3,687 research outputs found

    Matrix Product Operators, Matrix Product States, and ab initio Density Matrix Renormalization Group algorithms

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    Current descriptions of the ab initio DMRG algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. In this work, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab-initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past, and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.Comment: 35 pages, 10 figure

    Seeing many-body effects in single- and few-layer graphene: Observation of two-dimensional saddle-point excitons

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    Significant excitonic effects were observed in graphene by measuring its optical conductivity in a broad spectral range including the two-dimensional {\pi}-band saddle-point singularities in the electronic structure. The strong electron-hole interactions manifest themselves in an asymmetric resonance peaked at 4.62 eV, which is red-shifted by nearly 600 meV from the value predicted by ab-initio GW calculations for the band-to-band transitions. The observed excitonic resonance is explained within a phenomenological model as a Fano interference of a strongly coupled excitonic state and a band continuum. Our experiment also showed a weak dependence of the excitonic resonance in few-layer graphene on layer thickness. This result reflects the effective cancellation of the increasingly screened repulsive electron-electron (e-e) and attractive electron-hole (e-h) interactions.Comment: 9 pages, 3 figures, In PR

    Collapse of Vacuum Bubbles in a Vacuum

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    Motivated by the discovery of a plenitude of metastable vacua in a string landscape and the possibility of rapid tunneling between these vacua, we revisit the dynamics of a false vacuum bubble in a background de Sitter spacetime. We find that there exists a large parameter space that allows the bubble to collapse into a black hole or to form a wormhole. This may have interesting implications to inflationary physics.Comment: 8 pages including 6 figures, LaTex; references adde

    A state interaction spin-orbit coupling density matrix renormalization group method

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    We describe a state interaction spin-orbit (SISO) coupling method using density matrix renormalization group (DMRG) wavefunctions and the spin-orbit mean-field (SOMF) operator. We implement our DMRG-SISO scheme using a spin-adapted algorithm that computes transition density matrices between arbitrary matrix product states. To demonstrate the potential of the DMRG-SISO scheme we present accurate benchmark calculations for the zero-field splitting of the copper and gold atoms, comparing to earlier complete active space self-consistent-field and second-order complete active space perturbation theory results in the same basis. We also compute the effects of spin-orbit coupling on the spin-ladder of the iron-sulfur dimer complex [Fe_2S_2(SCH_3)_4]^(3−), determining the splitting of the lowest quartet and sextet states. We find that the magnitude of the zero-field splitting for the higher quartet and sextet states approaches a significant fraction of the Heisenberg exchange parameter

    An electrostatic levitator for high-temperature containerless materials processing in 1-g

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    This article discusses recent developments in high-temperature electrostatic levitation technology for containerless processing of metals and alloys. Presented is the first demonstration of an electrostatic levitation technology which can levitate metals and alloys (2–4 mm diam spheres) in vacuum and of superheating-undercooling-recalescence cycles which can be repeated while maintaining good positioning stability. The electrostatic levitator (ESL) has several important advantages over the electromagnetic levitator. Most important is the wide range of sample temperature which can be achieved without affecting levitation. This article also describes the general architecture of the levitator, electrode design, position control hardware and software, sample heating, charging, and preparation methods, and operational procedures. Particular emphasis is given to sample charging by photoelectric and thermionic emission. While this ESL is more oriented toward ground-based operation, an extension to microgravity applications is also addressed briefly. The system performance was demonstrated by showing multiple superheating-undercooling-recalescence cycles in a zirconium sample (Tm=2128 K). This levitator, when fully matured, will be a valuable tool both in Earth-based and space-based laboratories for the study of thermophysical properties of undercooled liquids, nucleation kinetics, the creation of metastable phases, and access to a wide range of materials with novel properties

    Possible Constraints on the Duration of Inflationary Expansion from Quantum Stress Tensor Fluctuations

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    We discuss the effect of quantum stress tensor fluctuations in deSitter spacetime upon the expansion of a congruence of timelike geodesics. We treat a model in which the expansion fluctuations begin on a given hypersurface in deSitter spacetime, and find that this effect tends to grow, in contrast to the situation in flat spacetime. This growth potentially leads to observable consequences in inflationary cosmology in the form of density perturbations which depend upon the duration of the inflationary period. In the context of our model, the effect may be used to place upper bounds on this duration.Comment: 21 pages, no figures; Sect. IV rewritten and expanded, several comments and references adde

    Rotating Black Holes at Future Colliders. III. Determination of Black Hole Evolution

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    TeV scale gravity scenario predicts that the black hole production dominates over all other interactions above the scale and that the Large Hadron Collider will be a black hole factory. Such higher dimensional black holes mainly decay into the standard model fields via the Hawking radiation whose spectrum can be computed from the greybody factor. Here we complete the series of our work by showing the greybody factors and the resultant spectra for the brane localized spinor and vector field emissions for arbitrary frequencies. Combining these results with the previous works, we determine the complete radiation spectra and the subsequent time evolution of the black hole. We find that, for a typical event, well more than half a black hole mass is emitted when the hole is still highly rotating, confirming our previous claim that it is important to take into account the angular momentum of black holes.Comment: typoes in eqs(82)-(84) corrected; version to appear in Phys. Rev. D; references and a footnote added; same manuscript with high resolution embedded figures available on http://www.gakushuin.ac.jp/univ/sci/phys/ida/paper

    Conversion of projected entangled pair states into a canonical form

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    We propose an algorithm to convert a projected entangled pair state (PEPS) into a canonical form, analogous to the well-known canonical form of a matrix product state. Our approach is based on a variational gauging ansatz for the QR tensor decomposition of PEPS columns into a matrix product operator and a finite depth circuit of unitaries and isometries. We describe a practical initialization scheme that leads to rapid convergence in the QR optimization. We explore the performance and stability of the variational gauging algorithm in norm calculations for the transverse-field Ising and Heisenberg models on a square lattice. We also demonstrate energy optimization within the PEPS canonical form for the transverse-field Ising and Heisenberg models. We expect this canonical form to open up improved analytical and numerical approaches for PEPS.Comment: 8 pages, 6 Figure
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