How to get off-diagonal Green's function matrix elements?

[chillenb]

I'm following the example here and would like to get off-diagonal elements of the Green's function. The example suggests the use of driver.expectation(). Unfortunately, I haven't been able to get it to work:

In [3]: driver.greens_function(bra, mpo, dmpo, ket, 0, eta, n_sweeps=6, bra_bond_dims=[200], ket_bond_dims=[200], thrds=[1E-6] * 10, iprint=0)
(0.9686338401489134-0.010675119181648821j)

In [4]: driver.expectation(bra, driver.get_identity_mpo(), dket)
-0.010675119181648438

In [5]: driver.expectation(bra, dmpo, ket)
-0.0106751191816489

It looks like driver.expectation() is only giving the imaginary component of the inner product because block2 is in real mode. I've tried running the example in complex mode, but it throws an error:

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
Cell In[48], line 41
     39 for iw, freq in enumerate(freqs):
     40     bra = driver.copy_mps(dket, tag="BRA") # initial guess
---> 41     gfmat[iw] = driver.greens_function(bra, mpo, dmpo, ket, freq, eta, n_sweeps=6,
     42         bra_bond_dims=[200], ket_bond_dims=[200], thrds=[1E-6] * 10, iprint=0)
     43     print("FREQ = %8.2f GF[%d,%d] = %12.6f + %12.6f i" % (freq, isite, isite, gfmat[iw].real, gfmat[iw].imag))
     45 ldos = -2 [/](http://pizza:8888/) np.pi * gfmat.imag # account for both spin

File [~/miniforge3/envs/block2prod/lib/python3.11/site-packages/pyblock2/driver/core.py:4021](http://pizza:8888/home/chillenb/miniforge3/envs/block2prod/lib/python3.11/site-packages/pyblock2/driver/core.py#line=4020), in DMRGDriver.greens_function(self, bra, mpo, rmpo, ket, omega, eta, n_sweeps, tol, bra_bond_dims, ket_bond_dims, noises, thrds, cutoff, linear_max_iter, iprint)
   4018 cps.gf_omega = omega
   4020 cps.solve(n_sweeps, ket.center == 0, tol)
-> 4021 rgf, igf = cps.targets[-1]
   4023 if self.clean_scratch:
   4024     lme.remove_partition_files()

ValueError: not enough values to unpack (expected 2, got 1)

If somebody could show me the right way to do this, I'd be very grateful!

[hczhai]

The complex mode problem is fixed in a5e1e84.

For the real mode, you may need to apply H to the imag part to get the real part MPS (using driver.multiply, for example), and then compute the expectations.

If you want to do these more efficiently (without doing multiple sweeps), you need to use the low-level Python interface like what is done in https://github.com/ZhuGroup-Yale/fcdmft/blob/main/fcdmft/solver/gfdmrg.py#L952-L1038. This highly optimized procedure is too complicated so currently it is not fully supported in the DMRGDriver high-level interface.

[chillenb]

Got it! Thank you so much for the quick response.
I will try both methods, particularly the one from fcdmft. That one has everything I need and looks like it is worth studying in detail to become more familiar with block2.