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Answer by Everett You for Confusion about duality transformation in 1+1D...
This is a very good question. The same operator algebra does not imply that $H(J,h)$ and $H(h,J)$ have the same spectrum. As has been mentioned in Dominic's answer, even the ground state degeneracy is...
View ArticleAnswer by Dominic Else for Confusion about duality transformation in 1+1D...
1) In general, an algebra can have many representations. In this case, however, if you assume that there is a unique joint +1 eigenstate of the $\sigma_i$'s, that determines the representation...
View ArticleConfusion about duality transformation in 1+1D Ising model in a transverse field
In 1+1D Ising model with a transverse field defined by the Hamiltonian\begin{equation}H(J,h)=-J\sum_i\sigma^z_i\sigma_{i+1}^z-h\sum_i\sigma_i^x\end{equation}There is a duality transformation which...
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