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Most Two-Dimensional Bosonic Topological Orders Forbid Sign-Problem-Free Quantum Monte Carlo Simulation: Nonpositive
Donghae Seo1,2, Minyoung You3,4, Hee-Cheol Kim1,5
1Pohang University of Science and Technology, Department of Physics, Pohang 37673, Republic of Korea.
Physical Review Letters
|October 19, 2025
Summary
Researchers identified a new criterion for the intrinsic sign problem in two-dimensional bosonic topological orders. Most topological orders exhibit this sign problem, limiting quantum Monte Carlo simulations.
Area of Science:
- Condensed Matter Physics
- Quantum Information Science
Background:
- Quantum Monte Carlo (QMC) is vital for quantum many-body physics.
- The sign problem severely limits QMC's applicability.
Purpose of the Study:
- Introduce a novel criterion to identify intrinsic sign problems in 2D bosonic topological orders.
- Determine the prevalence of sign-problem-free topological orders.
Main Methods:
- Define intrinsic sign problem based on higher Gauss sums.
- Analyze Gauss sums for 405 bosonic topological orders (up to rank 12).
Main Results:
- Positivity of higher Gauss sums is necessary for stoquastic Hamiltonians (sign-problem-free).
- A nonpositive higher Gauss sum indicates an intrinsic sign problem.
- 398 out of 405 analyzed topological orders exhibit intrinsic sign problems.
Conclusions:
- Intrinsic sign problems are common in 2D bosonic topological orders.
- Sign-problem-free QMC simulations may require time-reversal symmetry and gapped boundaries.
- This work provides insights into the classical simulability of topological phases.
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