Sharif Digital Repository

Recent experimental progress in approximating closed quantum many-body systems such as ultra-cold atomic gases, has leads to surge of interest in the dynamics of closed quantum systems. In addition, driving a closed quantum system out of its equilibrium can create an appropriate conditions in order to archive novel phases of matter such as discrete Time-Crystals.In the present work, following a brief introduction, we start with basic principles of the Floquet theory. According to the matrix representation of the Floquet theory, we examine solutions of a quantum system which is driven by external periodic perturbation.We then turn to study of thermalization in closed quantum system and... 

The anisotropic Heisenberg ferrimagnet which is composed of two different kind of spins is studied. We have found the exact (factorized) ground state of a general class of ferrimagnets in the presence of a magnetic field which includes the frustrated, anisotropic and long range interactions for arbitrary dimensional space. The factorized ground state is a product of single particle kets on a bipartite lattice composed of two different spins (σ, ρ) which is characterized by two angles, a bi-angle state. The spin waves analysis around the exact ground state show two branch of excitations which is the origin of two dynamics of the model. The signature of these dynamics is addressed as a peak... 

We are interested in the relation between entanglement and quantum phase transitions. We have presented a formulation on how the entanglement of a very large the system is related to the entanglement of a small part of system. The renormalization of entanglement is an indicator of the critical behavior of the models. The framework of our approach is introduced about the Ising model. In particular, we show that derivative of entanglement developes a minimum close to the critical point. We further clarify that this minimum point approaches to the exact critical point of the system as the system becomes thermodynamic. This phenomenon is governed by an exponent that is closely related to the... 

Strongly correlated materials are kind of materials in which novel electric and magnetic properties will appear as a result of strong correlations among their electrons like “heavy fermion materials”. Kondo lattice model is a model to describe heavy fermion materials. If we are merely interested in the magnetic properties of heavy fermions we can replace the Kondo lattice Model with the simpler model called the Kondo-necklace model which consists of the interactions only among the spins of the itinerant (conduction) and localized electrons (magnetic impurities) and also the interactions between the spins of the itinerant electrons. In this thesis we investigate the properties of the one... 

In this thesis, we consider the Kondo-necklace model to investigate the quantum phase transition between the Kondo-singlet and antiferromagnetic phases. There is no exact solution for this model. We would like to study the quantum critical behaviour of this model on one, two and three dimensional spaces in addition to ladder geometry. In this respect, we looked for a proper method which can give us some information for our model on any spaces mentioned above. Therefore, we implemented the perturbation continuous unitary transformation (PCUT) for the Kondo-necklace model. By using this method, we can not only calculate the ground state energy for 1, 2, 3 dimension and n-leg ladder... 

The fascinating subject of heavy fermion physics in rare-earth and actinide systems has been a challenge for theoretical and experimental investigations for decades. Kondo Necklace model is one of the promising models in the study of strongly-correlated heavy fermion compounds, which is studied in this project.One of the methods to diagonalize a Hamiltonian properly, regardless of system size, is the continuous unitary transformation. In this approach, the Hamiltonian is considered as a function of a flow parameter. The Hamiltonian is transformed to a simpler form (diagonal or band-block diagonal) under a flow equation which is based on applying infinite numbers of infinitesimal unitary... 

Entanglement spectrum is the set of eigenvalues of reduced density matrix for a definite state. It contains more information than the entanglement entropy. This spectrum can show entanglement measure, quantum phase transition and topological order in a system. In recent years, the entanglement spectrum for several models has been studied. The entanglement spectrum shows a correspondence to the energy spectrum within some specific regions, which are related to the edge state of the system; It has been verified for the Heisenberg ladder [1] and fractional quantum Hall effect [3]. Moreover, the topological order can be seen in the entanglement spectrum. There exists an acceptable adaption... 

In this thesis, we have implemented the quantum renormalization group method to study quantum spin systems. We reviewed the recent progress to calculate the quantum information properties of these models. The recent investigations show that concurrence and entanglement are two quantities which can show quantum critical properties of the quantum systems. More specifically, the derivative of entanglement and the second derivative of ground state energy show divergent behavior at the quantum critical point. Moreover, the ground state fidelity for two different parameters close to quantum critical point shows a drop which leads to a divergent behavior in its corresponding susceptibility. We have... 

In this thesis, we study the effect of quantum fluctuations by means of a transverse magnetic field () on the ground state of frustrated antiferromagnetic Ising models on the checkerboard and square lattices with nearest neigbor couplings J1 and next-to-nearest neighbor couplings J2. At zero field, such models have exponentially large degenerate classical ground states at J2 ... J1 for the checkerboard lattice and at J2 = 0:5J1 for the square lattice. Quantum fluctuations can have a major role to lift the degeneracies toward a unique quantum ground states. We consider two types of quantum fluctuations, harmonic ones by using linear spin wave theory (LSWT) with single-spin flip excitations... 

Thermalizing quantum systems are conventionally described by statistical mechanics at equilibrium. In contrast, the interplay of disorder and interactions leads to manybody localization (MBL) which avoids thermalization in a closed quantum system.This phenomenon is the only known generic mechanism in which the “eigenstate thermalization hypothesis” is violated. In this vein, localization can protect quantum order even in finite temperature and create emergent nonergodic phases (e.g., time crystal), having no equilibrium counterpart. Yet in the conventional wisdom, the presence of disorder along with the excellent isolation from thermal bath are both necessary for the appearance of the MBL.In... 

The aim of this thesis is to review the spin systems with cluster-type inter-actions. We restrict our attention to one dimentional and exactly solvable models. By "exactly solvable models",we mean the systems which can be mapped to free fermionic systems by Jordan-Wigner transformation.In 2nd chapter we introduce one of the simplest spin systems with cluster-type intraction, the cluster Ising model, and completely derive its statis-tics[10].In chapter 3, we present a classification of topologic phases which can oc-cur in free fermionic gapped systems. This classification is based on sym-metries. Also we'll see that with the help of topological invariants, one can diagnose different... 

Except of few cases the exact, analytic forms of most applicable many-body Hamiltonian ground-states are unknown. Our knowledge in most cases come through computer-based simulations. In recent years a well-structured method has been developed to derive an analytic form for spin Hamiltonian ground-states. ?is method through whi? an analytical fully-factorized ground-state can be derived for many-spin Hamiltonians is independent of the model structure and has unique procedure for any spin Hamiltonian. ?e fully-factorized ground state whi? has been developed, minimizes the energy of the Hamiltonian by minimizing ea? pair-interaction in the Hamiltonian. However, this approval can not be...