Parity implementation in ALPS

I would like share a patch to the ALPS code which allows it to handle problems with parity-like constraints. Some typical examples of this kind of symmetry are transversal spin Hamiltonias (XY mode, Dzyaloshinskii Moriya), bosonic and fermionic pairing couplings,Jaynes-Cummings like models, etc, for which Sz and N quantum numbers are not conserved.

This kind of constraints has the form

P=\prod_{j} \exp(i \pi Q_j )

being Q_j a local parity quantum number (for instance, n_j in a bosonic/fermionic model, or Sz_i+S in a spin model). At the end of this post you will find a couple of references with more details about this symmetry in some models in which I have worked.

The utility of take implement this kind of symmetry is twofold: on the one side, it allows to reduce the size of the Hilbert space, allowing to carry out simulations that would otherwise be imposible. On the other hand, it improves the convergence to the true ground state of these systems, because the gap between the ground state  of both different parity sectors are often very small.

The current code just working now for the full and sparse diagonalization code, and I am working on an implementation to the dmrg code.


Here is an example for the parameter file:

MODEL_LIBRARY="models.xml"
MODEL="spin-parity";
LATTICE="chain lattice";
CONSERVED_QUANTUMNUMBERS="

Parity(ParityCharge)";
Jxy=-1.;
Jz=0.;
L=20;
local_S=.5;
{h=.46;}

An example for the definition of the local basis, the global basis and the hamiltonian was included in the default model.xml file.


References
Two soluble models of an antiferromagnetic chain,
E. Lieb, T. Schultz and D. Mattis,
Ann. Phys. (NY) 16 , 407 (1961).

Entanglement of finite cyclic chains at factorizing fields,
R. Rossignoli, N. Canosa, J.M.Matera,
Physical Review A 77 (2008) 052322.
Separability and entanglement in finite dimer-type chains in general transverse fields,
N. Canosa, R. Rossignoli, J.M. Matera,
Physical Review B 81 (2010) 054415.
Factorization and entanglement in general XYZ spin arrays in non-uniform transverse fields,
R. Rossignoli, N. Canosa, J.M. Matera,
Physical Review A 80 (2009) 062325.