TITLE:
Finite Temperature Lanczos Method with the Stochastic State Selection and Its Application to Study of the Higgs Mode in the Antiferromagnet at Finite Temperature
AUTHORS:
Tomo Munehisa
KEYWORDS:
Higgs Mode, Heisenberg Antiferromagnet, Dynamical Correlation, Finite Temperature Lanczos Method, Stochastic State Selection Method
JOURNAL NAME:
World Journal of Condensed Matter Physics,
Vol.7 No.1,
February
9,
2017
ABSTRACT: We propose an improved finite temperature Lanczos
method using the stochastic state selection method. In the finite temperature
Lanczos method, we generate Lanczos states and calculate the eigenvalues. In
addition we have to calculate matrix elements that are the values of an
operator between two Lanczos states. In the calculations of the matrix elements
we have to keep the set of Lanczos states on the computer memory. Therefore the
memory limits the system size in the calculations. Here we propose an
application of the stochastic state selection method in order to weaken this
limitation. This method is to select some parts of basis states stochastically
and to abandon other basis state. Only by the selected basis states we
calculate the inner product. After making the statistical average, we can
obtain the correct value of the inner product. By the stochastic state
selection method we can reduce the number of the basis states for calculations.
As a result we can relax the limitation on the computer memory. In order to
study the Higgs mode at finite temperature, we calculate the dynamical
correlations of the two spin operators in the spin-1/2 Heisenberg antiferromagnet
on the square lattice using the improved finite temperature Lanczos method. Our
results on the lattices of up to 32 sites show that the Higgs mode exists at
low temperature and it disappears gradually when the temperature becomes large.
At high temperature we do not find this mode in the dynamical correlations.