a way that for a spin chain(spin-1/2), which has only two single-particle states, even using modern classical computers we are barely able to find an exact solution of a 30-40 particles system which is far smaller than the... 

After the discovery of integer and fractional quantum Hall effects, a comprehensive effort started to understand the physics behind these findings thoroughly. At the end, these efforts resulted in the introduction of topological phases of matter and the notion of topological phase transition. With the recent developments in this field, as the introduction and synthesis of 3D topological insulators, many researchers began inspecting the effects of disorders and impurities in the lattice structure on the topological phases, As these imperfections are inevitable in the lab-created instances. Since, in the previous works only on-site disorders was studied, the concentration of this thesis is on... 

In the past few years, topological insulators (TIs), topological superconductors and their experimental observation have been in the center of condensed maer physicists’ aention. Kane and Mele proposed the simplest and the first model exhibiting TI phase for non-interacting electrons on the two dimensional honeycomb laice. On the other hand, in the Hubbard model for nonzero doping and near the half filling, the high temperature superconductivity is predicted theoretically. In this thesis, we fist investigate the interacting topological insulators by adding the Hubbard interaction to the Kane-Mele model. en, in the strong correlation limit we find an effective spin model -the so called... 

In the era of the internet and with the emergence of online stores, the possibility of changing prices for these e-commerce platforms has become simple and virtually cost-free. This allows them to adjust prices optimally in response to environmental and surrounding factors, maximizing their revenue from product sales. This development has led to numerous applications of statistical learning methods, particularly online learning, in these markets. In this thesis, we explore the issue of online pricing from various perspectives. One aspect is that product pricing is based on their features, which can be numerous. This leads us to the use of online learning methods and statistical learning in... 

Performance based design was first introduced in order to evaluate seismic vulnerability of structures in retrofitting topic and was rapidly implemented in new design codes. The main cause conducting widely developing of performance based design methods, has been accurate estimation of seismic demand parameters. Since seismic structural members displacement during earthquake has a direct effect on the amount of sustained damages, displacement index has always been a key concept in performance based design. The main goal followed by this research is comparing the results obtained from the standard pushover method (with two theorems of distributed plasticity and plastic hinges) and the... 

During times, reinforced concrete sturctures might need to be strengthened due to environmental factors, material properties, design errors or changes indesign guidelines.Fibre-reinforced-polymer (FRP)composites are prominentmaterialsfor this purpose. Externally full bonding systemhas been widely used for flexural strengthening of reinforced concrete sturctures with FRP. However, the drawback of using this strengthening system is the high reduction of structure's deformability.In this research, partially bonding system used in finite element modeling of a bridge’s deck to increase deformability compared to full bonding system. Results showed that not only deformability but also load... 

Vibration of a stationary structure excited by another structure moving on the surface of the stationary Structure is very common in engineering, such as vibration of bridges or railway track under travelling vehicles. In the simplest case, the moving structure maybe modeled as a constant load or a mass or an oscillator, in this case the moving mass is attached to the structure either by a spring or by a mass-spring assembly.The model of a moving mass brings some improvements to the model of the moving load where there is no inertia effect. However, the relative displacement between the moving structures and the beam cannot be considered in the moving mass model. A more appropriate model in... 

Through the recent years application of FRP material in structural engineering has been developed significantly. According to possible changes of a building function during its lifetime or alteration of the building codes, building structures usually need to be strengthened. Referring to merits of FRP material, its application seems to be a convenient idea toward the cited requirement. Curved beam and slab are known as highly used elements in building structures. Bridges composed of horizontal or vertical arches could be noted as common examples which need to be reinforced by FRP. However curved concrete surfaces, reinforced by FRP plates, seem to be studied than it is really required; For,... 

In this study the dynamic responses of finite Euler-Bernoulli beams and homogeneous isotropic 2D half-spaces, as one and two dimensional structures, under a moving object are investigated. First, the dynamic responses of finite beams with various boundary conditions were investigated. The results illustrated that the speed of a moving mass has direct influence on the entire structural dynamic response, depending on its boundary conditions. Critical influential speeds in the moving mass problems were introduced and obtained in numerical examples for various BC’s. Dynamic response of a half-space under an inertial foundation subjected to a time-harmonic loading was investigated in the next... 

Finding suitable locations for installing conventional concentric bracings such as X and V, without interfering with building architecture and its openings, is a routine challenge in building design. One of the less known forms of concentric bracings which can be used to solve this issue, is the y-shaped bracing composed of three braces. In the current thesis, results of analytical studies, computer modeling and experimental tests are presented to extend the knowledge of structural behavior of y-bracings. As the first step, effective buckling lengths of braces with rigid connections were found from equilibrium equations incorporating the effect of axial force on rotational stiffness of... 

OFDMA multi-hop cellular network (MCN) is the topic of a wide range of research today. In this thesis, we analyse this type of networks, regarding shadowing status, mobility patterns and different service requirements. In the multi-hop (MH) scenario, six fixed relays are set up in each cell, which split the cell into seven subcells. For mobility modeling, each subcell is split into several sub-regions. Mobile nodes are able to maintain at each sub-region with a random time distribution and migrate from it to one of its neighboring sub-regions. We also consider three types of services requiring specific number of subcarriers with specific BERs. The set of subcarriers is distributed among... 

We consider extending the visibility polygon of a given point q inside a simple polygon by converting one or some of the edges to mirrors. It is known that the visibility polygon of a point inside a polygon in the presence of a mirror can be computed in linear time. We propose a linear time algorithm that checks whether a given segment inside a simple polygon is visible by a given point q via a mirror-edge, and finds all such edges. And we prove that finding edges to add exactly k unit squares to the visibility polygon of a query point q in most cases is NP-complete and its minimization is NP-hard. These cases contain single and muliple, either with secular or difuse reflections. Moreover,... 

The present study is concerned with the development of a rubric which can help to have an objective, valid, and reliable assessment of short stories and novels written by creative writing students. The 30 participants of the study who were literature and creative writing experts took part in rubric development, validation, and reliability estimation. Review of the related literature, as well as the administration of a Likert scale questionnaire and a series of unstructured interviews led to the identification of ten elements which were used to construct the first version of the creative writing rubric. To ensure validity of the developed rubric, 18 literature and creative writing experts...