3
$\begingroup$

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.

$\endgroup$
2
  • 3
    $\begingroup$ Why don't you start by hacking out $[H,PT]$. Should be easy enough, but I'm tired. $\endgroup$
    – wsc
    May 31, 2011 at 4:42
  • $\begingroup$ Sorry to reopen the debate, but what the hell is a non-Hermitian Hamiltonian? $\endgroup$
    – Dani
    Mar 11, 2012 at 12:35

1 Answer 1

0
$\begingroup$

It is the Hamiltonian of the 1D PT-symmetric SSH model in real gauge. In that case, the operators P and T can be denoted as $[1,0;0,-1]$ and $[1,0;0,-1]K$, respectively. Then $PT=K$ is commutated with the real Bloch Hamiltonian, i.e., $(PT)H(k)(PT)^{-1}=H(k)$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.