The exact energy per site in the thermodynamic limit is 4/pi \simeq 1.27323954474. Is there any particular reason you use periodic boundary conditions? For a critical model, with open or infinite boundary conditions, there is a power-law relationship between system size and number of states, (correlation length \propto states^\kappa, for some exponent kappa that, for the IRF model, equals 2).

So for 100 sites, of order 10 states sould be sufficient (or, to be safe, pick m=20!). With periodic boundary conditions, you need approximately the square of this number, so order 100 - 400. Much better to use open boundary conditions and a larger system size, or, preferably, make use of translational invariance and solve for an infinite system with iTEBD or iDMRG.

Even for a finite system, with 100 states kept and open boundaries, you could quite accurately do a system of length around 100^2 = 10,000 for this model. Or something in between, say 40 states and 1000 sites.

The connection between the exponent kappa and the central charge of the critical system is described in http://lanl.arxiv.org/abs/0712.1976 (and references therein)

Regards, Ian

On Thu, 26 May 2011, zhian asadzadeh wrote:

Hi shuai cui,

your model is correct, and the result for the second run is fair but not so near to exact result, I suggest you increase the number of maxstates (=300), and also your lattice size, you will get a better result, just for check point I give you the exact energy (per site) at h=1 (which is critical h in this model) J=-1, h=1 L=100, E0=-1.2732919 ( This is exact energy not DMRG result)

Zhian.

On Thu, May 26, 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:

    1. tebd will not be built (Cristian Degli Esposti Boschi)
    2. Re: tebd will not be built (Matthias Troyer)
    3.  transverse Ising model with DMRG (shuai cui)


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

  Message: 1
  Date: Wed, 25 May 2011 13:16:52 +0200
  From: Cristian Degli Esposti Boschi <degliesposti@bo.imm.cnr.it>
  Subject: [ALPS-users] tebd will not be built
  To: comp-phys-alps-users@lists.phys.ethz.ch
  Message-ID: <4DDCE524.6070605@bo.imm.cnr.it>
  Content-Type: text/plain; charset=ISO-8859-1; format=flowed

  Dear users,

  I'm installing ALPS 2 on a Debian 6 (squeeze) machine. After issuing
  cmake -DCMAKE_INSTALL_PREFIX... I get the following (I extracted the
  last relevant part):


  ...
  Falling back to CMake provied LAPACK/BLAS detection.
  -- A library with BLAS API found.
  -- A library with BLAS API found.
  -- A library with LAPACK API found.
  -- SQLite Library: not found
  -- LPSolve Library: not found
  -- Could NOT find SZIP  (missing:  SZIP_LIBRARIES SZIP_INCLUDE_DIRS)
  -- HDF5 version found is 1.8.4-patch1 in /usr/include
  -- Python interpreter /usr/bin/python
  -- Python interpreter ok : version 2.6.6
  -- PYTHON_INCLUDE_DIRS =  /usr/include/python2.6
  -- PYTHON_NUMPY_INCLUDE_DIR =
  /usr/lib/pymodules/python2.6/numpy/core/include
  -- PYTHON_SITE_PKG = /usr/lib/python2.6/dist-packages
  -- PYTHON_LIBRARY = /usr/lib/python2.6/config/libpython2.6.so
  -- PYTHON_EXTRA_LIBS =-lssl -lcrypto  -lssl -lcrypto      -L/usr/lib -lz
  -lpthread -ldl  -lutil
  -- PYTHON_LINK_FOR_SHARED =  -Xlinker -export-dynamic -Wl,-O1
  -Wl,-Bsymbolic-functions
  -- Numpy include in /usr/lib/pymodules/python2.6/numpy/core/include
  -- ALPS XML dir is
  /usr/local/ALPS/alps-2.0.1-r5565-src-with-boost/alps/lib/xml
  -- Adding Boost dir: /usr/local/ALPS/alps-2.0.1-r5565-src-with-boost/boost
  -- HDF5 version found is 1.8.4-patch1 in /usr/include
  -- HDF5 version found is 1.8.4-patch1 in /usr/include
  -- tebd will not be built
  -- Configuring done
  -- Generating done
  -- Build files have been written to:
  /usr/local/ALPS/alps-2.0.1-r5565-src-with-boost


  Now, my problem is that "tebd will not be built" and I wonder why.
  Is it related to the problem of "Falling back to CMake provied
  LAPACK/BLAS detection" or maybe to what reported in the installation
  guidelines that "The tebd code requires a fortran compiler and that HDF5
  be built with the --enable-fortran configure option."
  In the latter case how can I fix the things in Debian-provided HDF5?


