Browsing by Subject "Hubbard model."

Now showing 1 - 7 of 7

Open Access
Ground-state properties of double-wire semiconducting systems
(1997) Mutluay Müstecaplıoğlu, Nihal
With the recent advances in nanometer-scale semiconductor device fabrication technology, it became experimentally possible to produce strongly confined electron systems. Quantum wires are among these systems, and are attracting increasing interest due to their potential applications in solid-state device technology such as high-speed transistors, efficient photodetectors and lasers. Quantum wires are quasi-one-dimensional systems where electrons are free to move in one dimension, but their motion is restricted in the remaining two dimensions. Various models for qucisi-one-dimensional structures have been proposed in the literature, such as cylindrical, square-well and parabolic confinements. in this thesis, we examine ground-state correlations in double-quantum-wire systems within the self-consistent scheme of Singwi et ai, namely the STLS approximation. The model we adopt consists of two parallel cylindrically-confined quantum wires. The cases when both wires have electrons as charge carriers and when one wire has electrons while the other has holes are considered. Under the assumption that only one subband is occupied in each quantum wire and there is no tunneling between them, we calculate the local-field factors and static correlation functions. Ground-state energy and collective modes are discussed within the RPA, Hubbard and STLS approximations in order to compare the results. Charge-density-wave instabilities in these structures are examined at small and finite q values. Our numerical results are given for systems where the carrier densities and the radii of both wires are equal. As the charge carrier density is lowered, we observe that the importance of local field corrections increases so that the RPA or Hubbard approximations do not give reliable results in this region. We find that the interwire correlations become quite important for electron-hole systems. Taking into account the exchange-correlation hole around electrons, STLS provides a much better description to this many-body problem compared to the previous models.
Open Access
Hubbard model In Square Lattices: A Mean-field Hartree-fock Approach
(2005) Yönaç, Muhammed
This thesis is mainly an effort to reproduce the well-known results that HartreeFock approximation gives for the Hubbard Model in two dimensions. As the area of application magnetic phases in the finite-size square lattices was chosen. The reason of choosing this particular area is that in the sources we went through mean-field theory was used only for examining the magnetic phases for rectangular density of state not for the actual density of states of a square lattice. We used the mean-field Hartree-Fock approximation and obtained the phase diagrams for the paramagnetic, ferromagnetic, charge density wave (CDW) and spin density wave (SDW) phases. The antiferromagnetic phase was found to be a special kind of the SDW phase. The hamiltonians used for the ferromagnetic and paramagnetic cases were identical. However because of the non-diagonal correlations present in the system the CDW and SDW hamiltonian was different.
Open Access
Mean-field renormalization group theory of the t-J model
(2002) Şen, Cengiz
The quantum nature of the high temperature superconductivity models makes analytical approaches to these systems almost impossible to implement. In this thesis, a computational study of the one and two dimensional t − J models that combines mean-field treatments with renormalization group techniques will be presented. This allows one to deal with the noncommutations of the operators at two consecutive sites of the lattices on which these models are defined. The resulting phase diagram for the 1D t − J model reveals an antiferromagnetic ground state, which may, upon doping with increasing temperature, show striped formation that is seen in the high-Tc cuprates. The qualitative features of the phase diagram of the 2D case is also presented, which reveals a phase transition between the disordered and antiferomagnetically ordered phases.
Open Access
Rotating two leg Bose Hubbard ladder
(2009) Keleş, Ahmet
We analyze two leg Bose Hubbard model under uniform magnetic field within various methods. Before studying the model, we discuss the background on rotating Bose Einstein condensates, Bose Hubbard model and superfluid Mott insulator transition. We give a general overview of Density Matrix Renormalization Group (DMRG) theory and show some of the applications. Introducing two leg system Hamiltonian, we solve the single particle problem and find distinct structures above and belove a critical magnetic field αc = 0.21π. Above this value of the field, it is found that system has travelling wave solutions. To see the effects of interactions, we use Gross Pitaevskii approximation. Spectrum of the system below the critical field and the change of αc with the interaction strength are obtained for small interactions, i.e Un/t < 1. To specify Mott insulator boundary, variational mean field theory and strong coupling perturbation (SCP) theories are used. The travelling wave solutions found in single particle spectrum above αc is found to be persistent in mean field description. On the other hand, comparing with the strong coupling expansion results, it has been found that the mean field theory gives poor results, because of the one dimensional structure of the system. The change of the tip of the lobe where BKT transition takes place is found as a function of magnetic field by SCP. Finally we use DMRG to obtain the exact shape of the phase diagram. It is found that second order strong coupling perturbation theory gives very good results. System is found to display reenterant phase to Mott insulator. Looking at the infinite onsite interaction limit via DMRG, the critical value of the magnetic field is found to be exactly equal to the single particle solution. We have calculated the particle-hole gap for various fillings and different magnetic fields and found Fractional Quantum Hall like behaviors.
