Citation
Makivic, Miloje S. (1991) Monte Carlo studies of two dimensional quantum spin systems. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd07202007094134
Abstract
Spin1/2 nearest neighbor Heisenberg antiferromagnet and XY model on a square lattice are studied via large scale quantum Monte Carlo simulations using a fast and efficient multispin coding algorithm on the Caltech/JPL MarkIIIfp parallel supercomputer, based on the SuzukiTrotter transformation. We performed simulations with very good statistics on lattices as large as 128x128 spins, in the temperature range from 0.1 to 2.5 in units of the effective exchange coupling J. We calculated energy, specific heat, magnetic susceptibilities and also spin correlation functions from which we deduce the correlation lengths.
For the Heisenberg model, at temperatures higher than J the results are in excellent agreement with hightemperature series expansion. At low temperatures the long wavelength behavior is essentially classical. Our data show that the correlation length and staggered susceptibility are quantitatively well described by the renormalized classical picture at the 2loop level of approximation. From the divergence of the correlation length, we deduce the value of the quantum renormalized spin stiffness, [rho][subscript s]/J = 0.199(2). We give evidence that the correlation function is of the OrnsteinZernicke type. By comparing the largest measured correlation lengths with neutron scattering experiments on La2CuO4, we deduce the value of effective exchange coupling J = 1450±30 K. By measuring the imaginary timedependent correlation functions, we show that the dynamics of the model can be well understood within a Bose liquidtype picture. The spin waves are rather sharp throughout most of the Brillouin zone and the damping is weakly dependent on the wave vector.
In the case of the XY model, convincing numerical evidence is obtained on square lattices as large as 96x96 that the spin1/2 XY model undergoes a KosterlitzThouless (KT) phase transition at kTc/J = 0.350(4). The correlation length and inplane susceptibility diverge at Tc precisely according to the form predicted by Kosterlitz and Thouless for the classical XY model. The specific heat increases very rapidly on heating near Tc and exhibits a peak around kT/J = 0.45. We also measure the spin stiffness and the correlation function exponent below the transition temperature. Within the statistical accuracy of the measurements, the results are well described by the square root singularity (with a nonuniversal amplitude) below Tc, and they have the universal values in agreement with KT theory at Tc.
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:  2 August 1990 
Record Number:  CaltechETD:etd07202007094134 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd07202007094134 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  2952 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  20 Jul 2007 
Last Modified:  26 Dec 2012 02:55 
Thesis Files
PDF (Makivic_ms_1991.pdf)
 Final Version
Restricted to Caltech community only See Usage Policy. 5Mb 
Repository Staff Only: item control page