Matthias, et al.,
Could you please post how to code this for one, two, three and four spins? From there I should be able to extend it out to N spins. I'll likely be working with N<=16.
Thanks,
Matt Stone
For many spins you need to code each number of spins separately, but it gets ugly pretty soon.
Matthias
On 24 Jan 2012, at 19:36, Stone, Matthew B. wrote:
Has anyone written an ALPS operator for the operator S^2 for a general number of spins in a system?
For example, I would like to list the Sztotal and S^2 values for different energy levels calculated.
The S^2 operator can be written as
S^2 = (S_1 + S_2 + S_3 +?)^2
where S_1, S_2, etc. are the vector operators.
for two spins one can write this as
S^2 = (S_1 + S_2)^2
= (S_1)^2 + (S_2)^2 + 2 S_1 \dot S_2
= s(s+1) + s(s+1) + 2S_{1z}S_{2z} + S_{1+}S_{2-} + S_{1-}S_{2+}
But I don?t see how to generalize this for a system of many spins
using the ALPS ?spin? sitebasis and basis in order to have this operator value listed in the output calculations.
Any help would be appreciated.
Thanks,
Matthew B. Stone
Neutron Scattering Science Division
Oak Ridge National Laboratory
PO box 2008 MS6475
Oak Ridge, TN 37831-6475
Phone: 1-865-202-6898
Fax: 1-865-574-6080
Hi Matt,
we don't currently support operators acting on more than two sites. This will need an extension of the library and codes, which is planned but has not been done yet. A 16-spin operator for calculating S^2 will be horrible, by tghe way - there are usually better ways of getting S^2 than measuring it directly. If you tell us what you need to measure we might be able to find out the best way of doing it.
Matthias
On 3 Feb 2012, at 20:43, Stone, Matthew B. wrote:
Matthias, et al.,
Could you please post how to code this for one, two, three and four spins? From there I should be able to extend it out to N spins. I’ll likely be working with N<=16.
Thanks,
Matt Stone
For many spins you need to code each number of spins separately, but it gets ugly pretty soon.
Matthias
On 24 Jan 2012, at 19:36, Stone, Matthew B. wrote:
Has anyone written an ALPS operator for the operator S^2 for a general number of spins in a system?
For example, I would like to list the Sztotal and S^2 values for different energy levels calculated.
The S^2 operator can be written as S^2 = (S_1 + S_2 + S_3 +?)^2 where S_1, S_2, etc. are the vector operators.
for two spins one can write this as S^2 = (S_1 + S_2)^2 = (S_1)^2 + (S_2)^2 + 2 S_1 \dot S_2 = s(s+1) + s(s+1) + 2S_{1z}S_{2z} + S_{1+}S_{2-} + S_{1-}S_{2+}
But I don?t see how to generalize this for a system of many spins using the ALPS ?spin? sitebasis and basis in order to have this operator value listed in the output calculations.
Any help would be appreciated. Thanks,
Matthew B. Stone Neutron Scattering Science Division Oak Ridge National Laboratory PO box 2008 MS6475 Oak Ridge, TN 37831-6475
Phone: 1-865-202-6898 Fax: 1-865-574-6080
Can you calculate a correlation function? S^2 is proportional to the integral of the correlation function, Sx(i)Sx(j) + Sy(i)Sy(j) + Sz(i)Sz(j). Ideally you want all pairs (i,j), but if the system is translationally invariant then fixing i=1 is enough.
Ian
On Sat, 4 Feb 2012, Matthias Troyer wrote:
Hi Matt, we don't currently support operators acting on more than two sites. This will need an extension of the library and codes, which is planned but has not been done yet. A 16-spin operator for calculating S^2 will be horrible, by tghe way - there are usually better ways of getting S^2 than measuring it directly. If you tell us what you need to measure we might be able to find out the best way of doing it.
