Glossary

Glossary

Terminology used in ALF and auxiliary-field quantum Monte Carlo.

Term	Definition
AFQMC	Auxiliary-field quantum Monte Carlo — the family of methods ALF implements
Amplitude	Width of the box distribution for proposing continuous auxiliary field updates (&VAR_QMC)
Beta	Inverse temperature $\beta = 1/T$ (&VAR_Model_Generic)
Bin	A block of NSweep Monte Carlo sweeps. Observables are averaged within each bin; error bars come from bin-to-bin fluctuations (Jackknife)
Bravais lattice	A periodic lattice defined by primitive vectors and a unit cell. See Predefined Lattices
Bulk	Twist-angle implementation flag: .true. = vector potential in bulk, .false. = boundary condition (&VAR_Model_Generic)
Calc_Fl	Boolean array indicating which flavors require explicit Green function computation
Channel	String ('P', 'PH', 'PP', 'PH_C', 'P_PH', 'T0') selecting the analytic continuation kernel. See Analytic Continuation
Checkerboard	Decomposition of the hopping matrix into commuting sub-blocks for efficient exponentiation (&VAR_Model_Generic)
confin / confout	Configuration input/output files. confout_N saves the auxiliary field state for MPI rank N; renamed to confin_N for restarts
CPU_MAX	Wall-clock time limit in hours. ALF exits cleanly when this is reached (&VAR_QMC)
Dtau	Imaginary-time discretization step $\Delta\tau$. Controls the Trotter error (&VAR_Model_Generic)
Green's function	The central quantity: $G_{ij} = \langle c_i c_j^\dagger \rangle$. Updated incrementally and recomputed periodically for stability
HMC	Hybrid (Hamiltonian) Monte Carlo — a global update scheme using molecular dynamics trajectories. See HMC Parameters
Hubbard-Stratonovich	Transformation that decouples the interaction into auxiliary fields, enabling determinantal QMC
Langevin	Stochastic update scheme for continuous auxiliary fields. Cannot be combined with sequential updates
LOBS_ST / LOBS_EN	Start and end time slices for measurements (&VAR_QMC)
Ltau	Flag: 1 = compute time-displaced correlations, 0 = equal-time only (&VAR_QMC)
Ltrot	Total number of imaginary-time slices: $L_\text{trot} = \text{nint}(\beta/\Delta\tau) + 2\Theta_\text{trot}$
N_FL	Number of fermion flavors. Propagation is block-diagonal in flavor (&VAR_Model_Generic)
N_SUN	Number of colors in SU(N) symmetry. Propagation is color-independent (&VAR_Model_Generic)
NBin	Number of bins per simulation (&VAR_QMC)
Ndim	Total number of orbitals: (unit cells) × (orbitals per cell)
NSweep	Number of MC sweeps per bin (&VAR_QMC)
Nwrap	Number of time slices between QR stabilizations. See Stabilization Parameters
Op_T	Hopping (kinetic) operators $e^{T_n}$ — defined per Hamiltonian
Op_V	Interaction operators $e^{V_n(\tau)}$ — coupled to auxiliary fields
Phi_X / Phi_Y	Twist angles in units of flux quanta (&VAR_Model_Generic)
Projector	If .true., use projective (zero-temperature) QMC instead of finite-temperature (&VAR_Model_Generic)
RUNNING	Lock file created by ALF at startup, removed on clean exit. Prevents duplicate runs
Sequential	Local (single-field) update scheme — the default starting point. See Tuning and Best Practices
Sign problem	When the fermion determinant weight becomes negative (or complex), sampling efficiency degrades exponentially with system size and inverse temperature
Sweep	One pass through all auxiliary fields on all time slices
Symm	Symmetric Trotter decomposition flag. When .true., the Green function is symmetrized before measurements (&VAR_Model_Generic)
Tempering	Parallel tempering — exchanges configurations between parameter sets to improve ergodicity. See Tempering
Theta	Projection parameter $\Theta$ for projective QMC; controls ground-state projection accuracy (&VAR_Model_Generic)
Thtrot	Projection parameter in units of $\Delta\tau$: $\Theta_\text{trot} = \text{nint}(\Theta/\Delta\tau)$
Trotter error	Systematic error from the imaginary-time discretization, $O(\Delta\tau^2)$ or $O(\Delta\tau)$ depending on the decomposition. See Discretization
UDV	Matrix decomposition $M = U \cdot D \cdot V$ used for numerical stabilization of the Green's function
Warmup	Initial sweeps discarded to let the Markov chain equilibrate before measurements begin
WF_L / WF_R	Left and right trial wave functions for projective QMC