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Assume I have the Hamiltonian for a 1D topological insulators as: $$H=\sin(P_x) \sigma_x+i \Delta \sigma_{y}+[1-m-\cos(P_x)] \sigma_z $$ where $m$ is the mass term, $P_x$ is the momentum and $\Delta$ is an extra term to make the Hamiltonian non-Hermitian. If I choose the time reversal operator $T=i \sigma_y K$ and the parity operator $P=\sigma_{y}$, will the Hamiltonian be $PT$-symmetric?

If you wonder what is a non-Hermitian Hamiltonian, see this question and references therein.

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Why don't you start by hacking out $[H,PT]$. Should be easy enough, but I'm tired. – wsc May 31 '11 at 4:42
Sorry to reopen the debate, but what the hell is a non-Hermitian Hamiltonian? – DaniH Mar 11 '12 at 12:35

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