Research

Introduction

    Its not without a reason that advances of a civilization have been named after materials -- Stone-age, Bronze-age, Iron-age to today's Silicon age. Through time, we as human learn more about condensed matter properties of materials, and in turn also learn the ways to use them skillfully in our daily lives¹.
    Condensed matter physics, that is, the physics of everyday length or energy scales, now tells us that several aspects of a material crucially depend on quantum mechanics. Otherwise we can not start to explain different phenomena such as specific heat of a metal, localization in semiconductors, superconductivity, the quantum hall effect, magnetism -- to name a few.
    We have neoteric materials today that posses several interesting and exotic properties. Though many material's behavior may appear quite distinct from each other on everyday length scale; they do share some underlying similarities, some common origin at the quantum level as they give rise to such disparate behaviors. For example, in a family of systems, that includes materials as varied as superfluid helium film deposited on different substrates, superfluid atomic gas trapped in optical lattice, copper-oxide superconductors or quantum magnets -- the common physics comes from strong quantum interaction on their microscopic level.
    In systems, where basic constituents are strongly correlated, strong fluctuation over many length scales are seen. In such systems, a desired physical insight that normally comes from first principles analysis of conventional Hamiltonian, becomes difficult to gain. Numerical solutions on the other hand often comes from Hamiltonian specifically suited for simulation. Fortunately in the vicinity of a phase transition², many interesting properties for a variety of rich and real world systems can be probed by some straight modifications of the XY model. With this spirit, we do a numerical analysis of the pahse space using a very effcient algorithm known as the directed loop algorithm³ in our Monte Carlo simulation.
    Though disorder is suppose to break U(1) symmetry locally, our simulations show when we tweak the disorder zero mean upto a fairly high value, the quantum coherence over large distance still survives. We have also found that different effective low energy physics near phase transition viz. Mean-Field, 3D-XY, and the new universality class⁴ in the disorder case can also be studied and understood by a simple parameter tweaking in our setup.

1. Using the tools and lessons from the same front, we are now attempting to explain how we came about from the quark-gluon plasma soup, how neurons behave (subject of living condensed matter) in the brain, or how an event can be a tell-tale sign of a large fluctuation in the stock market.

2. A phase transition is marked by some qualitative change in physical properties of a system. In case of ice-melting, atom arrangement or ordering into crystal form breaks down, when thermal fluctuation wins. Thermal transition is normally first order and called classical transitions In case of superconductor, electrons in some material (eg Hg) below a temperature, start moving along a field without offering any resistance, due to new arrangement it assumes.

3. A. W. Sandvik, PRB 59, R14157(1999)
4. A. Priyadarshee et.al., PRL 97, 115703 (2006)

Thesis

Here is a Pdf version of my freshy minted thesis.

Abstract

Hard core bosons (HCB), hopping on a two dimensional bipartite lattice is a suitable model to study the superfluid to normal (superconductor to insulator) transition. In this work, we present large-scale numerical simulation of the HCB Hamiltonian under the influence of three types of background potentials: Staggered, Uniform and Random. We employ a recently developed directed loop quantum Monte Carlo algorithm in the discrete time path-integral (world-line) formalism; also suitably adapt some finite size scaling relations to study thermodynamics of the system across classical as well as quantum phase transitions. These topics are of current research interests in theory as well as experiments; thus attempts are made to compare our work with physical results that are known. As we explore the temperature-chemical potential (T − µ) phase space, the classical phase transitions appears to be of the Kosterlitz-Thouless type for different background potentials. On the other hand, at T = 0, we find evidence that quantum fluctuations lead the three systems to three different buniversality classes. The system ground state changes from a superfluid phase at small potentials to one with normal phase at large potentials. We calculate the phase transition exponents ν, β, and z . As expected, the uniform chemical potential leads the system to the mean field universality with dynamical exponent z = 2; while the staggered case, that maintains particle-hole symmetry, belongs to the XY universality with z = 1. On the other hand, the disorder driven transition that also maintains particle-hole symmetry on an average is clearly different from both. In fact, we find a dynamical exponent z ∼ 1.4, which is more consistent with some recent experimental results on superfluid films and superconducting films. This is in contrast to z = 2 that is generally believed to be true for the dirty boson models. Using our extensive analysis, we also measure other exponents for this new universality class as ν ∼ 1 and β ∼ 0.6.

Acknowledgement

Pdf version is linked here.

Lyx Thesis Template: I have extensively used Lyx (a Latex wyswtg) for writing the thesis. It was not always trivial to get the format right for the university standard. I tried to find template of a thesis-directory online and personally, I would have appreciated it very much. There is one tar-zip files here for anyone who wants to start writing your chapters. Please feel free to contact me in case some clarification is need.

Good Luck!

Publications

Conferences:

"Quantum Phase Transitions of Hard-Core Bosons Due to Background Potentials," A. Priyadarshee, S. Chandrasekharan, JW. Lee, and H.U. Baranger, American Physical Society March Meeting, Baltimore, March 13-17, 2006.

"Quantum Critical Behavior of Disordered Hard-Core Bosons," A. Priyadarshee, JW. Lee, S. Chandrasekharan, and H.U. Baranger, American Physical Society March Meeting, Los Angeles, March 21-25, 2005.

"Phase Diagram of Disordered Quantum XY Model," Anand Priyadarshee, Shailesh Chandrasekharan, Ji-Woo Lee, and Harold U. Baranger, American Physical Society March Meeting, Montreal, March 22-26, 2004.

"Superconductivity with Disorder: a Quantum Monte Carlo Study," J. Osborn, S. Chandrasekharan, A. Priyadarshee, and H.U. Baranger, American Physical Society March Meeting, Austin, March 3-7, 2003.

Journals:

"Quantum Phase Transitions of Hard-Core Bosons in Background Potentials," Anand Priyadarshee, Shailesh Chandrasekharan, Ji-Woo Lee, and Harold U. Baranger, Physical Review Letter 97, 115703, 2006.

"Phase Diagram of Spin-1/2 XY Model under Transverse Magnetic Field," Anand Priyadarshee, Shailesh Chandrasekharan, and Harold U. Baranger, In preperation for PRB.