A general cluster dual fermion approach to nonlocal correlations in crystals is formulated. The scheme allows the treatment of long-range correlations beyond the cluster dynamical mean field theory and nonlocal effects in realistic calculations of multiorbital systems. The simplest approximation is shown to exactly correspond to the free-cluster dynamical mean field theory. This approach is applied to the one-dimensional Hubbard model. Already the first dual-fermion correction to the free cluster leads to a drastic improvement of the calculated Green’s function.
Abstract We study the moments of the partial transpose of the reduced density matrix of two intervals for the free massless Dirac fermion. By means of a direct calculation based on a coherent state path integral, we find an analytic form for these moments in terms of the Riemann theta function. We show that moments of arbitrary order are equal to the same quantities for the compactified boson at the self-dual point. These equalities also imply the non-trivial result that the negativity of the free fermion and the self-dual boson are equal.
Systems of free fermions are classified by symmetry, space dimensionality, and topological properties described by
K homology. Those systems belonging to different classes are inequivalent. In contrast, we show that by taking a many-body/Fock-space viewpoint it becomes possible to establish equivalences of topological insulators and superconductors in terms of duality transformations. These mappings connect topologically inequivalent systems of fermions, jumping across entries in existent classification tables, because of the phenomenon of symmetry transmutation by which a symmetry and its dual partner have identical algebraic properties but very different physical interpretations. To constrain our study to established classification tables, we define and characterize mathematically Gaussian dualities as dualities mapping free fermions to free fermions (and interacting to interacting). By introducing a large, flexible class of Gaussian dualities we show that any insulator is dual to a superconductor, and that fermionic edge modes are dual to Majorana edge modes, that is, the Gaussian dualities of this paper preserve the bulk-boundary correspondence. Transmutation of relevant symmetries, particle number, translation, and time reversal is also investigated in detail. As illustrative examples, we show the duality equivalence of the dimerized Peierls chain and the Majorana chain of Kitaev, and a two-dimensional Kekul\'e-type topological insulator, including graphene as a special instance in coupling space, dual to a
p-wave superconductor. Since our analysis extends to interacting fermion systems, we also briefly discuss some such applications.