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ED2 Output Files

This page documents the concrete output files produced by QS³-ED2, using examples/chain as a canonical reference.

All physics quantities are written in plain-text format and are intended to be stable across versions for reproducibility.

Example: examples/chain

A typical ground-state calculation with

  • cal_lm = 1
  • cal_cf = 1
  • eigenvectors disabled

produces:

examples/chain/
 ├ input.dat
 ├ eigenvalues.dat
 ├ local_mag.dat
 ├ two_body_cf_xyz.dat
 ├ two_body_cf_z+-.dat
 └ output.dat   (stdout redirect)

These correspond to:

  • energy eigenvalues
  • local magnetization
  • two-body spin correlations (Cartesian basis)
  • two-body spin correlations (\(z,+,-\) basis)
  • human-readable diagnostic log

Overview

ED2 constructs the many-body Hilbert space explicitly and computes eigenstates of the Hamiltonian. Unless otherwise specified, observables are evaluated in the lowest-energy eigenstate.

Generated files depend on input flags such as

cal_lm
cal_cf
eigvec

The detailed specification of all input keys and auxiliary files (FILE_*, list_*.dat) is given in input-format.md.

Energy Eigenvalues

File: eigenvalues.dat

This file contains the computed energy eigenvalues.

Format

Column Meaning
1 Eigenstate index (1-based)
2 Energy \(E_n\)

Properties:

  • Energies are sorted in ascending order: \(E_1 \le E_2 \le \cdots\)
  • The first row corresponds to the ground state \(E_1\).
  • Units are identical to the Hamiltonian parameters.

Local Magnetization (cal_lm = 1)

File: local_mag.dat

This file contains expectation values of local spin operators evaluated in the lowest eigenstate: \(\langle S_i^x \rangle, \langle S_i^y \rangle, \langle S_i^z \rangle.\)

Format

Column Meaning
1 Site index \(i\)
2 \(\langle S_i^x \rangle\)
3 \(\langle S_i^y \rangle\)
4 \(\langle S_i^z \rangle\)

Remarks:

  • Values of order \(\sim 10^{-8}\) indicate vanishing moments within numerical precision.
  • If the Hamiltonian preserves spin symmetry, local moments may vanish even in symmetry-broken phases due to finite-size effects.

Two-Body Correlation Functions (cal_cf = 1)

ED2 evaluates pairwise spin correlations for all site pairs specified in the pair list file (see FILE_two_cf in input-format.md).

File: two_body_cf_xyz.dat

This file contains the full Cartesian correlation tensor \(\langle S_i^\alpha S_j^\beta \rangle, \qquad \alpha,\beta \in \{x,y,z\}.\)

Format

Column Meaning
1 Site \(i\)
2 Site \(j\)
3 \(\langle S_i^x S_j^x \rangle\)
4 \(\langle S_i^x S_j^y \rangle\)
5 \(\langle S_i^x S_j^z \rangle\)
6 \(\langle S_i^y S_j^x \rangle\)
7 \(\langle S_i^y S_j^y \rangle\)
8 \(\langle S_i^y S_j^z \rangle\)
9 \(\langle S_i^z S_j^x \rangle\)
10 \(\langle S_i^z S_j^y \rangle\)
11 \(\langle S_i^z S_j^z \rangle\)

Thus each row represents the full \(3\times3\) spin correlation tensor for a fixed pair \((i,j)\).

File: two_body_cf_z+-.dat

This file expresses correlations in the basis \(S^z, S^+, S^-\), where \(S^\pm = S^x \pm i S^y\).

It contains matrix elements such as $ \langle S_i^z S_j^z \rangle, \langle S_i^z S_j^+ \rangle, \langle S_i^+ S_j^- \rangle, \text{etc.}$

This representation is particularly useful for:

  • models with Dzyaloshinskii–Moriya interactions,
  • non-collinear magnetic order,
  • chiral correlations.

Each row corresponds to a site pair \((i,j)\), followed by all \(z,+,-\) operator combinations.

Eigenvectors (optional)

If wr_wf = 1, ED2 writes files of the form

eigenvec_XXXX.dat

containing eigenvector components in the explicit many-body basis.

Let \(\{ |b_k\rangle \}\) denote the internally constructed basis. The eigenvector is written as

\[ |\psi_n\rangle = \sum_k c_k^{(n)} |b_k\rangle. \]

Notes:

  • Basis ordering follows ED2’s internal convention.
  • Indices correspond directly to the constructed Hilbert space (no hidden symmetry projection).
  • Files may become very large for large Hilbert spaces.

Standard Output (output.dat)

When standard output is redirected, output.dat contains:

  • model and lattice information,
  • Hilbert-space dimension \(\dim \mathcal{H}\),
  • solver configuration,
  • Lanczos / TRLan iteration history,
  • convergence diagnostics.

This file is intended for human inspection and debugging.

Mapping Between Input Flags and Outputs

Input flag Generated files
cal_lm = 1 local_mag.dat
cal_cf = 1 two_body_cf_xyz.dat, two_body_cf_z+-.dat
wr_wf = 1 eigenvec_*.dat

The precise definitions of FILE_spin, FILE_NODmax, FILE_two_cf, and other auxiliary input files are given in input-format.md.

Reproducibility Checklist

For published calculations, archive:

  • all input files (input.dat and referenced list_*.dat),
  • all output .dat files used in analysis,
  • ED2 git commit hash,
  • compiler and BLAS/LAPACK versions,
  • OpenMP configuration.

These records ensure that numerical results can be independently reproduced.

Minimal Workflow

  1. Prepare input.dat and required list_*.dat files.
  2. Run ED2.
  3. Inspect eigenvalues.dat for ground-state energy \(E_1\).
  4. Verify convergence using output.dat.