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**Simulations / Simulating spectrum with Hamiltonian involving one spin 1 particle in 2 spin sys**

« **on:**December 16, 2012, 04:21:45 PM »

I attempt to simulate the spectrum from my Hamiltonian:

H0t[\[Beta]_] := 2 \[Pi] 10^3 Sqrt[6]/ 4 (3/5 \[Omega]d*(3 Cos[\[Beta]]^2 - 1)*opT[2, {2, 0}]* opT [1, {2, 0}] + cf ((3 Cos[\[Beta]]^2 - 1)*opT [1, {2, 0}] + s/Sqrt[6] (-(3/2) Sin[\[Beta]]^2*opT[1, {2, 2}] - 3/2 Sin[\[Beta]]^2*opT[1, {2, -2}]))) ,

with SetSpinSystem[{{1, 1}, {2, 1}}].

However, it took an exceptionally long time to simulate. So I tried simulating only the part of the Hamiltonian which only involves a single spin 1 particle:

H0t[\[Beta]_] := 2 \[Pi] 10^3 Sqrt[6]/ 4 cf*((3 Cos[\[Beta]]^2 - 1)*opT [1, {2, 0}] + s/Sqrt[6] *(3*Sin[\[Beta]]^2*opT[1, {2, 2}] + 3*Sin[\[Beta]]^2*opT[1, {2, -2}]))

and the spectrum showed that there is an additional line in the middle of the spectrum.

I then changed the spin system to SetSpinSystem[{{1, 1}}] and re-simulated this partial Hamiltonian and the middle line disappears. So I was wondering where does the middle line come from?

H0t[\[Beta]_] := 2 \[Pi] 10^3 Sqrt[6]/ 4 (3/5 \[Omega]d*(3 Cos[\[Beta]]^2 - 1)*opT[2, {2, 0}]* opT [1, {2, 0}] + cf ((3 Cos[\[Beta]]^2 - 1)*opT [1, {2, 0}] + s/Sqrt[6] (-(3/2) Sin[\[Beta]]^2*opT[1, {2, 2}] - 3/2 Sin[\[Beta]]^2*opT[1, {2, -2}]))) ,

with SetSpinSystem[{{1, 1}, {2, 1}}].

However, it took an exceptionally long time to simulate. So I tried simulating only the part of the Hamiltonian which only involves a single spin 1 particle:

H0t[\[Beta]_] := 2 \[Pi] 10^3 Sqrt[6]/ 4 cf*((3 Cos[\[Beta]]^2 - 1)*opT [1, {2, 0}] + s/Sqrt[6] *(3*Sin[\[Beta]]^2*opT[1, {2, 2}] + 3*Sin[\[Beta]]^2*opT[1, {2, -2}]))

and the spectrum showed that there is an additional line in the middle of the spectrum.

I then changed the spin system to SetSpinSystem[{{1, 1}}] and re-simulated this partial Hamiltonian and the middle line disappears. So I was wondering where does the middle line come from?