EPW Forum

Dear Developers,

I have noticed that in Quantum ESPRESSO 7.5, the output of PHONON 7.5 and EPW 6.0 has changed compared to previous versions. In particular, the printed electron–phonon matrix elements, which previously appeared as a single column |g| [meV], are now reported as four columns:

|g_sym| [meV] |g| [meV] Re(g) [meV] Im(g) [meV]

Together with Jack, I share the same confusion regarding the magnitudes of the real part and image part - (viewtopic.php?p=9618&hilit=Real+part+g#p9618). In addition to this issue, I have encountered a new and related question, which I would like to clarify.

After carefully comparing QE 7.3 and QE 7.5, I found that the |g| [meV] values printed in QE 7.3 numerically correspond to what is now labeled as |g_sym| [meV] in the latest version. Moreover, in QE 7.5, the column |g| [meV] seems to lose the degeneracy pattern that was present in earlier versions.

For example, for the degenerate TA-1 and TA-2 phonon modes, previous versions yielded exactly identical values of |g| [meV] for these two modes(0.5552548874E-02). However, in QE 7.5, only |g_sym| [meV] remains identical for TA-1 and TA-2, while the corresponding |g| [meV] values are no longer degenerate.

I would therefore like to ask:

Does this loss of degeneracy in |g| [meV] have a clear physical meaning, or is it purely a consequence of a change in definition, gauge choice, or implementation?

When plotting or analyzing electron–phonon matrix elements, which quantity should now be considered the physically meaningful one: |g_sym| [meV] or |g| [meV]?

I attach the relevant numerical data for reference:
"
QE7.3:
Electron-phonon vertex |g| (meV)

q coord.: 0.3535534 0.3535534 0.3535534
k coord.: 0.0000000 0.0000000 0.0000000
ibnd jbnd imode enk[eV] enk+q[eV] omega(q)[meV] |g|[meV]
------------------------------------------------------------------------------
1 1 1 -5.8090 -3.5323 13.8064072826 0.5552548874E-02
1 1 2 -5.8090 -3.5323 13.8064072826 0.5552548874E-02
1 1 3 -5.8090 -3.5323 45.8882468165 0.1772401947E+03
1 1 4 -5.8090 -3.5323 49.5725453448 0.1850565805E-02
1 1 5 -5.8090 -3.5323 59.2070488333 0.5479921432E-02
1 1 6 -5.8090 -3.5323 59.2070488333 0.5479921432E-02

QE7.5:
Electron-phonon vertex |g| (meV)

q coord.: 0.3535534 0.3535534 0.3535534
k coord.: 0.0000000 0.0000000 0.0000000
ibnd jbnd imode enk[eV] enk+q[eV] omega(q)[meV] |g_sym|[meV] |g|[meV] Re(g)[meV] Im(g)[meV]
------------------------------------------------------------------------------
1 1 1 -5.8090 -3.5323 13.8063967950 0.5552551664E-02 0.6267875427E-02 0.8638173494E-01 0.1767861720E+00
1 1 2 -5.8090 -3.5323 13.8063967950 0.5552551664E-02 0.4730264008E-02 0.6508876375E-01 0.1334675203E+00
1 1 3 -5.8090 -3.5323 45.8882460534 0.1772402039E+03 0.1772402039E+03 0.2746166620E+04 -0.1331438661E+04
1 1 4 -5.8090 -3.5323 49.5725508690 0.1850565793E-02 0.1850565793E-02 0.1338367468E-01 0.2758245487E-01
1 1 5 -5.8090 -3.5323 59.2070534471 0.5479920550E-02 0.7749533926E-02 -0.5135070373E-01 -0.1056585002E+00
1 1 6 -5.8090 -3.5323 59.2070534471 0.5479920550E-02 0.6150113009E-04 0.2265005319E-03 0.9043854886E-03

"

Thank you very much for your time and for your continued development of Quantum ESPRESSO and EPW

Sincerely,
Neal Li

Hi Neal,

Thanks for the question. Of these four entries, "|g_sym|" is the quantity that corresponds to the |g| printed in older verions of PH and EPW: it is obtained by symmetrizing (algebraically averaging) over degenerate electronic states and phonon modes, as you noticed.

Unless you have a specific reason to use the unsymmetrized values, |g_sym| is the recommended gauge-invariant quantity to plot and analyze, and it should match the previously reported |g|.

We added the unsymmetrized |g| and the complex values (Re(g), Im(g)) mainly for development purposes. For degenerate bands or modes, these quantities need not match between equivalent representations because the matrix lives in a non-trivial degenerate subspace, while |g_sym| retains the invariant information (effectively the trace over that subspace).

The issue you reported regarding the printed magnitudes of Re(g) and Im(g) has been fixed and will be included in the next release. Since this bug only affected the printing of the complex g elements in ph.x, you can safely ignore the unsymmetrized |g|, Re(g), and Im(g) for now and rely on |g_sym| without concern.

I hope it helps.

Best,
Kaifa