  Thanks for your time,

  Cristian Degli Esposti Boschi
  CNR-IMM, Sezione di Bologna,
  via Gobetti, 101, 40129, Bologna, Italia
  tel. ++39 051 6399152, fax ++39 051 6399216
  degliesposti -AT- bo.imm.cnr.it


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

  Message: 2
  Date: Wed, 25 May 2011 06:51:39 -1000
  From: Matthias Troyer <troyer@phys.ethz.ch>
  Subject: Re: [ALPS-users] tebd will not be built
  To: comp-phys-alps-users@lists.phys.ethz.ch
  Message-ID: <291CA21C-BF47-48EC-881E-27DD21C9F49D@phys.ethz.ch>
  Content-Type: text/plain; charset=us-ascii

  Did you specify a Fortran-90 compiler?

  On May 25, 2011, at 1:16 AM, Cristian Degli Esposti Boschi wrote:

  > Dear users,
  >
  > I'm installing ALPS 2 on a Debian 6 (squeeze) machine. After issuing
  > cmake -DCMAKE_INSTALL_PREFIX... I get the following (I extracted the last relevant part):
  >
  >
  > ...
  > Falling back to CMake provied LAPACK/BLAS detection.
  > -- A library with BLAS API found.
  > -- A library with BLAS API found.
  > -- A library with LAPACK API found.
  > -- SQLite Library: not found
  > -- LPSolve Library: not found
  > -- Could NOT find SZIP  (missing:  SZIP_LIBRARIES SZIP_INCLUDE_DIRS)
  > -- HDF5 version found is 1.8.4-patch1 in /usr/include
  > -- Python interpreter /usr/bin/python
  > -- Python interpreter ok : version 2.6.6
  > -- PYTHON_INCLUDE_DIRS =  /usr/include/python2.6
  > -- PYTHON_NUMPY_INCLUDE_DIR = /usr/lib/pymodules/python2.6/numpy/core/include
  > -- PYTHON_SITE_PKG = /usr/lib/python2.6/dist-packages
  > -- PYTHON_LIBRARY = /usr/lib/python2.6/config/libpython2.6.so
  > -- PYTHON_EXTRA_LIBS =-lssl -lcrypto  -lssl -lcrypto      -L/usr/lib -lz -lpthread -ldl  -lutil
  > -- PYTHON_LINK_FOR_SHARED =  -Xlinker -export-dynamic -Wl,-O1 -Wl,-Bsymbolic-functions
  > -- Numpy include in /usr/lib/pymodules/python2.6/numpy/core/include
  > -- ALPS XML dir is /usr/local/ALPS/alps-2.0.1-r5565-src-with-boost/alps/lib/xml
  > -- Adding Boost dir: /usr/local/ALPS/alps-2.0.1-r5565-src-with-boost/boost
  > -- HDF5 version found is 1.8.4-patch1 in /usr/include
  > -- HDF5 version found is 1.8.4-patch1 in /usr/include
  > -- tebd will not be built
  > -- Configuring done
  > -- Generating done
  > -- Build files have been written to: /usr/local/ALPS/alps-2.0.1-r5565-src-with-boost
  >
  >
  > Now, my problem is that "tebd will not be built" and I wonder why.
  > Is it related to the problem of "Falling back to CMake provied LAPACK/BLAS detection" or maybe to what reported in the installation
  > guidelines that "The tebd code requires a fortran compiler and that HDF5 be built with the --enable-fortran configure option."
  > In the latter case how can I fix the things in Debian-provided HDF5?
  >
  >
  > Thanks for your time,
  >
  > Cristian Degli Esposti Boschi
  > CNR-IMM, Sezione di Bologna,
  > via Gobetti, 101, 40129, Bologna, Italia
  > tel. ++39 051 6399152, fax ++39 051 6399216
  > degliesposti -AT- bo.imm.cnr.it
  >



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

  Message: 3
  Date: Thu, 26 May 2011 11:28:42 +0800 (CST)
  From: shuai cui <cuishuai_757@yahoo.com.cn>
  Subject: [ALPS-users]  transverse Ising model with DMRG
  To: comp-phys-alps-users@lists.phys.ethz.ch
  Message-ID: <606168.86645.qm@web15904.mail.cnb.yahoo.com>
  Content-Type: text/plain; charset="iso-8859-1"

