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      Spectral functions in one-dimensional quantum systems at T>0

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          Abstract

          We present for the first time time-dependent density-matrix renormalization-group simulations (t-DMRG) at finite temperatures. It is demonstrated how a combination of finite-temperature t-DMRG and time-series prediction allows for an easy and very accurate calculation of spectral functions in one-dimensional quantum systems, irrespective of their statistics, for arbitrary temperatures. This is illustrated with spin structure factors of XX and XXX spin-1/2 chains. For the XX model we can compare against an exact solution and for the XXX model (Heisenberg antiferromagnet) against a Bethe Ansatz solution and quantum Monte Carlo data.

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          Linear prediction: A tutorial review

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            Grand Unification, Gravitational Waves, and the Cosmic Microwave Background Anisotropy

            We re-examine the gravitational wave background resulting from inflation and its effect on the cosmic microwave background radiation. The new COBE measurement of a cosmic background quadrupole anisotropy places an upper limit on the vacuum energy during inflation of \(\approx 5 \times 10^{16}\) GeV. A stochastic background of gravitational waves from inflation could produce the entire observed signal (consistent with the observed dipole anisotropy and a flat spectrum) if the vacuum energy during inflation was as small as \(1.5 \times 10^{16}\) GeV at the 95\% confidence level. This coincides nicely with the mass scale for Grand Unification inferred from precision measurements of the electroweak and strong coupling constants, for the SUSY Grand Unified Theories. Thus COBE could be providing the first direct evidence, via gravitational waves, for GUTs, and supersymmetry. Further tests of this possibility are examined, based on analyzing the energy density associated with gravitational waves from inflation.
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              Real time evolution using the density matrix renormalization group

              We describe an extension to the density matrix renormalization group method incorporating real time evolution into the algorithm. Its application to transport problems in systems out of equilibrium and frequency dependent correlation functions is discussed and illustrated in several examples. We simulate a scattering process in a spin chain which generates a spatially non-local entangled wavefunction.
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                Author and article information

                Journal
                15 January 2009
                2009-07-28
                Article
                10.1103/PhysRevB.79.245101
                0901.2342
                72dbf07b-fb1e-4b01-b056-d1a6c3010bb0

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                Phys. Rev. B 79, 245101 (2009)
                6 pages, 8 figures; added comparison to quantum Monte Carlo, extended discussion of the method, 4 figures added; published version
                cond-mat.str-el

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