Regarding 1D QMC using external potential

[KN_Pathak]

Dear Sir,

I did not find any example for 1D quantum wire in the presence of external potential as done in the paper Lee and Neil Drummond, PRB 83, 2011.
We wish to start with this model and study the correlation energy.

Thanks and best regards,
Pathak

[Neil Drummond]

Dear Pathak,

Here is an input file:

Code: Select all

#-------------------#
# CASINO input file #
#-------------------#

# SYSTEM
neu               : 0              #*! Number of up electrons (Integer)
ned               : 0              #*! Number of down electrons (Integer)
periodic          : T              #*! Periodic boundary conditions (Boolean)
%block free_particles
dimensionality 1
r_s 1.0
cell_geometry
1
particle 1 det 1 : 55 orbitals free
%endblock free_particles

# RUN
runtype           : vmc            #*! Type of calculation (Text)
newrun            : T              #*! New run or continue old (Boolean) 
 
# VMC
nequil            : 8000           #*! Number of equilibration steps (Integer)
nmove             : 2000           #*! Number of moves (Integer)
nblock            : 10             #*! Number of blocks (Integer)
nwrcon            : 0              #*! Number of configs to write (Intege
dtvmc             : 1.78           #*! VMC time step (Double Precision)

# DMC
nmove_dmc_equil   : 1000           #*! Number of moves (Integer)
nblock_dmc_equil  : 10             #*! Number of blocks (Integer)
nmove_dmc_stats   : 1000           #*! Number of moves (Integer)
nblock_dmc_stats  : 20             #*! Number of blocks (Integer)
nconfig           : 256            #*! Number of configs (DMC) (Integer)
dtdmc             : 0.04           #*! DMC time step (Double Precision)
 
# OPTIMIZATION
opt_method        : emin           #*! Opt method (varmin/varmin_linjas/emin) 
opt_cycles        : 8              #*! Number of optimization cycles (Integer) 
opt_jastrow       : T              #*! Optimize Jastrow factor (Boolean) 
opt_backflow      : T              #*! Optimize backflow parameters (Boolean) 
 
# GENERAL PARAMETERS
use_jastrow       : T              #*! Use a Jastrow function (Boolean)
backflow          : T              #*! Use backflow corrections (Boolean)
complex_wf        : F              #*! Wave function real or complex (Boolean) 
interaction       : ewald          #*! Interaction type (Text) 
 
# EXPECTATION VALUES
density           : F              #*! Accumulate density (Boolean)
pair_corr_sph     : F              #*! Accumulate sph. real space PCF (Boolean)
structure_factor  : F              #*! Accumulate structure factor (Boolean)
struc_factor_sph  : F              #*! Accumulate sph. struc. factor (Boolean) 
onep_density_mat  : F              #*! Accumulate 1p density matrix (Boolean) 
twop_density_mat  : F              #*! Accumulate 2p density matrix (Boolean) 
cond_fraction     : F              #*! Accumulate cond fraction (Boolean) 
expval_cutoff     : 30.d0 hartree  #*! G vector cutoff for expval (Physical) 

and here is a correlation.data file

Code: Select all

 START JASTROW
 Title
 1D HEG
 Truncation order C
   3
 START U TERM
 Number of sets
   1
 START SET 1
 Spherical harmonic l,m
   0 0
 Expansion order N_u
   8
 Spin dep (0->uu=dd=ud; 1->uu=dd/=ud; 2->uu/=dd/=ud)
   0
 Cutoff (a.u.)     ;  Optimizable (0=NO; 1=YES)
   6.44308667660985                0
 Parameter values  ;  Optimizable (0=NO; 1=YES)
  3.119046254631353E-003           1       ! alpha_0,1
 -9.587513004977645E-005           1       ! alpha_2,1
 -2.571888715890599E-005           1       ! alpha_3,1
  5.460839594582479E-005           1       ! alpha_4,1
 -2.642987437897909E-005           1       ! alpha_5,1
  6.278649706159839E-006           1       ! alpha_6,1
 -7.500901901406922E-007           1       ! alpha_7,1
  3.611827811608129E-008           1       ! alpha_8,1
 END SET 1
 END U TERM
 START P TERM
 Spin dep (0->uu=dd=ud; 1->uu=dd/=ud; 2->uu/=dd/=ud)
   0
 Number of simulation-cell G-vectors (NB, cannot have both G & -G)
   20
 G-vector (in terms of rec latt vects) ; label
       1     0     0         1
       2     0     0         2
       3     0     0         3
       4     0     0         4
       5     0     0         5
       6     0     0         6
       7     0     0         7
       8     0     0         8
       9     0     0         9
      10     0     0        10
      11     0     0        11
      12     0     0        12
      13     0     0        13
      14     0     0        14
      15     0     0        15
      16     0     0        16
      17     0     0        17
      18     0     0        18
      19     0     0        19
      20     0     0        20
 Parameter value ; Optimizable (0=NO; 1=YES)
 -0.586921389439081                1       ! a_1,1
 -0.237977886758898                1       ! a_2,1
 -0.134687411700656                1       ! a_3,1
 -8.818073540950276E-002           1       ! a_4,1
 -6.243835615227333E-002           1       ! a_5,1
 -4.623828259197607E-002           1       ! a_6,1
 -3.508599845121017E-002           1       ! a_7,1
 -2.686653447473849E-002           1       ! a_8,1
 -2.051127442456281E-002           1       ! a_9,1
 -1.540318585054688E-002           1       ! a_10,1
 -1.139269090480447E-002           1       ! a_11,1
 -8.144548574992706E-003           1       ! a_12,1
 -5.626187708956253E-003           1       ! a_13,1
 -3.718243227575007E-003           1       ! a_14,1
 -2.333350206057186E-003           1       ! a_15,1
 -1.359231615273054E-003           1       ! a_16,1
 -7.245789991533628E-004           1       ! a_17,1
 -3.434757032439278E-004           1       ! a_18,1
 -1.383560943096786E-004           1       ! a_19,1
 -3.743688235067957E-005           1       ! a_20,1
 END P TERM
 END JASTROW
 
