1
$\begingroup$

If we have a (2+1)-dimensional electronic gapped system with a unique ground state and it has a nonzero integer quantum Hall conductance, then the system (or its ground state) must break the time-reversal symmetry explicitly.

My question is how about its converse and to what extent the converse holds. Since the Chern-Simons is the only relevant characterizing response theory at an infinite-length scale in (2+1) dimensions, my guess is that a vanishing quantum Hall conductance sufficiently implies that the unique ground state is time-reversal symmetric at the low-energy (or long-range) limit. Is my guess correct or how to prove it? Can we further generalize to general ground-state degeneracies?

$\endgroup$
2
$\begingroup$

There are other long-wavelength responses that break time-reversal symmetry other than Hall conductance, for example thermal Hall conductance. I believe Hall conductance and thermal Hall conductance are the only ones for a system with only $U(1)$ symmetry that has no fractionalized excitations (e.g. anyons), but if you have anyonic excitations, then their braiding statistics can also violate time-reversal symmetry, for example.

$\endgroup$
  • $\begingroup$ Thanks for the reminder and it seems we need to take into consideration of gravitational response. $\endgroup$ – Smart Yao Feb 23 at 14:46

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.