Theoretical Study of Interacting Electrons in One Dimension Ground States and Experimental Signatures a Dissertation

ii Dedicated to my parents Subhra and Utpal Datta iii ACKNOWLEDGMENTS I would like to begin by acknowledging my thesis advisor Prof. Erica W. Carlson for offering me an opportunity to pursue a doctoral degree under her guidance and for suggesting the thesis problem. Her constant mentoring and support, throughout my doctoral work, has helped me to organize my thought process, sharpen my research skills, and improve my scientific writing ability. Thanks to Prof. Carlson for having faith in my abilities. The careful mentoring of Prof. Gabriele F. Giuliani, during my initial years as a graduate student provided me the chance to build a strong foundation in condensed matter physics for later years. My special thanks goes to Prof. Sherwin Love who has taught me materials ranging from quantum mechanics to quantum field theory and whose insights in physics have strengthened my knowledge of the subject. Thanks to Prof. Jiangping Hu and to Prof. Yuli Lyanda Geller for the numerous fruitful discussions and meetings I have had with them on condensed matter physics. Dr. office mate Zoltan Gecse for many useful and illuminating discussions that I have had with them about physics in general. I also wish to thank Dr. Robert Grantham for his great friendship over the years. Finally, I would like to acknowledge the love and patience of my wife, Joya, without whose support this journey would not have been possible.