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## MpTridiagThe Matrix Product Toolkit version HEAD-0.7.3.0 (subversion tree rev 280M) Compiled on Oct 9 2006 at 23:51:17 usage: mp-tridiag [options] Allowed options: --help show this help message -H [ --Hamiltonian ] arg operator to use for the Hamiltonian (right Lanczos vector attribute "Hamiltonian") -w [ --wavefunction ] arg input wavefunction to generate the effective basis (zero or more) -r [ --right ] arg right-hand Lanczos vector |R> (defaults to the first --wavefunction) -l [ --left ] arg Left-hand Lanczos vector <L| (defaults to --right) -G [ --GroundstateEnergy ] arg groundstate energy of the Hamiltonian (wavefunction attribute "GroundstateEnergy", not needed if --no-preamble) -m [ --max-states ] arg Maximum number of states to keep in the effective basis [default 100000] -t [ --min-trunc ] arg Minimum desired truncation error per site of the effective basis [default 1.77635683940025e-15] -b [ --bond ] arg Generate the basis at this bond, valid is 1 .. L-1 [default L/2] -i [ --max-iter ] arg maximum number of iterations -s [ --threshold ] arg stopping criteria for the orthogonality of the Krylov vector <kn|k0> [default 0.01] -e [ --epsilon ] arg stopping criteria for the magnitude of Beta [default 1e-05] --no-preamble only show the tridiagonal coefficients, don't show the groundstate energy -v [ --verbose ] arg (=0) increase verbosity The required options are It is possible to restrict the final basis size either by number of states The output is a single line showing the groundstate energy (this is not needed for the tridiagonal coefficients themselves, but is required by mp-trispectral to get the energy offset correct), followed by a table of 5 columns:
By default, the tridiagonalization is performed using the effective basis at the central bond of the chain. This can be changed using the There are three possible stopping criteria: if the coefficient {$\beta$} ever reaches zero, then an invariant subspace has been found and the tridiagonalization is exact within the effective Hilbert space. It also indicates loss of orthogonality of the basis, so a stopping criteria is used in case {$\beta$} gets too small. This is controlled by the To calculate a Green's function with any accuracy you must specify at least one more more ## See Also |

Page last modified on October 16, 2006, at 08:07 AM