 START BACKFLOW
 Title
 1D HEG
 Truncation order
   3
 START ETA TERM
 Expansion order
   8
 Spin dep (0->uu=dd=ud; 1->uu=dd/=ud; 2->uu/=dd/=ud)
   0
 Cut-off radii ;      Optimizable (0=NO; 1=YES; 2=YES BUT NO SPIN-DEP)
   10.4288707261570                0       ! L_1
 Parameter ;          Optimizable (0=NO; 1=YES)
  5.927471851582147E-002           1       ! c_0,1
 -3.075881630220147E-002           1       ! c_2,1
  1.754733351466090E-002           1       ! c_3,1
 -5.530536452676682E-003           1       ! c_4,1
  1.037731448938550E-003           1       ! c_5,1
 -1.145577892650072E-004           1       ! c_6,1
  6.840147738920511E-006           1       ! c_7,1
 -1.699609095807096E-007           1       ! c_8,1
 END ETA TERM
 END BACKFLOW

for a 1D electron gas.

Best wishes,

Neil.

[KN_Pathak]

Dear Neil,

Thank you for your useful comments and code for 1D wire.

With best regards,
Pathak

[KN_Pathak]

Dear Sir,

We tried to run the input file you sent. It seems that it is for infinitely thin wire. But could not understand following points:

(i) how the input file changes for Harmonic wire model ( mentioned in Lee and Neil Drummond, PRB 83, 2011).
(ii) how different V(x_ij ) has been used in the program.
(iii) Does the Madelung energy is calculated by default in the program for any model.

Thanks and regards,
Pathak

[Neil Drummond]

Dear Pathak,

To use a harmonic wire with width parameter b, add

Code: Select all

harmwire_b <b_value>

to the free_particles input block.

I'm not sure what your other two questions mean.

Best wishes,

Neil.

[KN_Pathak]

Dear Neil,

Thank you for promt reply. It seems we could not clear other questions, which we restate again:
(ii) how different confining potential, V(x), such as trapping through an square well potential or other trapping potential can be used in the program? How does the program will modifies for trapping potential other than harmonic?
(iii) Does the Madelung energy appearing in equation (1) of the paper Lee and Neil Drummond, PRB 83, 2011 is calculated by the program itself?

With best regards,
Pathak

[Neil Drummond]

Dear Pathak,

If you want to use an effective interaction corresponding to a different confining potential then you will need to first derive it and then implement it in CASINO... If you decide to do this you will need a developer version of CASINO and I would suggest searching for the variable harmwire_b in CASINO/src and making your changes at those points.

The Madelung constant v_M is the number printed to the out file by CASINO: look for the line "Electron self-image term v_M (au) : ..."

Best wishes,

Neil.

[KN_Pathak]

Dear sir , Please inform me how to write additional program for using different external potential.
best regards
knpathak

[KN_Pathak]

Dear Sir,

We are trying to download Developer's version to add a new external potential to examine the property of 1d quantum wire. But we are unable to download. It asks for username and password. When we fill , it says Authentication fails. While registring we have not opted for Developer's version. Please advice what to do now?
Do we have to fill form again?

Thanks and regards,
Pathak