Dear ALPS users and developers
I want to re-produce the result of a 12x2 spin ladder with four-site interaction. The four-site interaction is between two nearest-neighboring rungs. Please see: [ Phys. Rev. B 74, 155119 (2006), http://prb.aps.org/abstract/PRB/v74/i15/e155119 ]
However, it seems that ALPS 2.0 do not support 4-site terms. Thus I define every rung as a single site, then the ladder becomes a one-dimensional chain (local degree of freedom is 4), and the four-site interaction becomes a two-site interaction.
In original ladder, the SITEBASIS is just {sz} = {-1/2, 1/2}. In this basis operators such as Sminus have very compact expressions thus they can be simply define as: <OPERATOR name="Sminus" matrixelement="sqrt(S*(S+1)-Sz*(Sz-1))">
However, in the new model, a possible choice of SITEBASIS is {J,Jz}={00, 1-1, 10, 11}. In this new basis, operators do not have very compact expressions, however, the elements of the operator can be easily obtained through unitary transformation. The problem is, I can figure out all the elements of an operator in basis{J, Jz}, but I do not know how to define the operator in "models.xml".
In other words, suppose an operator X in basis {J, Jz} is explicitly found to be [ 1, 0, 0, 0 0, 2, 1, 0 0, 1, 3, 0 0, 0, 0, 4] then in ALPS 2.0, is it possible to define X by simply writing down every elements Xij in "models.xml" ?
Any suggestion would be appreciated.
sunzhaoyu
Dear Sunzhaoyu,
This is not implemented yet. For now you will have to decompose it into more elementary operators.
Matthias
On Mar 18, 2011, at 12:38 AM, 孙照宇 wrote:
Dear ALPS users and developers
I want to re-produce the result of a 12x2 spin ladder with four-site interaction. The four-site interaction is between two nearest-neighboring rungs. Please see: [ Phys. Rev. B 74, 155119 (2006), http://prb.aps.org/abstract/PRB/v74/i15/e155119 ]
However, it seems that ALPS 2.0 do not support 4-site terms. Thus I define every rung as a single site, then the ladder becomes a one-dimensional chain (local degree of freedom is 4), and the four-site interaction becomes a two-site interaction.
In original ladder, the SITEBASIS is just {sz} = {-1/2, 1/2}. In this basis operators such as Sminus have very compact expressions thus they can be simply define as:
<OPERATOR name="Sminus" matrixelement="sqrt(S*(S+1)-Sz*(Sz-1))">
However, in the new model, a possible choice of SITEBASIS is {J,Jz}={00, 1-1, 10, 11}. In this new basis, operators do not have very compact expressions, however, the elements of the operator can be easily obtained through unitary transformation. The problem is, I can figure out all the elements of an operator in basis{J, Jz}, but I do not know how to define the operator in "models.xml".
In other words, suppose an operator X in basis {J, Jz} is explicitly found to be [ 1, 0, 0, 0 0, 2, 1, 0 0, 1, 3, 0 0, 0, 0, 4] then in ALPS 2.0, is it possible to define X by simply writing down every elements Xij in "models.xml" ?
Any suggestion would be appreciated.
sunzhaoyu
comp-phys-alps-users@lists.phys.ethz.ch