We introduce a general framework to study moiré structures of two-dimensional Van der Waals magnets using continuum field theory. The formalism eliminates quasiperiodicity and allows a full understanding of magnetic structures and their excitations. In particular, we analyze in detail twisted bilayers of Néel antiferromagnets on the honeycomb lattice. A rich phase diagram with noncollinear twisted phases is obtained, and spin waves are further calculated. Direct extensions to zigzag antiferromagnets and ferromagnets are also presented. We anticipate the results and formalism demonstrated to lead to a broad range of applications to both fundamental research and experiments.
In this paper we propose a Hamiltonian approach to gapped topological phases on open surfaces. Our setting is an extension of the Levin-Wen model to a 2d graph on an open surface, whose boundary is part of the graph. We systematically construct a series of boundary Hamiltonians such that each of them, when combined with the usual Levin-Wen bulk Hamiltonian, gives rise to a gapped energy spectrum which is topologically protected. It is shown that the corresponding wave functions are robust under changes of the underlying graph that maintain the spatial topology of the system. We derive explicit ground-state wavefunctions of the system on a disk as well as on a cylinder. For boundary quasiparticle excitations, we are able to construct their creation, annihilation, measuring and hopping operators etc. Given a bulk string-net theory, our approach provides a classification scheme of possible types of gapped boundary conditions by Frobenius algebras (modulo Morita equivalence) of the bulk fusion category; the boundary quasiparticles are characterized by bimodules of the pertinent Frobenius algebras. Our approach also offers a set of concrete tools for computations. We illustrate our approach by a few examples.
Abstract:In this paper, we use the replica approach to study the Rényi entropy S L of generic locally excited states in (1+1)D CFTs, which are constructed from the insertion of multiple product of local primary operators on vacuum. Alternatively, one can calculate the Rényi entropy S R corresponding to the same states using Schmidt decomposition and operator product expansion, which reduces the multiple product of local primary operators to linear combination of operators. The equivalence S L = S R translates into an identity in terms of the F symbols and quantum dimensions for rational CFT, and the latter can be proved algebraically. This, along with a series of papers, gives a complete picture of how the quantum information quantities and the intrinsic structure of (1+1)D CFTs are consistently related.
We study 3D pure Einstein quantum gravity with negative cosmological constant, in the regime where the AdS radius l is of the order of the Planck scale. Specifically, when the Brown-Henneaux central charge c = 3l/2GN (GN is the 3D Newton constant) equals c = 1/2, we establish duality between 3D gravity and 2D Ising conformal field theory by matching gravity and conformal field theory partition functions for AdS spacetimes with general asymptotic boundaries. This duality was suggested by a genus-one calculation of Castro et al. [Phys. Rev. D85 (2012) 024032]. Extension beyond genus-one requires new mathematical results based on 3D Topological Quantum Field Theory; these turn out to uniquely select the c = 1/2 theory among all those with c < 1, extending the previous results of Castro et al. Previous work suggests the reduction of the calculation of the gravity partition function to a problem of summation over the orbits of the mapping class group action on a “vacuum seed”. But whether or not the summation is well-defined for the general case was unknown before this work. Amongst all theories with Brown-Henneaux central charge c < 1, the sum is finite and unique only when c = 1/2, corresponding to a dual Ising conformal field theory on the asymptotic boundary.
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