Dear Matthias,

 by \Sigma_{i,j}, I mean \sum_{i,j},

for the exact result, we know the model is integrable, so by fermionization and finally diagonalizing the Hamiltonian we will end up to an Hamiltonian with sum over independent modes,
H=\sum_{k} E(k) (2 a_{k}^{dagger} a_{k}-1)  

for the T=0 ground state energy, I have compared with DMRG results which are exactly same, so I am sure up to this point the form of E(k) and my summation over k space is correct.

 so finally for E(T) simply we have:
E(T)=\sum_{k} E(k)(2*n(k,T)-1)  in which  n(k,T)=1/(exp(E(k)/T)+1)   ::with Boltzmann constant=1


Regards,
Zhian.


On Sun, Jul 24, 2011 at 12:00 PM, <comp-phys-alps-users-request@lists.phys.ethz.ch> wrote:
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Today's Topics:

  1. Quantum Monte Carlo for Ising in transverse field
     (zhian asadzadeh)
  2. Re: Quantum Monte Carlo for Ising in transverse field
     (Matthias Troyer)


----------------------------------------------------------------------

Message: 1
Date: Sat, 23 Jul 2011 16:29:39 +0200
From: zhian asadzadeh <zhian.asadzadeh@gmail.com>
Subject: [ALPS-users] Quantum Monte Carlo for Ising in transverse
       field
To: comp-phys-alps-users@lists.phys.ethz.ch
Message-ID:
       <CAEw6G6sPavSO0RMreyy701xo+LN4M4LGrBzOLJkonEKs9S=Wkw@mail.gmail.com>
Content-Type: text/plain; charset="iso-8859-1"

 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
>
> To subscribe or unsubscribe via the World Wide Web, visit
>        https://lists.phys.ethz.ch/listinfo/comp-phys-alps-users
> or, via email, send a message with subject or body 'help' to
>        comp-phys-alps-users-request@lists.phys.ethz.ch
>
> You can reach the person managing the list at
>        comp-phys-alps-users-owner@lists.phys.ethz.ch
>
> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of Comp-phys-alps-users digest..."
>
>
> Today's Topics:
>
>   1. restarting Lanczos iteration (jessica.alfonsi@unipd.it)
>   2. Quantum Monte Carlo for Ising in transvers field (zhian asadzadeh)
>   3. Re: Quantum Monte Carlo for Ising in transvers field
>      (Matthias Troyer)
>   4. 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.
> -------------- next part --------------
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> URL: <
> https://lists.phys.ethz.ch/pipermail/comp-phys-alps-users/attachments/20110722/3a51e71a/attachment-0001.htm
> >
>
> ------------------------------
>
> Message: 3
> Date: Fri, 22 Jul 2011 09:09:43 -0600
> From: Matthias Troyer <troyer@phys.ethz.ch>
> Subject: Re: [ALPS-users] Quantum Monte Carlo for Ising in transvers
>        field
> To: comp-phys-alps-users@lists.phys.ethz.ch
> Message-ID: <A3A66CE8-DA3B-4160-8952-42868D25C5AC@phys.ethz.ch>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Dear Zhian,
>
> What is the problem with the looper code? It should be perfect for a
> nonfrustrated Ising model in a transverse field. What is your model?
>
> Best regards
>
> Matthias
>
>
>
> On 22 Jul 2011, at 05:03, zhian asadzadeh wrote:
>
> > 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.
>
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL: <
> https://lists.phys.ethz.ch/pipermail/comp-phys-alps-users/attachments/20110722/fa041e0c/attachment-0001.htm
> >
>
> ------------------------------
>
> Message: 4
> Date: Fri, 22 Jul 2011 09:35:31 -0600
> From: Matthias Troyer <troyer@phys.ethz.ch>
> Subject: Re: [ALPS-users] restarting Lanczos iteration
> To: jessica.alfonsi@unipd.it, comp-phys-alps-users@lists.phys.ethz.ch
> Message-ID: <F50F2D14-EF41-4772-A2F8-8C0533C8A54F@phys.ethz.ch>
> Content-Type: text/plain; charset=us-ascii
>
> Hi Jessica,
>
> Resuming iterations is already possible now. The Lanczos algorithm allows
> you to continue iterating with a new iteration object. In your case I would
> not iterate until convergence but only for a fixed number of steps.
>
> Indeed, all you have to store are the member variables of the Lanczos (and
> underlying T-matrix) object, as well as the two last vectors of the
> iteration (not the starting vector!). It is not hard to add that.
>
> Matthias
>
>
>
> On 22 Jul 2011, at 04:22, jessica.alfonsi@unipd.it wrote:
>
> > 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
> >
> >
> >
>
>
>
> End of Comp-phys-alps-users Digest, Vol 64, Issue 6
> ***************************************************
>
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------------------------------

