For a system with basis $|m\rangle$, where $m=1,2,3...$ The frustration phase factor is defined in any path $C=\{m_1m_2...m_\alpha\}$ as: $$\Phi_C=\arg[(-1)^\alpha H_{m_1m_2} H_{m_2m_3}\dotsb H_{m_\alpha m_1}]$$ The product of elements of Hamiltonian can be understood directly from the view of path integral, but what's the origin of $(-1)^\alpha$ ? And why the physical phenomenon will be so different if $\Phi_C$ is non-zero?

In the other words, I am confused that why the sign of elements of Hamiltonian is so important?


Your Answer

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

Browse other questions tagged or ask your own question.