  Dear Prof. Troyer
  ?
  I am trying to calculate the ground state energy of the transverse Ising-Model ( -J*4*Sx(i)*Sx(j)-h*2*Sz(i) ) on a period 1d-chain-lattice with the DMRG. Though I had use both
  the default model and a modified model, the results are not satisfactory. So I ask for why the DMRG doesn't give a good result in transverse field Ising model as in other 1D
  model.
  the modified model is:
  <MODELS>
  <SITEBASIS name="spin">
  ? <PARAMETER name="local_spin" default="local_S"/>
  ? <PARAMETER name="local_S" default="1/2"/>
  ? <QUANTUMNUMBER name="S" min="local_spin" max="local_spin"/>
  ? <QUANTUMNUMBER name="Sz" min="-S" max="S"/>
  ? <OPERATOR name="Splus" matrixelement="sqrt(S*(S+1)-Sz*(Sz+1))">
  ??? <CHANGE quantumnumber="Sz" change="1"/>
  ? </OPERATOR>
  ? <OPERATOR name="Sminus" matrixelement="sqrt(S*(S+1)-Sz*(Sz-1))">
  ??? <CHANGE quantumnumber="Sz" change="-1"/>
  ? </OPERATOR>
  ? <OPERATOR name="Sz" matrixelement="Sz"/>
  </SITEBASIS>
  <BASIS name="spin">
  ? <SITEBASIS ref="spin">
  ??? <PARAMETER name="local_spin" value="local_S#"/>
  ??? <PARAMETER name="local_S#" value="local_S"/>
  ??? <PARAMETER name="local_S" value="1/2"/>
  ? </SITEBASIS>
  ? <CONSTRAINT quantumnumber="Sz" value="Sz_total"/>
  </BASIS>
  <SITEOPERATOR name="Sx" site="x">
  ? 1/2*(Splus(x)+Sminus(x))
  </SITEOPERATOR>
  <HAMILTONIAN name="trans_Ising">
  ?? <PARAMETER name="J" default="0"/>
  ?? <PARAMETER name="h" default="0"/>
  ?? <BASIS ref="spin"/>
  ?? <SITETERM site="i">
  ???? h*2*Sz(i)
  ?? </SITETERM>
  ?? <BONDTERM source="i" target="j">
  ???? J*4*Sx(i)*Sx(j)
  ?? </BONDTERM>
  </HAMILTONIAN>
  </MODELS>
  ?
  Separately, the parameter files are:
  LATTICE="chain lattice"
  MODEL= "spin"
  Jz=-4
  Gamma=2
  local_S=1/2
  SWEEPS=4
  NUMBER_EIGENVALUES=1
  L=8
  {MAXSTATES=20}?
  ?
  LATTICE="chain lattice"
  MODEL= "trans_Ising"
  J=-1
  h=-1
  local_S=1/2
  SWEEPS=4
  NUMBER_EIGENVALUES=1
  L=8
  {MAXSTATES=20}?

  Correspondingly, the results are:
  FINAL SWEEP - LAST ITERATION
  NUMBER OF STATES: 8 2 2 8 256
  E0 = -282.636028178
  ITER = 3 ENTROPY = 1.78546641552
  -------------------------------------------
  Truncation error = -4.98732999343e-17
  -------------------------------------------
  Checking if it is finished: not yet, next check in 60 seconds ( 0% done).
  Halted Simulation 1
  This task took 46 seconds.
  Checkpointing Simulation 1
  Finished with everything.
  FINAL SWEEP - LAST ITERATION
  NUMBER OF STATES: 8 2 2 8 256
  E0 = -9.11126807853
  ITER = 3 ENTROPY = 0.931162271124
  -------------------------------------------
  Truncation error = 2.22044604925e-16
  -------------------------------------------
  Checking if it is finished: not yet, next check in 60 seconds ( 0% done).
  Halted Simulation 1
  This task took 13 seconds.
  Checkpointing Simulation 1
  Finished with everything.
  ?
  but the correct data should be? -10.251661790966022
  which calculated by sparsediag.
  ?
  I don't understand why DMRG give a low precision result, even I had set h=0. Remarkably, the default model gives a wrong data, which far away from the correct one.
  I had exercise the XX model, which gives a very well data. I wonder if the transverse field Ising model has some special feature, or the DMRG parameter I used is not right?
  ?
  best regards,
  Shuai Cui
  ?