In this thesis, we investigate the entanglement and magnetic properties of frustrated spin systems and correlated electronic properties of conjugated carbon systems.
In chapter 1, we present different approaches to solve the time-independent, nonrelativistic Schr¨odinger equation for a many-body system. We start with the full
non-relativistic Hamiltonian of a multi nuclear system to describe the Born - Oppenheimer approximation which allows the study of electronic Hamiltonian which
treats nuclear positions parametrically. We then also describe ab initio techniques
such as the Hartree-Fock Method and density functional theories. We then introduce
model Hamiltonians for strongly correlated systems such as the Hubbard,
Pariser-Parr-Pople and Heisenberg models, and show how they result from the noninteracting
one-band tight-binding model.
In chapter 2, we discuss various numerical techniques like the exact diagonalization
methods and density matrix renormalization group (DMRG) method. We also discuss quantum entanglement and the success of DMRG which can be attributed to the area law of entanglement entropy.
In chapter 3, we study here different regions in phase diagrams of the spin-1/2,
spin-1 and spin-3/2 one-dimensional antiferromagnetic Heisenberg systems with
nearest-neighbor (J1) and next-nearest-neighbor (J2) interactions and dimerization
(d ). Frustration arises for specific relative signs of the interactions J1 and J2. In particular, we analyze the behavior of the bipartite entanglement entropy and fidelity
at the gapless to gapped phase transitions and across the lines separating
different phases in the J2−d plane. All the calculations in this work are based on
exact diagonalizations of finite systems.
In chapter 4, we study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (JF
1 ) and antiferromagnetic (JA
1 ) nearest-neighbor interactions and a
ferromagnetic next-nearest-neighbor interaction (JF
2 ). In this model frustration is
present due to non-zero JF
2 . The model with site spin s behaves like a Haldane spin chain with site spin 2s in the limit of vanishing JF 2 and large JF
1 /JA
1 . We show that the exact ground state of the model can be found along a line in the parameter space. For fixed JF
1 , the phase diagram in the space of JA
1 −JF
2 is determined
using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and
zero temperature magnetization, are studied to understand the complete phase diagram.
An interesting and potentially important feature of this model is that it can
exhibit a macroscopic magnetization jump in the presence of a magnetic field; we
study this using an effective Hamiltonian.
In chapter 5, we study correlated electronic properties of zigzag and armchair fused
naphthalenes and polyperylene systems in the presence of long-range electronelectron
interactions. We find that the ground state of zigzag fused naphthalene
system is a higher spin state, while the ground state of armchair fused naphthalene
is a singlet. The spin gap of polyperylene is unusually small and the ground
state is a singlet. Our calculations of optical gap and two-photon gap suggest that
polyperylene should exhibit fluorescence. From the charge gap calculation, we
predict that in zigzag fused naphthalene and polyperylene systems, excitons are
weakly binding. Peierls type of distortion is negligible in zigzag fused naphthalene
and polyperylene systems, however, in armchair fused naphthalene system, interior
bonds have tendency to distort in low-lying excited states.
In chapter 6, we study the ground state spin of the Heisenberg spin-1/2 nearestneighboring
antiferromagnetic exchange models of systems with fused odd member rings. In particular, we compute the ground state spin of fused three and five membered rings as well as fused five membered rings. In the thermodynamic limit, the ground state of the fused three and five membered system is a higher spin state, while fused five membered system shows a singlet ground state, for all system sizes.
| Identifer | oai:union.ndltd.org:IISc/oai:etd.ncsi.iisc.ernet.in:2005/3030 |
| Date | January 2014 |
| Creators | Goli, V M L Durga Prasad |
| Contributors | Ramasesha, S |
| Source Sets | India Institute of Science |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Relation | G26784 |
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