Twisted quantum double phases for finite groups can be realized in sign problem-free local Hamiltonians via stochastic series expansion, contrary to the prior belief that non-positive wavefunctions imply an intrinsic sign problem.
Braiding statistics of loop excitations in three dimensions
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abstract
While it is well known that three dimensional quantum many-body systems can support non-trivial braiding statistics between particle-like and loop-like excitations, or between two loop-like excitations, we argue that a more fundamental quantity is the statistical phase associated with braiding one loop $\alpha$ around another loop $\beta$, while both are linked to a third loop $\gamma$. We study this three-loop braiding in the context of $(\mathbb{Z}_N)^K$ gauge theories which are obtained by gauging a gapped, short-range entangled lattice boson model with $(\mathbb{Z}_N)^K$ symmetry. We find that different short-range entangled bosonic states with the same $(\mathbb{Z}_N)^K$ symmetry (i.e. different symmetry-protected topological phases) can be distinguished by their three-loop braiding statistics.
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cond-mat.str-el 2representative citing papers
Statistics of G-conserved invertible mixed-dimensional excitations in d-space are classified by H^{d+2}(BG; R/Z) and realized as boundary excitations of an ω-twisted higher-group gauge theory.
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Twisted quantum doubles are sign problem-free
Twisted quantum double phases for finite groups can be realized in sign problem-free local Hamiltonians via stochastic series expansion, contrary to the prior belief that non-positive wavefunctions imply an intrinsic sign problem.
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Holographic Theory of Mixed-Dimensional Statistics and Conservation-Encoding Hopping-Operator Algebras
Statistics of G-conserved invertible mixed-dimensional excitations in d-space are classified by H^{d+2}(BG; R/Z) and realized as boundary excitations of an ω-twisted higher-group gauge theory.