Predefined Observables - ALF — Algorithms for Lattice Fermions

Reference for the observable types available in ALF. These are implemented in Prog/Predefined_Obs_mod.F90 and can be used in any Hamiltonian’s Alloc_obs, Obser, and ObserT subroutines.

Observable Data Types¶

ALF provides three observable containers, defined in Prog/observables_mod.F90:

Type	Created with	Purpose	Output suffix
`Obser_Vec`	`Obser_Vec_make(obs, N, filename)`	Scalar quantities (one number per bin)	`_scal`
`Obser_Latt`	`Obser_Latt_make(obs, Nt, filename, Latt, Latt_unit, Channel, dtau)`	Lattice correlation functions	`_eq` or `_tau`

Equal-Time Observables¶

Called from your Obser subroutine using the predefined measurement routines:

Routine	Output file	What it measures	Requirements
`Predefined_Obs_eq_Green_measure`	`Green_eq`	Equal-time Green’s function $\sum_\sigma \langle c^\dagger_{i\sigma} c_{j\sigma} \rangle$	Any model
`Predefined_Obs_eq_Den_measure`	`Den_eq`	Density-density correlations $\langle N_i N_j \rangle - \langle N_i \rangle \langle N_j \rangle$	Any model
`Predefined_Obs_eq_SpinSUN_measure`	`SpinZ_eq`	SU(N) spin-spin correlations	`N_FL = 1`
`Predefined_Obs_eq_SpinMz_measure`	`SpinZ_eq`, `SpinXY_eq`, `SpinT_eq`	$S^z$ - $S^z$ , $S^x + S^y$ , total spin correlations	`N_FL = 2`, `N_SUN = 1`

Time-Displaced Observables¶

Called from your ObserT subroutine:

Routine	Output file	What it measures	Channel
`Predefined_Obs_tau_Green_measure`	`Green_tau`	$\langle c_i(\tau) c^\dagger_j(0) \rangle$	`P`
`Predefined_Obs_tau_Den_measure`	`Den_tau`	Time-displaced density correlations	`PH`
`Predefined_Obs_tau_SpinSUN_measure`	`SpinZ_tau`	Time-displaced SU(N) spin correlations	`PH`
`Predefined_Obs_tau_SpinMz_measure`	`SpinZ_tau`, `SpinXY_tau`, `SpinT_tau`	Time-displaced spin correlations	`PH`

The Channel string determines the kernel used for [[Analytic Continuation]]: 'P' (particle), 'PH' (particle-hole), 'PP' (particle-particle), 'T0' (zero temperature).

Scalar Observables¶

Standard scalar observables are model-defined (not in Predefined_Obs) but typically include:

Name	Output file	What it measures
`Kin`	`Kin_scal`	Kinetic energy
`Pot`	`Pot_scal`	Potential energy
`Part`	`Part_scal`	Particle number
`Ener`	`Ener_scal`	Total energy

Entanglement Observables¶

ALF also provides predefined Rényi entropy and mutual information measurements:

Routine	What it measures
`Predefined_Obs_scal_Renyi_Ent_indep` / `_gen_fl` / `_gen_all`	Rényi entanglement entropy (flavor-independent / general-flavor / all)
`Predefined_Obs_scal_Mutual_Inf_indep` / `_gen_fl` / `_gen_all`	Mutual information

Controlling Measurements¶

Ltau (in &VAR_QMC): Set to 1 to compute time-displaced correlations, 0 to skip them. Skipping saves time when only equal-time data is needed.
LOBS_ST, LOBS_EN (in &VAR_QMC): Measurement time-slice window. Default 1, 1 measures only once per sweep. Setting LOBS_EN = Ltrot measures on every time slice (better statistics but slower).

Adding a Custom Observable¶

To define a model-specific observable in your Hamiltonian:

In Alloc_obs: allocate and configure the observable with Obser_Vec_make or Obser_Latt_make
In Obser (equal-time) or ObserT (time-displaced): compute the Wick contractions from the Green function and store the result
The analysis tools handle the rest — Jackknife error analysis, Fourier transforms, and file output are automatic