Dear Dr. Chern, Cc: comp-phys-alps-users

From: "CHERN, Chyh-Hong" chern@issp.u-tokyo.ac.jp Date: Wed, 30 May 2007 13:58:20 +0900

Dear Professor Todo,

Sorry for occupying your valuable time. We encounter some problems when using your ALPS. We will appreciate highly if you can kindly help.

I am a postdoctoral researcher in Oshikawa's group in ISSP. Recently, we are interested in the transverse Ising model in the kagome system. We are doing the Monte Carlo simulation and would like use your exact diagonalization in ALPS to calibrate. I attached the lattice.xml and parm1 that I used. We doubt on the results and would like to listen to your comments. Let me list what happened to us.

1. We obtained the exactly the same results for L=1 and L=2 on energy,

entropy, specific heat, and the free energy. When running L=3, we failed to get any results even though the memory is only used ~ 25%.

Your kagome lattice with L=3 has 27 vertices, which obviously requires too much amount of memory (8*(2^27)^2 bytes = 10^8 GB!) to store the full Hamiltonian matrix...

Instead of the fulldiag code, you can use my qmc code (qmc/looper), as long as the diagonal (Sz) interaction is ferromagnetic (i.e. no frustration).

2. If we do not add CONSERVED_QUANTNUMBERS="Sz" in the parm1, we do not have

the result on the susceptibility but do have others. If we do include that line, we have susceptibility, but lose the results on other thermodynamics quantities. As we know, Sz is not the conserved quantum number for the Ising model in the transverse magnetic field.

Calculating canonical correlations of the operators which do not commute with the Hamiltonian requires substantial CPU time (N^3?). This is the reason why the fulldiag skips measuring the susceptibility unless total Sz is a conserved quantity.

Again you can use qmc/loop, which calculates the susceptibility even in this case, instead for calibrating your simulation code.

Best regards, Synge