Thermal states: two-branch law at the cylinder cross ratio, exponential shielding

Status: numerical — measured, with an error bar and a convergence order; not a theorem.

Area: Lattice, thermal, massive and gapped geometries (O7, O9, O10) · Card type: result · Knowledge-base id: thermal-shielding

Statement

KMS states of the free fermion obey the vacuum two-branch law at the thermal cross ratio eta_beta (sinh form). For L_B >> beta the error is shielded exponentially with rate 2 pi (fidelity) and pi (CMI) in thermal-length units (v = 2 sites/time); I_beta - I_vac = -pi^2 L_A L_C/(36 beta^2).

How to verify

numerics/lattice/petz_thermal_rg.out.

Evidence

• numerics/lattice/petz_thermal_rg.py — numerics
• rigor/thermal_rg_gap_summary.md — document

Related claims

None recorded.

Review

Review record: passed 2026-09-23 by REF-DEP-CFT-B2.

The referee's report and the card's event log stay in the private knowledge base; only the verdict, the date and the referee are published here.

Documentation map · All claims by area · What is open · Symbols · Definitions