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The purpose of this tutorial is to calculate the exponent of the isotropic spin-1/2 Heisenberg model using transfer matrix techniques.

The starting point is the wavefunction we obtained previously, using the xxx or xxx-u1 models. But now we will want to constuct a series of wavefunctions for successively larger number of states kept, for example m=10, 20, 30, 40, 50. Firstly, use mp-icorrelation to construct and plot the spin-spin correlation function for each of these wavefunctions.

The tool for constructing the transfer matrix spectrum is mp-ispectrum. We can use this to calculate both the correlation length \xi and the prefactor a in the transfer matrix expansion of the correlator. Plot the prefactor versus the correlation length for each value of m and verify that the exponent is close to the known value of 1.

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Page last modified on September 07, 2011, at 06:18 AM