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.
Highlights
The recent discovery of the Higgs particle [1] in the particle physics [2] [3] has stimulated study of the Higgs mode in the condensed matter physics [4].One can find many experimental reports on the existence of this mode [5]-[11]
We have proposed an improved finite temperature Lanczos method using the stochastic state selection method for calculations on the lattices of up to 32 sites
In the standard finite temperature Lanczos method we generate Lanczos states, calculate the eigenvalues and calculate matrix elements that are the values of the operator between two Lanczos states
Summary
The recent discovery of the Higgs particle [1] in the particle physics [2] [3] has stimulated study of the Higgs mode in the condensed matter physics [4].One can find many experimental reports on the existence of this mode [5]-[11]. In order to confirm that the Higgs mode exists at finite temperature, we would like to study the Higgs mode in the spin-1/2 Heisenberg antiferromagnet on the square lattice using the finite temperature Lanczos method (FTLM) [34]-[39]. We propose a use of the stochastic state selection (SSS) method [40] for calculations of the matrix elements in order to weaken the limitation on the computer memory. After numerical examinations of the SSS method in the FTLM, we present results about the Higgs mode at finite temperature. The final section is for summary and discussion of this work
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