Quantized gravitational responses, the sign problem, and quantum complexity

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Science Advances  27 Sep 2017:
Vol. 3, no. 9, e1701758
DOI: 10.1126/sciadv.1701758


  • Fig. 1 Sign-free manipulations of 2D lattices.

    All figures show lattices with on-site bosonic degrees of freedom (full circles) with non-negative Boltzmann weights (dashed lines) involving several neighboring sites. (A) Open boundaries can be introduced in a sign-free manner by adding fictitious ghost degrees of freedom (empty circles). (B) Global torsional twists are generated by reconnecting the lattice in a skewed manner. (C) Local curvature is generated by disclinations. The latter can be introduced by lattice reconnections. Notwithstanding, in the FQHE, a global torsional twist similar to (B) induces complex phases in the partition function.

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