Citation
Mukhopadhyay, Ranjan (1998) Quantum phase transitions in disordered Bose systems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd02022007104407
Abstract
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We study the nature of various quantum phase transitions corresponding to the onset of superfluidity, at zero temperature, of bosons in a quenched medium. Particlehole symmetry plays an essential role in determining the universality class of the transitions. To obtain a model with an exact particlehole symmetry it is necessary to use the Josephson junction array Hamiltonian, which may include disorder in the Josephson couplings between phases at different sates. The functional integral formulation of this problem in d spatial dimensions yields a (d + 1)dimensional classical XYmodel with extended disorder, constant along the extra imaginary time dimension  the socalled random rod problem. Particlehole symmetry may then be broken by adding nonzero chemical potentials or site energies, which may also be site dependent and random. We may then distinguish three cases: (i) exact particlehole symmetry, in which the site energies all vanish, (ii) statistical particlehole symmetry in which the site energy distribution is symmetric about zero and hence vanishes on average, and (iii) complete absence of particlehole symmetry in which the distribution is generic. We explore in each case the nature of the excitations in the nonsuperfluid Pose glass phase. We find, for example, that the compressibility, which has the interpretation of a temporal spin stiffness or superfluid density, is positive in cases (ii) and (iii), but that it vanishes with an essential singularity as full particlehole symmetry is restored. We then focus on the critical point and discuss the validity of various scaling arguments. In particular, we argue that the dynamical exponent z could be different from d, and the arguments leading to their equality are incorrect. We then discuss the relevance of a type (ii) particlehole symmetry breaking perturbation to the random rod critical behavior, identifying a nontrivial crossover exponent. This exponent cannot be calculated exactly but is argued to be positive and the symmetry breaking perturbation therefore relevant. We argue next that a perturbation of type (iii) is irrelevant to the resulting type (ii) critical behavior: the statistical symmetry is restored on large scales close to the critical point, and case (ii) therefore describes the dirty boson fixed point. Using various duality transformations we verify all of these ideas in one dimension. To study higher dimensions we attempt, with partial success, to generalize the DorogovtsevCardyBoyonovsky double epsilon expansion technique to this problem. We find that when the dimension of time [...] is sufficiently small the symmetry breaking perturbation of type (ii) is irrelevant, but that for sufficiently large [...] this is a relevant perturbation and a new stable commensurate fixed point appears. We speculate that this new fixed point becomes the dirty boson fixed point when [...] = 1. We also show that for [...], there exists a particlehole asymmetric fixed point of type (iii), but we provide evidence that it merges with the commensurate fixed point for some finite [...]. This tends to confirm symmetry restoration at the physical [...] = 1.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Physics, Mathematics and Astronomy 
Major Option:  Physics 
Thesis Availability:  Restricted to Caltech community only 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  12 June 1997 
Record Number:  CaltechETD:etd02022007104407 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd02022007104407 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  463 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  15 Feb 2007 
Last Modified:  26 Dec 2012 02:29 
Thesis Files
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