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

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

Computing the energy of a water molecule using MultiDeterminants: A simple, efficient algorithm

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave-functions are critical to ascertaining new physics. One such wave function is the multiSlater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wavefunctions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally we implement this method and use it to compute the ground state energy of a water molecule.Comment: 10 pages, 4 figure

Benchmark studies using quantum Monte Carlo: pressure estimators, energy, and entanglement

Trial wave function based quantum Monte Carlo is a promising family of methods for the solution of quantum mechanical Hamiltonians. These fundamentally non-perturbative methods can be used to treat bosons or fermions in weakly or strong interacting systems and in any phase. Properties computed for particles with bosonic statistics can be converged to their exact value at relatively moderate computational cost using diffusion quantum Monte Carlo. For fermions the problem is slightly more complicated. Exact methods, such as released-node diffusion quantum Monte Carlo, exist for computing unbiased fermion properties, however their computational expense increases rapidly with the Bose-Fermi energy gap and system size. It is possible to use a fixed-node version of diffusion quantum Monte Carlo, but it introduces a bias due to the nodes of the trial wave function. In this thesis we work towards reducing trial wave function bias in fixed-node calculations and then perform several benchmark studies. We begin with a pedagogical overview of the three methods used throughout the thesis, variational, diffusion, and reptation quantum Monte Carlo. Then we discuss the problem, trial wave function bias in the energy and other observables. Next we outline the Hamiltonians we are typically interested in for electronic systems and trial wave function forms used to solve them. The algorithm used to optimize the trial wave functions is presented along with special considerations for some particular cases. Next we present three studies of the pressure of the electron gas using improved estimators in variational, diffusion, and reptation quantum Monte Carlo. Benchmark results for a set of molecules are then presented for the massive multi-determinant expansion and optimization algorithm tailored to suit it. We conclude with two studies of the interacting Fermi liquid, one on the momentum properties of the electron gas in three dimensions and another on the entanglement properties of interacting Fermi liquids in two dimensions

An Analytic Framework for the Information Goods Market and Its Application to Microsoft

(Statement of Responsibility) by Jeremy B. McMinis(Thesis) Thesis (B.A.) -- New College of Florida, 2001(Electronic Access) RESTRICTED TO NCF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE(Bibliography) Includes bibliographical references.(Source of Description) This bibliographic record is available under the Creative Commons CC0 public domain dedication. The New College of Florida, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.(Local) Faculty Sponsor: Strobel, Frederic

The transition to the metallic state in low density hydrogen Calculation of metallic and insulating phases of V2O3 by hybrid density functionals Role of electronic correlation in high-low temperature phase transition of hexagonal nickel sulfide: A compara

Electronic structure, charge and orbital order and metal-insulator transition in nickelates AIP Conf. Proc. 1512, 82 [http://d

Molecular to atomic phase transition in hydrogen under high pressure

The metallization of high-pressure hydrogen, together with the associated molecular to atomic transition, is one of the most important problems in the field of high-pressure physics. It is also currently a matter of intense debate due to the existence of conflicting experimental reports on the observation of metallic hydrogen on a diamond-anvil cell. Theoretical calculations have typically relied on a mean-field description of electronic correlation through density functional theory, a theory with well-known limitations in the description of metal-insulator transitions. In fact, the predictions of the pressure-driven dissociation of molecules in high-pressure hydrogen by density functional theory is strongly affected by the chosen exchange-correlation functional. In this Letter, we use quantum Monte Carlo calculations to study the molecular to atomic transition in hydrogen. We obtain a transition pressure of 447(3) GPa, in excellent agreement with the best experimental estimate of the transition 450 GPa based on an extrapolation to zero band gap from experimental measurements. Additionally, we find that C2/c is stable almost up to the molecular to atomic transition, in contrast to previous density functional theory (DFT) and DFT + quantum Monte Carlo studies which predict large stability regimes for intermediary molecular phases.11Nsciescopu