Predefined Observables

Predefined Observables

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:

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