Open Access
Strongly correlated models of high-temperature superconductivity
(1999) Boyacı, Hüseyin
Son zamanlarda nanometrc büyüklüğündeki örneklerle ya|)dan tek ek'ktron ta.^ınma deneyleri, üstün iletkenlerin büyüklüklerinin alt sının ile ilgili soruyu yeniden gündeme getirmiştir, iler ne kadar, belirsiz tanecik sayısına dayalı standart BCS teorisi büyük örnekler için iyi sonuçlar vermekteyse de, nanometrc^ büyüklüğündeki örnekler için bu teorinin bazı temel noktalan tc^krar gözdi'iı geçirilmelidir. Bunun iıcin, sabit sayıda parçacık için bir eşleşme IIamiItoni;uı'ı, l'ernıi seviyesi etrafındaki dejenerasyon da göz önüne alınarak incelenmiştir. Dejenera.syona bağlı olarak, eşleşme etkisinin değişimi tartışılmıştır. İkinci bölümde, atomların elektron yörüngelerindeki daralmanın, eıı yakın komşular arasındaki atlama genliğine olan etkisini göz önüne alan bir ınodc'l llamiltonian üzerinde çalışılmıştır. Bu çalışma, zayıf etkileşim limitinde' analitik olarak, orta ve güçlü etkileşim limitlerinde ise sonlu bir atom geoiiK'trisinde sayısal hesaplama ile yapılmıştır. Atom sitelerindeki deşik yerleşiminin yörünge'sel daralmaya etkileri V ve W (to|)lam ve çarpım daralma terimleri) ('tkih'şim parametreleri ile verilmektedir. Çift parçacık Creen fonksiyonundaki belirsizlik noktası, kritik sıcaklık Tc’yj ve Tc üzerinde düzen parametresinin rahatlama hızı r (7 ’) ’yi belirlemektedir. Standart BCS üstımiletkenleriiıdeiı Farklı olarak, r sıfırdan farklı imajiner bir kısma sahiptir. Bu, nstiiailetkenin 7'^. lizeriıuh'ki direııciııin dalgalanmaları üzerine etki ediyor olabilir, 'lemel dnrmn ('iK'ijisi, parçacık sayısı ve manyetik akıya göre hesaplanmı.'jtır. Bir eı^leşnıe |)aramctresi olan A ,,’nin, Cooper kararsızlığı ile aynı bölgede ortaya çıktığı gösteriImiı^tiı·. llııbbard modeli {U > 0) ile yapılan hesaplar herhangi bir dolnInk değerinde hiçbir üstün iletkanlik özelliği göstermemiştir.
Open Access
Supercurrents and persistent currents in strongly correlated electron systems
(1995) Boyacı, Hüseyin
The lull understanding· ol’the solution Гог the 1-tl Hubbard model is of interest in its own right, and may provide clues to the understanding of higher dimensioned systiMiis. We have found tin? exact solution of tlie model for tw
Open Access
Variational Monte Carlo calculations for Bose-Hubbard model based on projected wavefunctions
(2014) Koç, Fulya
Bose-Hubbard model is mainly used to describe and study the interactions between neutral atomic gases trapped in an optical lattice [1] and Josephson junction arrays [2]. It is one of the toy models to understand quantum phase transitions, i.e. a phase transition exists between the Mott insulator state and the super- fluid state. Analytical solutions are limited to obtaining the ground state energy for small systems, whereas, computational studies can be done for larger system sizes. We applied the variational Monte Carlo method to the Bose-Hubbard model based on projected wavefunctions, i.e. Baeriswyl and Gutzwiller-Baeriswyl. Even though our method can be applicable to any dimension, we only consider the one dimensional case in this thesis. We expressed observables in forms of averages over configurations to which we can apply Monte Carlo sampling techniques. Our results for both Baeriswyl and Gutzwiller projections are in qualitatively good agreement with the known calculations of the phase diagram [3,4]. Furthermore, we introduced a new method, apart from other known methods [5, 6], based on the Drude weight [7–9] to calculate the superfluid fraction, which can also be extended to observe BCS superconductivity [10].