C*-algebras of separated graphs

The construction of the C*-algebra associated to a directed graph $E$ is extended to incorporate a family $C$ consisting of partitions of the sets of edges emanating from the vertices of $E$. These C*-algebras $C^*(E,C)$ are analyzed in terms of their ideal theory and K-theory, mainly in the case of partitions by finite sets. The groups $K_0(C^*(E,C))$ and $K_1(C^*(E,C))$ are completely described via a map built from an adjacency matrix associated to $(E,C)$. One application determines the K-theory of the C*-algebras $U^{\text{nc}}_{m,n}$, confirming a conjecture of McClanahan. A reduced C*-algebra \Cstred(E,C) is also introduced and studied. A key tool in its construction is the existence of canonical faithful conditional expectations from the C*-algebra of any row-finite graph to the C*-subalgebra generated by its vertices. Differences between \Cstred(E,C) and $C^*(E,C)$, such as simplicity versus non-simplicity, are exhibited in various examples, related to some algebras studied by McClanahan.Comment: 29 pages. Revised version, to appear in J. Functional Analysi

Primely generated refinement monoids

We extend both Dobbertin's characterization of primely generated regular refinement monoids and Pierce's characterization of primitive monoids to general primely generated refinement monoids.The first-named author was partially supported by DGI MINECO MTM2011-28992-C02-01, by FEDER UNAB10-4E-378 "Una manera de hacer Europa", and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya. The second-named author was partially supported by the DGI and European Regional Development Fund, jointly, through Project MTM2011-28992-C02-02, and by PAI III grants FQM-298 and P11-FQM-7156 of the Junta de Andalucía

Imaginary-time matrix product state impurity solver for dynamical mean-field theory

We present a new impurity solver for dynamical mean-field theory based on imaginary-time evolution of matrix product states. This converges the self-consistency loop on the imaginary-frequency axis and obtains real-frequency information in a final real-time evolution. Relative to computations on the real-frequency axis, required bath sizes are much smaller and less entanglement is generated, so much larger systems can be studied. The power of the method is demonstrated by solutions of a three band model in the single and two-site dynamical mean-field approximation. Technical issues are discussed, including details of the method, efficiency as compared to other matrix product state based impurity solvers, bath construction and its relation to real-frequency computations and the analytic continuation problem of quantum Monte Carlo, the choice of basis in dynamical cluster approximation, and perspectives for off-diagonal hybridization functions.Comment: 8 pages + 4 pages appendix, 9 figure

Towards a K-theoretic characterization of graded isomorphisms between Leavitt path algebras

Hazrat gave a K-theoretic invariant for Leavitt path algebras as graded algebras. Hazrat conjectured that this invariant classifies Leavitt path algebras up to graded isomorphism, and proved the conjecture in some cases. In this paper, we prove that a weak version of the conjecture holds for all finite essential graphs