Message: 2
Date: Sat, 23 Jul 2011 08:37:23 -0600
From: Matthias Troyer <troyer@phys.ethz.ch>
Subject: Re: [ALPS-users] Quantum Monte Carlo for Ising in transverse
       field
To: comp-phys-alps-users@lists.phys.ethz.ch
Message-ID: <2CC37437-71F7-436F-91E6-4AFBFE1DEFFA@phys.ethz.ch>
Content-Type: text/plain; charset="iso-8859-1"

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
>
> To subscribe or unsubscribe via the World Wide Web, visit
>        https://lists.phys.ethz.ch/listinfo/comp-phys-alps-users
> or, via email, send a message with subject or body 'help' to
>        comp-phys-alps-users-request@lists.phys.ethz.ch
>
> You can reach the person managing the list at
>        comp-phys-alps-users-owner@lists.phys.ethz.ch
>
> When replying, please edit your Subject line so it is more specific
> than "Re: Contents of Comp-phys-alps-users digest..."
>
>
> Today's Topics:
>
>   1. restarting Lanczos iteration (jessica.alfonsi@unipd.it)
>   2. Quantum Monte Carlo for Ising in transvers field (zhian asadzadeh)
>   3. Re: Quantum Monte Carlo for Ising in transvers field
>      (Matthias Troyer)
>   4. 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.
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL: <https://lists.phys.ethz.ch/pipermail/comp-phys-alps-users/attachments/20110722/3a51e71a/attachment-0001.htm>
>
> ------------------------------
>
> Message: 3
> Date: Fri, 22 Jul 2011 09:09:43 -0600
> From: Matthias Troyer <troyer@phys.ethz.ch>
> Subject: Re: [ALPS-users] Quantum Monte Carlo for Ising in transvers
>        field
> To: comp-phys-alps-users@lists.phys.ethz.ch
> Message-ID: <A3A66CE8-DA3B-4160-8952-42868D25C5AC@phys.ethz.ch>
> Content-Type: text/plain; charset="iso-8859-1"
>
> Dear Zhian,
>
> What is the problem with the looper code? It should be perfect for a nonfrustrated Ising model in a transverse field. What is your model?
>
> Best regards
>
> Matthias
>
>
>
> On 22 Jul 2011, at 05:03, zhian asadzadeh wrote:
>
> > 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.
>
> -------------- next part --------------
> An HTML attachment was scrubbed...
> URL: <https://lists.phys.ethz.ch/pipermail/comp-phys-alps-users/attachments/20110722/fa041e0c/attachment-0001.htm>
>
> ------------------------------
>
> Message: 4
> Date: Fri, 22 Jul 2011 09:35:31 -0600
> From: Matthias Troyer <troyer@phys.ethz.ch>
> Subject: Re: [ALPS-users] restarting Lanczos iteration
> To: jessica.alfonsi@unipd.it, comp-phys-alps-users@lists.phys.ethz.ch
> Message-ID: <F50F2D14-EF41-4772-A2F8-8C0533C8A54F@phys.ethz.ch>
> Content-Type: text/plain; charset=us-ascii
>
> Hi Jessica,
>
> Resuming iterations is already possible now. The Lanczos algorithm allows you to continue iterating with a new iteration object. In your case I would not iterate until convergence but only for a fixed number of steps.
>
> Indeed, all you have to store are the member variables of the Lanczos (and underlying T-matrix) object, as well as the two last vectors of the iteration (not the starting vector!). It is not hard to add that.
>
> Matthias
>
>
>
> On 22 Jul 2011, at 04:22, jessica.alfonsi@unipd.it wrote:
>
> > 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
> >
> >
> >
>
>
>
> End of Comp-phys-alps-users Digest, Vol 64, Issue 6
> ***************************************************
>

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