Dear Matthias,
my intention is doing finite T QMC for 2D ising in transverse field with the following Hamiltonian: H=-J \Sigma_{i,j} S_{i}^{z} S_{j}^{z}-h \Sigma_{i} S_{i}^{x} but for checking the accuracy of the numeric I did some checks for 1D case which we can have an exact results, probably I am expecting too much accuracy, for example:
L=100, T=0.32859 Exact:: E(T)=-105.29789708270407, Mx(T)=0.27030367598168420 looper:: E(T)=-105.61795 (0.00554), M(T)=0.4093185 (0.000138) ( I think it is in z direction) with SWEEPS:6000000, THERMALIZATION=2000000
I have checked also for other sizes and very large SWEEPS. I don't expect to get exact result but I need much more accuracy in the calculated energy.
and also other question: that magnetization which looper calculates is in the z direction? can I also measure M_{x} just with declaring it in parm file?
Thanks a lot, Zhian.
On Sat, Jul 23, 2011 at 12:00 PM, < comp-phys-alps-users-request@lists.phys.ethz.ch> wrote:
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Today's Topics:
- restarting Lanczos iteration (jessica.alfonsi@unipd.it)
- Quantum Monte Carlo for Ising in transvers field (zhian asadzadeh)
- Re: Quantum Monte Carlo for Ising in transvers field (Matthias Troyer)
- Re: restarting Lanczos iteration (Matthias Troyer)
Message: 1 Date: Fri, 22 Jul 2011 12:22:47 +0200 From: jessica.alfonsi@unipd.it Subject: [ALPS-users] restarting Lanczos iteration To: comp-phys-alps-users@lists.phys.ethz.ch Message-ID: 5b0ae17b0813c63a97720e0fbc6cc1c6.squirrel@webmail.unipd.it Content-Type: text/plain;charset=utf-8
Hi all, I'd like to modify the Lanczos *.cpp examples in IETL example folder to be able to restart the iteration from any interruption point during the Lanczos iteration. I suppose first one has to dump some information, for instance the cofficients of T-matrix and the starting vector, however the more difficult part would be the resuming of the iteration. Can somebody give me some hints on how accomplishing this task? Thanks in advance...
Best regards,
Jessica Alfonsi
Message: 2 Date: Fri, 22 Jul 2011 13:03:23 +0200 From: zhian asadzadeh zhian.asadzadeh@gmail.com Subject: [ALPS-users] Quantum Monte Carlo for Ising in transvers field To: comp-phys-alps-users@lists.phys.ethz.ch Message-ID: <CAEw6G6vLtP2G8kviZ97cxgZy9Dv1x_MqyUzFWs9ejnM8WvwnmA@mail.gmail.com
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Dear All,
I am trying to do QMC at finite temperature for calculating the magnetization of *Ising model in transverse field*, but I realized just looper code is working for this model, ( the others codes doesn't work with off diagonal matrix elements) but the result are not so good. I am interested to modify dirloop_sse for this model, is it possible? I appreciate your help, Thanks, zhian.
Dear Zhian,
The energy should actually be exact within error bars. How did you get the exact result that you compare to? and what was Sigma in that example?
Matthias
On Jul 23, 2011, at 8:29 AM, zhian asadzadeh wrote:
Dear Matthias,
my intention is doing finite T QMC for 2D ising in transverse field with the following Hamiltonian: H=-J \Sigma_{i,j} S_{i}^{z} S_{j}^{z}-h \Sigma_{i} S_{i}^{x} but for checking the accuracy of the numeric I did some checks for 1D case which we can have an exact results, probably I am expecting too much accuracy, for example:
L=100, T=0.32859 Exact:: E(T)=-105.29789708270407, Mx(T)=0.27030367598168420 looper:: E(T)=-105.61795 (0.00554), M(T)=0.4093185 (0.000138) ( I think it is in z direction) with SWEEPS:6000000, THERMALIZATION=2000000 I have checked also for other sizes and very large SWEEPS. I don't expect to get exact result but I need much more accuracy in the calculated energy. and also other question: that magnetization which looper calculates is in the z direction? can I also measure M_{x} just with declaring it in parm file? Thanks a lot, Zhian.On Sat, Jul 23, 2011 at 12:00 PM, comp-phys-alps-users-request@lists.phys.ethz.ch wrote: Send Comp-phys-alps-users mailing list submissions to comp-phys-alps-users@lists.phys.ethz.ch
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Today's Topics:
- restarting Lanczos iteration (jessica.alfonsi@unipd.it)
- Quantum Monte Carlo for Ising in transvers field (zhian asadzadeh)
- Re: Quantum Monte Carlo for Ising in transvers field (Matthias Troyer)
- Re: restarting Lanczos iteration (Matthias Troyer)
Message: 1 Date: Fri, 22 Jul 2011 12:22:47 +0200 From: jessica.alfonsi@unipd.it Subject: [ALPS-users] restarting Lanczos iteration To: comp-phys-alps-users@lists.phys.ethz.ch Message-ID: 5b0ae17b0813c63a97720e0fbc6cc1c6.squirrel@webmail.unipd.it Content-Type: text/plain;charset=utf-8
Hi all, I'd like to modify the Lanczos *.cpp examples in IETL example folder to be able to restart the iteration from any interruption point during the Lanczos iteration. I suppose first one has to dump some information, for instance the cofficients of T-matrix and the starting vector, however the more difficult part would be the resuming of the iteration. Can somebody give me some hints on how accomplishing this task? Thanks in advance...
Best regards,
Jessica Alfonsi
Message: 2 Date: Fri, 22 Jul 2011 13:03:23 +0200 From: zhian asadzadeh zhian.asadzadeh@gmail.com Subject: [ALPS-users] Quantum Monte Carlo for Ising in transvers field To: comp-phys-alps-users@lists.phys.ethz.ch Message-ID: CAEw6G6vLtP2G8kviZ97cxgZy9Dv1x_MqyUzFWs9ejnM8WvwnmA@mail.gmail.com Content-Type: text/plain; charset="iso-8859-1"
Dear All,
I am trying to do QMC at finite temperature for calculating the magnetization of *Ising model in transverse field*, but I realized just looper code is working for this model, ( the others codes doesn't work with off diagonal matrix elements) but the result are not so good. I am interested to modify dirloop_sse for this model, is it possible? I appreciate your help, Thanks, zhian.
Dear Zhian,
On 2011/07/23, at 23:29, zhian asadzadeh wrote:
L=100, T=0.32859 Exact:: E(T)=-105.29789708270407, Mx(T)=0.27030367598168420 looper:: E(T)=-105.61795 (0.00554), M(T)=0.4093185 (0.000138) ( I think it is in z direction) with SWEEPS:6000000, THERMALIZATION=2000000
The magnetization ("Magnetization" or "Magnetization Density") measured in the looper code is in z direction, and it should be exactly zero in the present case due to the symmetry. From which observable did you take the above figures?
and also other question: that magnetization which looper calculates is in the z direction?
Yes.
can I also measure M_{x} just with declaring it in parm file?
Please try the following patch to applications/qmc/looper/path_integral.C, which adds an observable named "Number of Site Operators". Since the average number of site operators is related to the total site-term energy (in this case Zeeman term by the transverse field) by
- Gamma * <Sum(S_i^x)> = - T * <Number of Site Operators> + C
with C = Gamma/2 in the present specific case, the transverse magnetization per site is given by
<S_i^x> = T * <Number of Site Operators> / N / Gamma - 1/2
where T is the temperature, N the number of sites.
Best, Synge
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