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QAtlas.jl

QAtlas (QUAntum Reference Table for Exact Tests) is a curated dictionary of rigorous results in quantum and statistical physics. Every stored value is traced to a specific publication and cross-validated against independent calculations.

Key Features

Unlike typical numerical libraries, QAtlas focuses on authoritative reference values — exact analytical results, high-precision conformal bootstrap bounds, and Bethe ansatz solutions. Each value is accompanied by:

  1. Precise citation: author, year, journal, equation number
  2. Derivation sketch: enough to independently verify
  3. Cross-validation: tested against independent computation
  4. Connections: linked to universality classes and other models

Two kinds of stored value, and the registry says which

The paragraph above describes most of the atlas but not all of it, and the difference is worth stating rather than leaving a reader to discover.

A row registered cost = :exponential is many-body dense exact diagonalisation on a d^N Hilbert space, with a declared max_size (12 for spin-½). Measured on the loaded registry: 69 of 518 rows (13.3%), concentrated in three models — S1Heisenberg1D (22 of 24), Heisenberg1D (23 of 35), XXZ1D (23 of 37), where they are the whole OBC surface.

Those rows are not "authoritative reference values" in the sense above. There is no publication for the local magnetisation of the eight-site open Heisenberg chain at β = 1, and any consumer with an ED routine reproduces the number in minutes. What they are is a cross-validation instrument:

  • the small-N ground truth an analytic closed form is checked against (the TFIM entanglement entropy documents exactly this — "matches the full-ED reference at every small N, verified to 1e-10");
  • the target a new DMRG / MPS / QMC implementation validates itself on before it is trusted at sizes where nothing exact exists.

Two things that are easy to assume and are false, both measured:

  • They do not duplicate the closed forms. Every (model, quantity) pair carrying both has the ED row at a finite OBC chain and the analytic row at Infinite — the thermodynamic limit is a different question, not a second route to the same number. No (model, quantity, bc) triple carries both, and a test asserts it stays that way. For 56 (model, quantity) pairs, ED is the only route there is.
  • The cost is not a detail. cost = :exponential requires max_size at registration precisely so a route cannot hide where it stops, and the limit bites in practice: one region-entropy bag costs 0.0 s on TFIM/OBC and 338.7 s on S1Heisenberg1D/OBC, which is why the latter carries an exclusion in region_registry.jl.

So: read cost alongside status. status = :exact says the value is right; cost = :exponential says it is an instrument you could have built yourself, and tells you the size beyond which it does not exist.

Quick Start

using QAtlas

# Onsager critical temperature
Tc = QAtlas.fetch(IsingSquare(), CriticalTemperature())

# TFIM ground-state energy
E₀ = QAtlas.fetch(:TFIM, :energy, OBC(); N=16, J=1.0, h=0.5)

# 2D Ising universality: exact exponents (Rational)
e = QAtlas.fetch(Universality(:Ising), CriticalExponents(); d=2)
# (β = 1//8, ν = 1//1, γ = 7//4, η = 1//4, ...)

Contents

  • Models — exact solutions for classical and quantum models
  • Universality Classes — critical exponents and scaling relations across dimensions
  • Verification — five-layer testing strategy ensuring physical correctness
  • Methods — computational techniques with physical justification
  • Derivation Notes — step-by-step calculations
  • API Reference — full Julia docstring index

Reporting Errors

Every page has a Report an issue button fixed at the top-right of the screen. Clicking it opens a pre-filled GitHub issue with the current page URL — no copy-paste needed.

Individual sections also show a small report link when you hover over an H2 or H3 heading. Use it to flag a specific derivation or formula that looks wrong.

All reports go to QAtlasHub/QAtlas.jl Issues. Corrections and pull requests are equally welcome.