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.
Twisted quantum double model of topological phases in two dimensions
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abstract
We propose a new discrete model---the twisted quantum double model---of 2D topological phases based on a finite group $G$ and a 3-cocycle $\alpha$ over $G$. The detailed properties of the ground states are studied, and we find that the ground--state subspace can be characterized in terms of the twisted quantum double $D^{\alpha}(G)$ of $G$. When $\alpha$ is the trivial 3-cocycle, the model becomes Kitaev's quantum double model based on the finite group $G$, in which the elementary excitations are known to be classified by the quantum double $D(G)$ of $G$. Our model can be viewed as a Hamiltonian extension of the Dijkgraaf--Witten topological gauge theories to the discrete graph case with gauge group being a finite group. We also demonstrate a duality between a large class of Levin-Wen string-net models and certain twisted quantum double models, by mapping the string--net 6j symbols to the corresponding 3-cocycles. The paper is presented in a way such that it is accessible to a wide range of physicists.
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UNVERDICTED 4representative citing papers
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A gauging method from abelian Dijkgraaf-Witten theories yields BF-type Lagrangians for non-abelian cases via local-coefficient cohomologies and homotopy analysis.
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.
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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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Constructing Bulk Topological Orders via Layered Gauging
A layered gauging method constructs (k+1)-dimensional topological orders, including fracton models like the X-cube, from k-dimensional symmetries such as subsystem, anomalous, or noninvertible ones.
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On Lagrangians of Non-abelian Dijkgraaf-Witten Theories
A gauging method from abelian Dijkgraaf-Witten theories yields BF-type Lagrangians for non-abelian cases via local-coefficient cohomologies and homotopy analysis.
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Exploring Entropic Orders: High Temperature Continuous Symmetry Breaking, Chiral Topological States and Local Commuting Projector Models
New analytic constructions yield quantum lattice models with continuous symmetry breaking and chiral topological order at arbitrarily high temperatures via entropic stabilization.