arXiv subjects

Norm M. Tubman

Publications and source records attributed to Norm M. Tubman.

60 records · Page 4Linked to original sources

arXiv2014

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.

cond-mat.str-el↗

arXiv2014

Beyond the Born-Oppenheimer approximation with quantum Monte Carlo

In this work we develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave function ansatz for electron-ion systems that can involve a combination of both fixed and quantum ions. We explicitly calculate the ground state energies of H$_{2}$, LiH, H$_{2}$O and FHF$^{-}$ using fixed-node quantum Monte Carlo with wave function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our results to the best theoretical and experimental results available and find excellent agreement.

physics.chem-ph↗

arXiv2014

Direct calculation of the Entanglement Spectrum in Quantum Monte Carlo with application to \textit{ab initio} Hamiltonians

Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order Renyi entropies. In this work we present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix and we determine an estimator that can be used in variational Monte Carlo as well as other Monte Carlo methods. The algorithm is based on using a generalization of the Swap operator, which can be extended to calculate a general class of density matrices that can include combinations of spin, space, particle and even momentum coordinates. We demonstrate the method by applying it to the Hydrogen and Nitrogen molecules and describe for the first time how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.

cond-mat.str-el↗

arXiv2012

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.

cond-mat.str-el↗

arXiv2012

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 Pöschl-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.

cond-mat.str-el↗

arXiv2012

Renyi Entanglement Entropy of Molecules: Interaction Effects and Signatures of Bonding

Recent proposals of measuring bipartite Renyi entropy experimentally involve techniques that hold exactly for non-interacting quantum particles. Here we consider the difference between such measurements and the actual Renyi entropy for ground state fermion ab initio molecular systems. To calculate various entanglement measures we extended several different techniques for use with variational Monte Carlo, Hartree-Fock and quantum chemistry methods. Our results show that in systems with strong electron correlations the Renyi entropy may not be accurately determined with the proposed measurements. In addition, we find significant physical insight can be gained by calculating entanglement properties in molecular systems. We see that the Renyi entropy and the entanglement Hamiltonian encode information about the character of the covalent bonds in a molecular system and that such information may lead to better descriptions of bonded systems that have been traditionally hard to describe with standard techniques. In particular our results for the C$_{2}$ dimer suggests all eight valence electrons play a significant role in covalent bonding.

cond-mat.str-el↗