Matthias
On 3 Feb 2012, at 20:43, Stone, Matthew B. wrote:
Matthias, et al.,Could you please post how to code this for one, two, three and four spins? From there I should be able to extend it out to N spins. I’ll likely be working with N<=16. Thanks,
Matt Stone
For many spins you need to code each number of spins separately, but it gets ugly pretty soon. Matthias
On 24 Jan 2012, at 19:36, Stone, Matthew B. wrote: Has anyone written an ALPS operator for the operator S^2 for a general number of spins in a system? For example, I would like to list the Sztotal and S^2 values for different energy levels calculated. The S^2 operator can be written as S^2 = (S_1 + S_2 + S_3 +?)^2 where S_1, S_2, etc. are the vector operators. for two spins one can write this as S^2 = (S_1 + S_2)^2 = (S_1)^2 + (S_2)^2 + 2 S_1 \dot S_2 = s(s+1) + s(s+1) + 2S_{1z}S_{2z} + S_{1+}S_{2-} + S_{1-}S_{2+} But I don?t see how to generalize this for a system of many spins using the ALPS ?spin? sitebasis and basis in order to have this operator value listed in the output calculations. Any help would be appreciated. Thanks, Matthew B. Stone Neutron Scattering Science Division Oak Ridge National Laboratory PO box 2008 MS6475 Oak Ridge, TN 37831-6475 Phone: 1-865-202-6898 Fax: 1-865-574-6080
Indeed, you are right. Ut can be written as
(\sum_i S_i)^2 = \sum_{i,j} S_i*S_j
but it can be done even easier if the model is SU(2) symmetric, then if it is an ED code one just needs to see at which value of total Sz the eigenvalue disappears from the spectrum.
Matthias
On 4 Feb 2012, at 01:35, Ian McCulloch wrote:
Can you calculate a correlation function? S^2 is proportional to the integral of the correlation function, Sx(i)Sx(j) + Sy(i)Sy(j) + Sz(i)Sz(j). Ideally you want all pairs (i,j), but if the system is translationally invariant then fixing i=1 is enough.
Ian
On Sat, 4 Feb 2012, Matthias Troyer wrote:
Hi Matt, we don't currently support operators acting on more than two sites. This will need an extension of the library and codes, which is planned but has not been done yet. A 16-spin operator for calculating S^2 will be horrible, by tghe way - there are usually better ways of getting S^2 than measuring it directly. If you tell us what you need to measure we might be able to find out the best way of doing it. Matthias On 3 Feb 2012, at 20:43, Stone, Matthew B. wrote:
Matthias, et al.,Could you please post how to code this for one, two, three and four spins? From there I should be able to extend it out to N spins. I’ll likely be working with N<=16.
Thanks, Matt Stone
For many spins you need to code each number of spins separately, but it gets ugly pretty soon.
Matthias
On 24 Jan 2012, at 19:36, Stone, Matthew B. wrote:
Has anyone written an ALPS operator for the operator S^2 for a general number of spins in a system?
For example, I would like to list the Sztotal and S^2 values for different energy levels calculated.
The S^2 operator can be written as S^2 = (S_1 + S_2 + S_3 +?)^2 where S_1, S_2, etc. are the vector operators.
for two spins one can write this as S^2 = (S_1 + S_2)^2 = (S_1)^2 + (S_2)^2 + 2 S_1 \dot S_2 = s(s+1) + s(s+1) + 2S_{1z}S_{2z} + S_{1+}S_{2-} + S_{1-}S_{2+}
But I don?t see how to generalize this for a system of many spins using the ALPS ?spin? sitebasis and basis in order to have this operator value listed in the output calculations.
Any help would be appreciated. Thanks,
Matthew B. Stone Neutron Scattering Science Division Oak Ridge National Laboratory PO box 2008 MS6475 Oak Ridge, TN 37831-6475
Phone: 1-865-202-6898 Fax: 1-865-574-6080
comp-phys-alps-users@lists.phys.ethz.ch