Description
What's up
As I was performing some initial tests on the incoming changes on fit_overhaul branch, I noticed something is wrong with the Weiss field analytical gradient, as it is currently on master. By wrong I mean that the fitted field is qualitatively different from the original one, so seriously wrong.
Note that this happens only if I request the analytic gradient: switching to CG_METHOD=1 (minimize routine) solves everything, switching only CG_GRAD=1 but remaining with the NR routine gives the correct fit but takes forever to compute, basically freezing for several minutes (✨holy minimize, mighty va10a✨).
Also note that the hybridization gradient appears to work fine, so maybe the actual problem lies within grad_g0and_replica. If that's the case I'll hit the wall very soon, when testing the gradients for the new 'elemental' norm. We'll see...
Evidence
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I did not include the real part in the figure for it is basically correct (but not totally: even with the numerical gradient I see some unwanted weight near the origin). Don't know if this could help, but I report it.
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No restart file has been used, and here we are at one loop: we do not expect a brilliant fit, but a fair one yes.
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I attach down here the input file, so that the problem could be reproduced with the current master head (dc046d8)
Notes
I've already added a warning for the user in commit b6351ff (fit_overhaul), we might want to copy those lines on master without waiting for merge, if this is considered urgent.
inputHM2D.conf
WMIXING=0.500000000 !Mixing bath parameter
TS=2.500000000E-01 !hopping parameter
NX=1 !Number of cluster sites in x direction
NY=1 !Number of cluster sites in y direction
NKX=30 !Number of kx point for BZ integration
NKY=30 !Number of ky point for BZ integration
NLAT=1 !Number of cluster sites
NORB=1 !Number of impurity orbitals (max 5).
NBATH=7 !Number of bath sites:(normal=>Nbath per orb)(hybrid=>Nbath total)(replica=>Nbath=Nreplica)
NSPIN=1 !Number of spin degeneracy (max 2)
ULOC=1.000000000,0.d0,0.d0,0.d0,0.d0 !Values of the local interaction per orbital (max 5)
UST=0.d0 !Value of the inter-orbital interaction term
JH=0.d0 !Hunds coupling
JX=0.d0 !S-E coupling
JP=0.d0 !P-H coupling
BETA=300.000000000 !Inverse temperature, at T=0 is used as a IR cut-off.
XMU=0.d0 !Chemical potential. If HFMODE=T, xmu=0 indicates half-filling condition.
NLOOP=1 !Max number of DMFT iterations.
DMFT_ERROR=1.000000000E-05 !Error threshold for DMFT convergence
SB_FIELD=1.000000000E-01 !Value of a symmetry breaking field for magnetic solutions.
GF_FLAG=T !flag to evaluate GFs and related quantities.
DM_FLAG=F !flag to evaluate the cluster density matrix \rho_IMP = Tr_BATH(\rho))
ED_TWIN=F !flag to reduce (T) or not (F,default) the number of visited sector using twin symmetry.
ED_SECTORS=F !flag to reduce sector scan for the spectrum to specific sectors +/- ed_sectors_shift.
ED_SECTORS_SHIFT=1 !shift to ed_sectors
ED_SPARSE_H=T !flag to select storage of sparse matrix H (mem--, cpu++) if TRUE, or direct on-the-fly H*v product (mem++, cpu--) if FALSE
ED_GF_SYMMETRIC=F !flag to assume Gij = Gji
ED_PRINT_SIGMA=T !flag to print impurity Self-energies
ED_PRINT_G=T !flag to print impurity Greens function
ED_PRINT_G0=T !flag to print non-interacting impurity Greens function
ED_VERBOSE=5 !Verbosity level: 0=almost nothing --> 5:all. Really: all
NSUCCESS=1 !Number of successive iterations below threshold for convergence
LMATS=5000 !Number of Matsubara frequencies.
LREAL=5000 !Number of real-axis frequencies.
LTAU=1024 !Number of imaginary time points.
LFIT=1000 !Number of Matsubara frequencies used in the \Chi2 fit.
NREAD=0.d0 !Objective density for fixed density calculations.
NERR=1.000000000E-04 !Error threshold for fixed density calculations.
NDELTA=1.000000000E-01 !Initial step for fixed density calculations.
NCOEFF=1.000000000 !multiplier for the initial ndelta read from a file (ndelta-->ndelta*ncoeff).
WINI=-5.000000000 !Smallest real-axis frequency
WFIN=5.000000000 !Largest real-axis frequency
HFMODE=T !Flag to set the Hartree form of the interaction (n-1/2). see xmu.
EPS=1.000000000E-02 !Broadening on the real-axis.
CUTOFF=1.000000000E-09 !Spectrum cut-off, used to determine the number states to be retained.
GS_THRESHOLD=1.000000000E-09 !Energy threshold for ground state degeneracy loop up
HWBAND=2.000000000 !half-bandwidth for the bath initialization: flat in -hwband:hwband
LANC_METHOD=arpack !select the lanczos method to be used in the determination of the spectrum. ARPACK (default), LANCZOS (T=0 only), DVDSON (no MPI)
LANC_NSTATES_SECTOR=2 !Initial number of states per sector to be determined.
LANC_NSTATES_TOTAL=1 !Initial number of total states to be determined.
LANC_NSTATES_STEP=2 !Number of states added to the spectrum at each step.
LANC_NCV_FACTOR=10 !Set the size of the block used in Lanczos-Arpack by multiplying the required Neigen (Ncv=lanc_ncv_factor*Neigen+lanc_ncv_add)
LANC_NCV_ADD=0 !Adds up to the size of the block to prevent it to become too small (Ncv=lanc_ncv_factor*Neigen+lanc_ncv_add)
LANC_NITER=512 !Number of Lanczos iteration in spectrum determination.
LANC_NGFITER=200 !Number of Lanczos iteration in GF determination. Number of momenta.
LANC_TOLERANCE=1.000000000E-12 !Tolerance for the Lanczos iterations as used in Arpack and plain lanczos.
LANC_DIM_THRESHOLD=1024 !Min dimension threshold to use Lanczos determination of the spectrum rather than Lapack based exact diagonalization.
CG_METHOD=0 !Conjugate-Gradient method: 0=NR, 1=minimize.
CG_GRAD=0 !Gradient evaluation method: 0=analytic (default), 1=numeric.
CG_FTOL=1.000000000E-05 !Conjugate-Gradient tolerance.
CG_STOP=0 !Conjugate-Gradient stopping condition: 0-3, 0=C1.AND.C2, 1=C1, 2=C2 with C1=|F_n-1 -F_n|<tol*(1+F_n), C2=||x_n-1 -x_n||<tol*(1+||x_n||).
CG_NITER=500 !Max. number of Conjugate-Gradient iterations.
CG_WEIGHT=1 !Conjugate-Gradient weight form: 1=1.0, 2=1/n , 3=1/w_n.
CG_SCHEME=weiss !Conjugate-Gradient fit scheme: delta or weiss.
CG_POW=2 !Fit power for the calculation of the Chi distance function as 1/L*|G0 - G0and|**cg_pow
CG_MINIMIZE_VER=F !Flag to pick old/.false. (Krauth) or new/.true. (Lichtenstein) version of the minimize CG routine
CG_MINIMIZE_HH=1.000000000E-04 !Unknown parameter used in the CG minimize procedure.
HFILE=hamiltonian !File where to retrieve/store the bath parameters.
IMPHFILE=inputHLOC.in !File read the input local H.
LOGFILE=6 !LOG unit.