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.