40,609 research outputs found

    Searching for topological density wave insulators in multi-orbital square lattice systems

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    We study topological properties of density wave states with broken translational symmetry in two-dimensional multi-orbital systems with a particular focus on t2g_{2g} orbitals in square lattice. Due to distinct symmetry properties of d-orbitals, a nodal charge or spin density wave state with Dirac points protected by lattice symmetries can be achieved. When an additional order parameter with opposite reflection symmetry is introduced to a nodal density wave state, the system can be fully gapped leading to a band insulator. Among those, topological density wave (TDW) insulators can be realized, when an effective staggered on-site potential generates a gap to a pair of Dirac points connected by the inversion symmetry which have the same topological winding numbers. We also present a mean-field phase diagram for various density wave states, and discuss experimental implications of our results.Comment: 15 pages, 10 figures, 7 table

    A Shift Selection Strategy for Parallel Shift-invert Spectrum Slicing in Symmetric Self-consistent Eigenvalue Computation

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    © 2020 ACM. The central importance of large-scale eigenvalue problems in scientific computation necessitates the development of massively parallel algorithms for their solution. Recent advances in dense numerical linear algebra have enabled the routine treatment of eigenvalue problems with dimensions on the order of hundreds of thousands on the world's largest supercomputers. In cases where dense treatments are not feasible, Krylov subspace methods offer an attractive alternative due to the fact that they do not require storage of the problem matrices. However, demonstration of scalability of either of these classes of eigenvalue algorithms on computing architectures capable of expressing massive parallelism is non-trivial due to communication requirements and serial bottlenecks, respectively. In this work, we introduce the SISLICE method: a parallel shift-invert algorithm for the solution of the symmetric self-consistent field (SCF) eigenvalue problem. The SISLICE method drastically reduces the communication requirement of current parallel shift-invert eigenvalue algorithms through various shift selection and migration techniques based on density of states estimation and k-means clustering, respectively. This work demonstrates the robustness and parallel performance of the SISLICE method on a representative set of SCF eigenvalue problems and outlines research directions that will be explored in future work

    Surface Counterterms and Regularized Holographic Complexity

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    The holographic complexity is UV divergent. As a finite complexity, we propose a "regularized complexity" by employing a similar method to the holographic renormalization. We add codimension-two boundary counterterms which do not contain any boundary stress tensor information. It means that we subtract only non-dynamic background and all the dynamic information of holographic complexity is contained in the regularized part. After showing the general counterterms for both CA and CV conjectures in holographic spacetime dimension 5 and less, we give concrete examples: the BTZ black holes and the four and five dimensional Schwarzschild AdS black holes. We propose how to obtain the counterterms in higher spacetime dimensions and show explicit formulas only for some special cases with enough symmetries. We also compute the complexity of formation by using the regularized complexity.Comment: Published version with some small improvement
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