Date of Completion


Embargo Period



Density Matrix Renormalization Group, frustrated quantum systems, many-body effects

Major Advisor

Susanne Yelin

Associate Advisor

Juha Javanainen

Associate Advisor

Robin Cote

Field of Study



Doctor of Philosophy

Open Access

Open Access


In this dissertation, we study the many-body effects of dipoles in a quasi-one-dimensional zigzag optical lattice, which we call the zigzag chain. We study this system using the Density Matrix Renormalization Group (DMRG) method, which has established itself as the most powerful numerical method to simulate one-dimensional lattices. For the implementation of DMRG, we have used the open-source package Intelligent Tensor, or simply ITensor. The first part of this research focuses on dipoles polarized in the plane of the zigzag chain by an external electric field with the condition that the dipoles can hop around and interact with their first and second neighbors and the number of dipoles is exactly a half of the number of lattice sites. With the interactions much stronger than the hopping, the system comprises of frustrated and non-frustrated regimes owing to the combination of attractive and repulsive interactions in different directions. The consequence is a complex phase diagram featuring the trivial ferromagnetic and antiferromagnetic phases as well as the non-trivial dimerized and superfluid phases. The second part of the research deals with randomly oriented dipoles in the zigzag chain such that each lattice site has exactly one dipole and each dipole interacts with its first and second neighbors but in the absence of any hopping. We study the second system classically allowing many different orientations for each dipole in a lattice site as well as quantum mechanically by allowing a few quantized degrees of freedom to each dipole. The result is a phase diagram showing ferromagnetic, antiferromagnetic and paramagnetic phases.