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MpDmrg

NOTE: This documentation describes the old SVN version of mp-dmrg. It needs to be updated for the git version of mp-dmrg.

The mp-dmrg program is intended for quick prototype calculations. For larger calculations, MpDmrgInitResume might be a better choice as it supports checkpoint-restart, automatic convergence criteria etc.

Matrix Product Toolkit version HEAD-0.7.4.0 (subversion tree rev 709:712)
Compiled on Jul 16 2007 at 21:23:57
usage: mp-dmrg [options]
Allowed options:
  --help                    show this help message
  -H [ --Hamiltonian ] arg  operator to use for the Hamiltonian (wavefunction attribute "Hamiltonian")
  -w [ --wavefunction ] arg wavefunction to apply DMRG (required)
  -2 [ --two-site ]         modify 2 neighboring sites at once (traditional DMRG)
  -i [ --iter ] arg         Number of Lanczos iterations per step [default 4]
  -m [ --max-states ] arg   Maximum number of states to keep [default 100000]
  --min-states arg          Minimum number of states to keep [default 50]
  -r [ --trunc ] arg        Truncation error cutoff [default 0]
  -d [ --eigen-cutoff ] arg Cutoff threshold for density matrix eigenvalues (alternative to truncation error) [default -1]
  -f [ --mix-factor ] arg   Mixing coefficient for the density matrix [default 0.01]
  -s [ --sweeps ] arg       Number of half-sweeps to perform [default 2]
  --orthogonal arg          force the wavefunction to be orthogonal to this state

The only required option is --wavefunction. This wavefunction is used as both input and output, so you should make a copy of it if you want to keep the original. Also, if you interrupt the calculation the wavefunction file will be corrupted, so it is always a good idea to have a backup of the wavefunction anyway.

In addition, you need to specify the Hamiltonian, either via the --Hamiltonian option, or you can set the Hamiltonian attribute of the initial wavefunction (see MpAttr).

The number of states to keep is specified by a bound on the truncation error per sweep, supplied by the min-trunc parameter. For this to be meaningful, the maximum number of states to keep (max-states) needs to be set to some value that is very large; the only purpose of the max-states in this scenario is to prevent the calculation from going haywire in the case that the truncation error is unreasonably small.

The program will try to keep at least min-states states, and never more than max-states, thus you can fix the number of states simply by ignoring the min-trunc parameter (ie. using the default value of zero), and using the max-states option.

The mix-factor option uses the density matrix mixing scheme suggested by White (cond-mat/0508709), where only a single site is optimized at a time and instead a mixing term is added to the density matrix. For most cases, the default value seems to work fine. The traditional DMRG style of optimizing two sites at a time can be reproduced by the two-site option, and setting the mix-factor to zero. There isn't much reason to do this, however the truncation error might sometimes be more stable with the two-site variation.

Examples

To evolve the wavefunction initial.psi towards the groundstate of the Hamiltonian operator supplied by the lattice file spinchain.lattice, with at most 100 states kept, and 4 half-sweeps:

To do the same, but now with a bound on the truncation error per half-sweep of 1.0E-6:

Assuming groundstate.psi is an approximation of the groundstate, we can evolve a state towards the first excited state: