Rigorous wave function embedding with dynamical fluctuations

The dynamical fluctuations in approaches such as dynamical mean-field theory (DMFT) allow for the self-consistent optimization of a local fragment, hybridized with a true correlated environment. We show that these correlated environmental fluctuations can instead be efficiently captured in a wave function perspective in a computationally cheap, frequency-independent, zero-temperature approach. This allows for a systematically improvable, short-time wave function analogue to DMFT, which entails a number of computational and numerical benefits. We demonstrate this approach to solve the correlated dynamics of the paradigmatic Bethe lattice Hubbard model, as well as detailing cluster extensions in the one-dimensional Hubbard chain where we clearly show the benefits of this rapidly convergent description of correlated environmental fluctuations

Thermal pump-compressor for space use Patent

Thermal pump-compressor for converting solar energ

Hadron masses from dynamical, non-perturbatively O(a) improved Wilson fermions

We present results on light hadron masses from simulations of full QCD and report on experiences in running such simulations on a Hitachi SR8000-F1 supercomputer.Comment: Lattice 2000 (Spectrum), 4 pages, 6 eps figure

Spectral functions of strongly correlated extended systems via an exact quantum embedding

Density matrix embedding theory (DMET) [Phys. Rev. Lett., 109, 186404 (2012)], introduced a new approach to quantum cluster embedding methods, whereby the mapping of strongly correlated bulk problems to an impurity with finite set of bath states was rigorously formulated to exactly reproduce the entanglement of the ground state. The formalism provided similar physics to dynamical mean-field theory at a tiny fraction of the cost, but was inherently limited by the construction of a bath designed to reproduce ground state, static properties. Here, we generalize the concept of quantum embedding to dynamic properties and demonstrate accurate bulk spectral functions at similarly small computational cost. The proposed spectral DMET utilizes the Schmidt decomposition of a response vector, mapping the bulk dynamic correlation functions to that of a quantum impurity cluster coupled to a set of frequency dependent bath states. The resultant spectral functions are obtained on the real-frequency axis, without bath discretization error, and allows for the construction of arbitrary dynamic correlation functions. We demonstrate the method on the 1D and 2D Hubbard model, where we obtain zero temperature, thermodynamic limit spectral functions, and show the trivial extension to two-particle Green functions. This advance therefore extends the scope and applicability of DMET in condensed matter problems as a computationally tractable route to correlated spectral functions of extended systems, and provides a competitive alternative to dynamical mean-field theory for dynamic quantities.Comment: 6 pages, 6 figure

Non-linear biases, stochastically-sampled effective Hamiltonians and spectral functions in quantum Monte Carlo methods

In this article we study examples of systematic biases that can occur in quantum Monte Carlo methods due to the accumulation of non-linear expectation values, and approaches by which these errors can be corrected. We begin with a study of the Krylov-projected FCIQMC (KP-FCIQMC) approach, which was recently introduced to allow efficient, stochastic calculation of dynamical properties. This requires the solution of a sampled effective Hamiltonian, resulting in a non-linear operation on these stochastic variables. We investigate the probability distribution of this eigenvalue problem to study both stochastic errors and systematic biases in the approach, and demonstrate that such errors can be significantly corrected by moving to a more appropriate basis. This is lastly expanded to include consideration of the correlation function QMC approach of Ceperley and Bernu, showing how such an approach can be taken in the FCIQMC framework.Comment: 12 pages, 7 figure