Please check the attachment, can you please let me know what is the origin of the term 'h.c' in eqn. (4) of the attached paper?
"h.c." stands for "Hermitian conjugated". If it were omitted, the Hamiltonian would not be a Hermitian operator. Inherent to this is that if there is an amplitude for hopping from (basis) state A to B then there is also an amplitude for the reverse process, due to the very same interaction. writing "+ h.c." shortens the notation.
Term "h.c." stands for "Hermitian conjugation". Its presence in (any) Hamiltonian Is necessary to ensure that the resulting Hamiltonian is Hermitian, because only Hermitian Hamiltonian has real (not complex or imaginary) eigenvalues (energy spectrum). This is a general property for ANY Hamiltonian in quantum mechanics (not just the one given by Eq.(4) from the attached paper), For example, "h.c." term for the product of operators (c_m)^{+}c_n is simply (c_n)^{+}c_m. Therefore, the combination H=(c_m)^{+}c_n +h.c.=(c_m)^{+}c_n +(c_n)^{+}c_m is Hermitian, leading to real values of the energy spectrum E, which is defined via the appropriate wave functions (states) |psi> as follows: E=.
"h.c." stands for "Hermitian conjugated". If it were omitted, the Hamiltonian would not be a Hermitian operator. Inherent to this is that if there is an amplitude for hopping from (basis) state A to B then there is also an amplitude for the reverse process, due to the very same interaction. writing "+ h.c." shortens the notation.
@ Sergei and Kai
Sir,
Thank you so much for the explanation and thanks to Researchgate even more so.
Thank you once again.
Sincerely,
Dinesh
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