Oscillating terms in the Renyi entropy of Fermi liquids

In this work we compute subleading oscillating terms in the Renyi entropy of Fermi gases and Fermi liquids corresponding to $2k_F$-like oscillations. Our theoretical tools are the one dimensional formulation of Fermi liquid entanglement familiar from discussions of the logarithmic violation of the area law and quantum Monte Carlo calculations. The main result is a formula for the oscillating term for any region geometry and a spherical Fermi surface. We compare this term to numerical calculations of entanglement using the correlation function method and find excellent agreement. We also compare with quantum Monte Carlo data on interacting Fermi liquids where we also find excellent agreement up to moderate interaction strengths.Comment: 8 pages, 2 figure

Dynamical Mean-Field Theory Simulations with the Adaptive Sampling Configuration Interaction Method

In the pursuit of accurate descriptions of strongly correlated quantum many-body systems, dynamical mean-field theory (DMFT) has been an invaluable tool for elucidating the spectral properties and quantum phases of both phenomenological models and ab initio descriptions of real materials. Key to the DMFT process is the self-consistent map of the original system into an Anderson impurity model, the ground state of which is computed using an impurity solver. The power of the method is thus limited by the complexity of the impurity model the solver can handle. Simulating realistic systems generally requires many correlated sites. By adapting the recently proposed adaptive sampling configuration interaction (ASCI) method as an impurity solver, we enable much more efficient zero temperature DMFT simulations. The key feature of the ASCI method is that it selects only the most relevant Hilbert space degrees of freedom to describe the ground state. This reduces the numerical complexity of the calculation, which will allow us to pursue future DMFT simulations with more correlated impurity sites than in previous works. Here we present the ASCI-DMFT method and example calculations on the one-dimensional and two-dimensional Hubbard models that exemplify its efficient convergence and timing properties. We show that the ASCI approach is several orders of magnitude faster than the current best published ground state DMFT simulations, which allows us to study the bath discretization error in simulations with small clusters, as well as to address cluster sizes beyond the current state of the art. Our approach can also be adapted for other embedding methods such as density matrix embedding theory and self-energy embedding theory.Comment: 12 pages, 11 figures, supplemental informatio

Molecular-Atomic Transition in the Deuterium Hugoniot with Coupled Electron Ion Monte Carlo

We have performed accurate simulations of the Deuterium Hugoniot using Coupled Electron Ion Monte Carlo (CEIMC). Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the principal Hugoniot, where the system undergoes a continuous transition from a molecular fluid to a monatomic fluid. We include all relevant physical corrections so that a direct comparison to experiment can be made. Around 50 GPa we found a maximum compression of 4.85, roughly 10% larger than previous theoretical predictions and experimental data but still compatible with the latter because of their large uncertainty.Comment: 7 pages, 3 figure

Renyi Entropy of the Interacting Fermi Liquid

We perform quantum Monte Carlo calculations to determine how the Renyi entropies, $S_n$, of the interacting Fermi liquid depend on Renyi order, $n$, and scale as a function of system size, $L$. Using the swap operator and an accurate Slater-Jastrow wave function, we compute Renyi entropies for spinless fermions interacting via the Coulomb and modified P\"{o}schl-Teller potentials across a range of correlation strengths. Our results show that interactions increase the Renyi entropies and increase the prefactor of their scaling laws. The relationships between Renyi entropies of different order $n$ are also modified. Additionally, we investigate the effect of the swap operator on the Fermi liquid wave function to determine the source of the $L\log L$ scaling form.Comment: 7 pages, 7 figure

Cluster decomposition of full configuration interaction wave functions: a tool for chemical interpretation of systems with strong correlation

Approximate full configuration interaction (FCI) calculations have recently become tractable for systems of unforeseen size thanks to stochastic and adaptive approximations to the exponentially scaling FCI problem. The result of an FCI calculation is a weighted set of electronic configurations, which can also be expressed in terms of excitations from a reference configuration. The excitation amplitudes contain information on the complexity of the electronic wave function, but this information is contaminated by contributions from disconnected excitations, i.e. those excitations that are just products of independent lower-level excitations. The unwanted contributions can be removed via a cluster decomposition procedure, making it possible to examine the importance of connected excitations in complicated multireference molecules which are outside the reach of conventional algorithms. We present an implementation of the cluster decomposition analysis and apply it to both true FCI wave functions, as well as wave functions generated from the adaptive sampling CI (ASCI) algorithm. The cluster decomposition is useful for interpreting calculations in chemical studies, as a diagnostic for the convergence of various excitation manifolds, as well as as a guidepost for polynomially scaling electronic structure models. Applications are presented for (i) the double dissociation of water, (ii) the carbon dimer, (iii) the {\pi} space of polyacenes, as well as (iv) the chromium dimer. While the cluster amplitudes exhibit rapid decay with increasing rank for the first three systems, even connected octuple excitations still appear important in Cr$_2$, suggesting that spin-restricted single-reference coupled-cluster approaches may not be tractable for some problems in transition metal chemistry.Comment: 15 pages, 5 figure