Quantum Monte Carlo for Ising in transverse field - Comp-phys-alps-users

26 Jul 2011

      Dear Matthias and Synge
I understood why there is that discrepancy for small clusters,
it is true that we can write the thermal energy as :
E(T)=\sum_{k} E(k)(2*n(k,T)-1)
but this expression is true for thermodynamic limit, because we know the
model has an even and odd parity sectors which they must be diagonalized
separately, for T=0 the ground state is in even sector, so the sum over K
points are for anti periodic boundary conditions, but for finite temperature
we cant arrive to that expression, unless with this approximation that
H(odd)=H(even) which is true in the thermodynamic limit, because the
dispersion will be continuous and there is no much difference between odd
and even space K points.
for small sizes I checked the looper and exact diagonalization are same but
with large difference with exact, but for large lattices the looper
converges to exact result which is thermodynamic result:
for L=200, h=0.3
looper:: -0.9238482(6.21e-05) with  SWEEPS=4000000
exact::   -0.92385063
@Synge
I took it from Magnetization density, I think also Magnetization in z
direction is not zero,
ok, thanks I will try that.
Thanks,
Zhian
On Mon, Jul 25, 2011 at 12:00 PM, <
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Today's Topics:

Quantum Monte Carlo for Ising in transverse field
(zhian asadzadeh)
Re: Quantum Monte Carlo for Ising in transverse field
(Matthias Troyer)
Re: Quantum Monte Carlo for Ising in transverse field (Synge Todo)
Custom measurements (Alexander Herzog)

Message: 1
Date: Sun, 24 Jul 2011 12:48:03 +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:
       <CAEw6G6sEs2aaE8oY5S+dFob35edARq12xKp9=4h4BUdrZZ1i7g@mail.gmail.com
...
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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, <
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Today's Topics:

Quantum Monte Carlo for Ising in transverse field
(zhian asadzadeh)
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
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       <CAEw6G6sPavSO0RMreyy701xo+LN4M4LGrBzOLJkonEKs9S=
Wkw@mail.gmail.com
...
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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:
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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
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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.