Dear ALPS users, I would like to build a non-symmetric Hamiltonian. To do so I started playing with definitions, defining
<SITEOPERATOR name="Sx" site="x"> 1/2*(Splus(x)+Sminus(x)) </SITEOPERATOR>
<SITEOPERATOR name="Syy" site="x"> 1/2*(Sminus(x)-Splus(x)) </SITEOPERATOR>
and the two Hamiltonians
<HAMILTONIAN name="H1"> <PARAMETER name="Kappa" default="0"/> <BASIS ref="spin"/> <SITETERM site="i"> Sz(i)+Kappa*Syy(i) </SITETERM> </HAMILTONIAN>
<HAMILTONIAN name="H2"> <PARAMETER name="Kappa" default="0"/> <BASIS ref="spin"/> <SITETERM site="i"> Sz(i)+Kappa*Sx(i) </SITETERM> </HAMILTONIAN>
Diagonalizing exactly these Hamiltonians for few sites of an open chain I expect different results, because there's no unitary transformation that connects Sx with Syy (there would be between Sx and Sy, but Syy=-i*Sy).
Strangely enough I get the same eigenvalues for both Hamiltonians. Do you know what is the problem here? Am I allowed at all to define antisymmetric operators in ALPS? Thank you in advance for your help.
Kindest regards.