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 (&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 . Controls the Trotter error (&VAR_Model_Generic) |
| Green’s function | The central quantity: . 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: |
| 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 — defined per Hamiltonian |
| Op_V | Interaction operators — 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 for projective QMC; controls ground-state projection accuracy (&VAR_Model_Generic) |
| Thtrot | Projection parameter in units of : |
| Trotter error | Systematic error from the imaginary-time discretization, or depending on the decomposition. See [[Discretization]] |
| UDV | Matrix decomposition 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 |