Table 5 Symmetry operation of a \(\mathscr{P}\mathscr{T}\) symmetric non-Hermitian model.

From: Critical scaling of a two-orbital topological model with extended neighboring couplings

Symmetry

Operation

Result

TRS

\(\mathscr {T}H(k)\mathscr {T}^{-1}=H(-k)\)

\(\checkmark\)

PHS

\(\mathscr {C}H(k)\mathscr {C}^{-1}=-H(-k)\)

\(\checkmark\)

CS

\(\mathscr{T}\mathscr{C}H(k)\mathscr {T}^{-1}\mathscr {C}^{-1}\ne -H(-k)\)

X

SLS

\(\mathscr {S}H(k)\mathscr {S}^{-1}=-H(k)\)

\(\checkmark\)

  1. Here TRS, PHS, CS and SLS represent time-reversal, particle-hole, chiral and sub-lattice symmetries respectively.