# Dresden 2020 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 73: Topology: Other Topics

### TT 73.2: Vortrag

### Freitag, 20. März 2020, 11:15–11:30, HSZ 103

**Topological Sign Problems** — •Adam Smith^{1} and Zohar Ringel^{2} — ^{1}Technical University Munich, Garching, Germany — ^{2}Racah Institute of Physics, The Hebrew University of Jerusalem, Israel

Sign-problems are one of the major obstacles for the numerical study of complex many-body quantum systems. They render such models intractable to otherwise powerful techniques, most famously demonstrated by the exponential difficultly of quantum Monte Carlo methods. Here we provide a simple criterion to diagnose incurable sign-problems in topologically ordered systems -- that is, whether the model has a sign-problem that cannot be removed by any local unitary transformation. Explicitly, if the exchange statistics of the anyonic excitations do not form complete sets of roots of unity, then the model has an incurable sign-problem. This establishes a concrete connection between the statistics of anyons, contained in the modular S and T matrices, and the presence of a sign-problem in a microscopic Hamiltonian. We prove this criterion for the large set of bosonic non-chiral models described by an abelian topological quantum field theory at low-energy, and offer evidence that it applies more generally.