A subpolynomial-time algorithm for the free energy of one-dimensional...
summary
Algorithm computes thermodynamic-limit free energy for translation-invariant 1D quantum chains with error ε in time exp(O(log(1/ε)/log log(1/ε))) — a subpolynomial runtime in 1/ε. Method builds finite noncommutative transfer maps (Araki’s construction), uses Collatz–Wielandt bounds, a quantitative primitivity estimate and Perron–Frobenius/Hilbert projective-metric arguments to extract spectral radius and local marginals. Implementation returns marginals directly and on the XY test it reaches machine-precision on seconds-scale compared to the analytic solution.
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chapters (12)
- 0:00Introduction
- 0:30Setup
- 2:17Partition function
- 4:39Alternative formulas
- 6:20Main result
- 8:48Hamiltonian
- 10:18Classical case
- 10:58Petition function
- 14:00Quantum case
- 16:19Noncommunity differential matrix
- 18:29Eigenvector
- 20:30Conclusion
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