Many-Body Density Matrices for Free Fermions

Building upon an analytical technique introduced by Chung and Peschel [M. Chung and I. Peschel, Phys. Rev. B 64, art. 064412 (2001)], we calculated the density matrix rho_B of a finite block of B sites within an infinite system of free spinless fermions. In terms of the block Green function matrix G (whose elements are G_ij = , where c_i^+ and c_j are fermion creation and annihilation operators acting on sites i and j within the block respectively), the density matrix can be written as rho_B = det(1 - G) exp[ sum_ij (log G(1 - G^{-1})_ij c_i^+ c_j]. Implications of such a result to Hilbert space truncation for real-space renormalization schemes is discussed.Comment: 12 pages in RevTeX4 format. Uses amsmath, bbold, dcolumn and mathrsfs package

Knowledge Evolution in Physics Research: An Analysis of Bibliographic Coupling Networks

Even as we advance the frontiers of physics knowledge, our understanding of how this knowledge evolves remains at the descriptive levels of Popper and Kuhn. Using the APS publications data sets, we ask in this letter how new knowledge is built upon old knowledge. We do so by constructing year-to-year bibliographic coupling networks, and identify in them validated communities that represent different research fields. We then visualize their evolutionary relationships in the form of alluvial diagrams, and show how they remain intact through APS journal splits. Quantitatively, we see that most fields undergo weak Popperian mixing, and it is rare for a field to remain isolated/undergo strong mixing. The sizes of fields obey a simple linear growth with recombination. We can also reliably predict the merging between two fields, but not for the considerably more complex splitting. Finally, we report a case study of two fields that underwent repeated merging and splitting around 1995, and how these Kuhnian events are correlated with breakthroughs on BEC, quantum teleportation, and slow light. This impact showed up quantitatively in the citations of the BEC field as a larger proportion of references from during and shortly after these events.Comment: 14 pages, 14 figures, 1 tabl

Using Machine Learning to Predict the Evolution of Physics Research

The advancement of science as outlined by Popper and Kuhn is largely qualitative, but with bibliometric data it is possible and desirable to develop a quantitative picture of scientific progress. Furthermore it is also important to allocate finite resources to research topics that have growth potential, to accelerate the process from scientific breakthroughs to technological innovations. In this paper, we address this problem of quantitative knowledge evolution by analysing the APS publication data set from 1981 to 2010. We build the bibliographic coupling and co-citation networks, use the Louvain method to detect topical clusters (TCs) in each year, measure the similarity of TCs in consecutive years, and visualize the results as alluvial diagrams. Having the predictive features describing a given TC and its known evolution in the next year, we can train a machine learning model to predict future changes of TCs, i.e., their continuing, dissolving, merging and splitting. We found the number of papers from certain journals, the degree, closeness, and betweenness to be the most predictive features. Additionally, betweenness increases significantly for merging events, and decreases significantly for splitting events. Our results represent a first step from a descriptive understanding of the Science of Science (SciSci), towards one that is ultimately prescriptive.Comment: 24 pages, 10 figures, 4 tables, supplementary information is include

Stochastic boundary conditions for molecular dynamics simulations

In this paper we develop a stochastic boundary conditions (SBC) for event-driven molecular dynamics simulations of a finite volume embedded within an infinite environment. In this method, we first collect the statistics of injection/ejection events in periodic boundary conditions (PBC). Once sufficient statistics are collected, we remove the PBC and turn on the SBC. In the SBC simulations, we allow particles leaving the system to be truly ejected from the simulation, and randomly inject particles at the boundaries by resampling from the injection/ejection statistics collected from the current or previous simulations. With the SBC, we can measure thermodynamic quantities within the grand canonical ensemble, based on the particle number and energy fluctuations. To demonstrate how useful the SBC algorithm is, we simulated a hard disk gas and measured the pair distribution function, the compressibility and the specific heat, comparing them against literature values.Comment: 24 pages, 16 figure

Correlation density matrix: an unbiased analysis of exact diagonalizations

Given the ground state wavefunction for an interacting lattice model, we define a "correlation density matrix"(CDM) for two disjoint, separated clusters $A$ and $B$, to be the density matrix of their union, minus the direct product of their respective density matrices. The CDM can be decomposed systematically by a numerical singular value decomposition, to provide a systematic and unbiased way to identify the operator(s) dominating the correlations, even unexpected ones.Comment: (4pp, 2 figures

Exact ground states and correlation functions of chain and ladder models of interacting hardcore bosons or spinless fermions

By removing one empty site between two occupied sites, we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions without nearest-neighbor repulsion respectively, and ultimately in terms of the one-dimensional Fermi sea. We then introduce the intervening-particle expansion, where we write correlation functions in such ground states as a systematic sum over conditional expectations, each of which can be ultimately mapped to a one-dimensional Fermi-sea expectation. Various ground-state correlation functions are calculated for the bosonic and fermionic chains with infinite nearest-neighbor repulsion, as well as for a ladder model of spinless fermions with infinite nearest-neighbor repulsion and correlated hopping in three limiting cases. We find that the decay of these correlation functions are governed by surprising power-law exponents.Comment: 20 pages, 18 figures, RevTeX4 clas