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      Simulation of strongly correlated fermions in two spatial dimensions with fermionic Projected Entangled-Pair States

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          Abstract

          We explain how to implement, in the context of projected entangled-pair states (PEPS), the general procedure of fermionization of a tensor network introduced in [P. Corboz, G. Vidal, Phys. Rev. B 80, 165129 (2009)]. The resulting fermionic PEPS, similar to previous proposals, can be used to study the ground state of interacting fermions on a two-dimensional lattice. As in the bosonic case, the cost of simulations depends on the amount of entanglement in the ground state and not directly on the strength of interactions. The present formulation of fermionic PEPS leads to a straightforward numerical implementation that allowed us to recycle much of the code for bosonic PEPS. We demonstrate that fermionic PEPS are a useful variational ansatz for interacting fermion systems by computing approximations to the ground state of several models on an infinite lattice. For a model of interacting spinless fermions, ground state energies lower than Hartree-Fock results are obtained, shifting the boundary between the metal and charge-density wave phases. For the t-J model, energies comparable with those of a specialized Gutzwiller-projected ansatz are also obtained.

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          Phase separation in the t-J model.

          Emery, Kivelson, Lin (1990)
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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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              Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations

              Quantum Monte Carlo simulations, while being efficient for bosons, suffer from the "negative sign problem'' when applied to fermions - causing an exponential increase of the computing time with the number of particles. A polynomial time solution to the sign problem is highly desired since it would provide an unbiased and numerically exact method to simulate correlated quantum systems. Here we show, that such a solution is almost certainly unattainable by proving that the sign problem is NP-hard, implying that a generic solution of the sign problem would also solve all problems in the complexity class NP (nondeterministic polynomial) in polynomial time.
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                Author and article information

                Journal
                03 December 2009
                2010-04-28
                Article
                10.1103/PhysRevB.81.165104
                0912.0646
                13f4412d-fa15-4923-ad01-e17273eb4822

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

                History
                Custom metadata
                Phys. Rev. B 81, 165104 (2010)
                25 pages, 35 figures (revised version)
                cond-mat.str-el

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