Measuring von Neumann entanglement entropies without wave functions

We present a method to measure the von Neumann entanglement entropy of ground states of quantum many-body systems which does not require access to the system wave function. The technique is based on a direct thermodynamic study of entanglement Hamiltonians, whose functional form is available from field theoretical insights. The method is applicable to classical simulations such as quantum Monte Carlo methods, and to experiments that allow for thermodynamic measurements such as the density of states, accessible via quantum quenches. We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law in the entanglement entropy, the number of Goldstone bosons, and to check a recent conjecture on geometric entanglement contribution at critical points described by strongly coupled field theories

Majorana Quasi-Particles Protected by Z2\mathbb{Z}_2 Angular Momentum Conservation

We show how angular momentum conservation can stabilise a symmetry-protected quasi-topological phase of matter supporting Majorana quasi-particles as edge modes in one-dimensional cold atom gases. We investigate a number-conserving four-species Hubbard model in the presence of spin-orbit coupling. The latter reduces the global spin symmetry to an angular momentum parity symmetry, which provides an extremely robust protection mechanism that does not rely on any coupling to additional reservoirs. The emergence of Majorana edge modes is elucidated using field theory techniques, and corroborated by density-matrix-renormalization-group simulations. Our results pave the way toward the observation of Majorana edge modes with alkaline-earth-like fermions in optical lattices, where all basic ingredients for our recipe - spin-orbit coupling and strong inter-orbital interactions - have been experimentally realized over the last two years.Comment: 12 pages (6 + 6 supplementary material

Real-time dynamics of lattice gauge theories with a few-qubit quantum computer

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic long-range interactions, which have a direct and efficient implementation on an ion trap architecture. We explore the Schwinger mechanism of particle-antiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the real-time evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments, the long-term vision being the extension to real-time quantum simulations of non-Abelian lattice gauge theories

Intrinsic Dimension of Path Integrals: Data-Mining Quantum Criticality and Emergent Simplicity

Quantum many-body systems are characterized by patterns of correlations defining highly nontrivial manifolds when interpreted as data structures. Physical properties of phases and phase transitions are typically retrieved via correlation functions, that are related to observable response functions. Recent experiments have demonstrated capabilities to fully characterize quantum many-body systems via wave-function snapshots, opening new possibilities to analyze quantum phenomena. Here, we introduce a method to data mine the correlation structure of quantum partition functions via their path integral (or equivalently, stochastic series expansion) manifold. We characterize path-integral manifolds generated via state-of-the-art quantum Monte Carlo methods utilizing the intrinsic dimension (ID) and the variance of distances between nearest-neighbor (NN) configurations: the former is related to data-set complexity, while the latter is able to diagnose connectivity features of points in configuration space. We show how these properties feature universal patterns in the vicinity of quantum criticality, that reveal how data structures simplify systematically at quantum phase transitions. This is further reflected by the fact that both ID and variance of NN distances exhibit universal scaling behavior in the vicinity of second-order and Berezinskii-Kosterlitz-Thouless critical points. Finally, we show how non-Abelian symmetries dramatically influence quantum data sets, due to the nature of (noncommuting) conserved charges in the quantum case. Complementary to neural-network representations, our approach represents a first elementary step towards a systematic characterization of path-integral manifolds before any dimensional reduction is taken, that is informative about universal behavior and complexity, and can find immediate application to both experiments and Monte Carlo simulations

Topological Devil's staircase in atomic two-leg ladders

We show that a hierarchy of topological phases in one dimension - a topological Devil's staircase - can emerge at fractional filling fractions in interacting systems, whose single-particle band structure describes a topological or a crystalline topological insulator. Focusing on a specific example in the BDI class, we present a field-theoretical argument based on bosonization that indicates how the system, as a function of the filling fraction, hosts a series of density waves. Subsequently, based on a numerical investigation of the low-lying energy spectrum, Wilczek-Zee phases, and entanglement spectra, we show that they are symmetry protected topological phases. In sharp contrast to the non-interacting limit, these topological density waves do not follow the bulk-edge correspondence, as their edge modes are gapped. We then discuss how these results are immediately applicable to models in the AIII class, and to crystalline topological insulators protected by inversion symmetry. Our findings are immediately relevant to cold atom experiments with alkaline-earth atoms in optical lattices, where the band structure properties we exploit have been recently realized

Iron Speciation and Iron Binding Proteins in Arthrospira platensis Grown in Media Containing Different Iron Concentrations

Cyanobacteria are characterized by high iron content. This study investigated the effects of varying iron concentrations (1, 5, and 10 mg L−1) in the culture media on the biochemical composition and the iron bioaccumulation and speciation in Arthrospira platensis F&M‐C256. Iron content measured in biomasses varied from 0.35 to 2.34 mg g−1 dry weight depending on the iron concentration in the culture media. These biomasses can be considered of interest for the production of spirulina‐based supplements with low and high iron content. Iron speciation was studied using size exclusion chromatography followed by atomic absorption spectrometry and proteomic analysis. The role of C‐phycocyanin as an iron binding protein was also investigated. Overall, the present results provide a better understanding of iron metabolism in cyanobacteria and a foundation for further studies

Boundary time crystals

This work was supported in part by \Progetti Interni - Scuola Normale Superiore" (A.R.), EU- 691 QUIC (R.F. and A.R.), CRF Singapore Ministry of Education (CPR-QSYNC 692) (R.F.), EPSRC program TOPNES (EP/I031014/1) (J.K.).In this work we introduce boundary time crystals. Here continuous time-translation symmetry breaking occurs only in a macroscopic fraction of a many-body quantum system. After introducing their definition and properties, we analyze in detail a solvable model where an accurate scaling analysis can be performed. The existence of the boundary time crystals is intimately connected to the emergence of a time-periodic steady state in the thermodynamic limit of a many-body open quantum system. We also discuss connections to quantum synchronization.PostprintPeer reviewe

Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons

One of the most remarkable results of quantum mechanics is the fact that many-body quantum systems may exhibit phase transitions even at zero temperature. Quantum fluctuations, deeply rooted in Heisenberg's uncertainty principle, and not thermal fluctuations, drive the system from one phase to another. Typically, the relative strength of two competing terms in the system's Hamiltonian is changed across a finite critical value. A well-known example is the Mott-Hubbard quantum phase transition from a superfluid to an insulating phase, which has been observed for weakly interacting bosonic atomic gases. However, for strongly interacting quantum systems confined to lower-dimensional geometry a novel type of quantum phase transition may be induced for which an arbitrarily weak perturbation to the Hamiltonian is sufficient to drive the transition. Here, for a one-dimensional (1D) quantum gas of bosonic caesium atoms with tunable interactions, we observe the commensurate-incommensurate quantum phase transition from a superfluid Luttinger liquid to a Mott-insulator. For sufficiently strong interactions, the transition is induced by adding an arbitrarily weak optical lattice commensurate with the atomic granularity, which leads to immediate pinning of the atoms. We map out the phase diagram and find that our measurements in the strongly interacting regime agree well with a quantum field description based on the exactly solvable sine-Gordon model. We trace the phase boundary all the way to the weakly interacting regime where we find good agreement with the predictions of the 1D Bose-Hubbard model. Our results open up the experimental study of quantum phase transitions, criticality, and transport phenomena beyond Hubbard-type models in the context of ultracold gases

Condensed Matter Theory of Dipolar Quantum Gases

Recent experimental breakthroughs in trapping, cooling and controlling ultracold gases of polar molecules, magnetic and Rydberg atoms have paved the way toward the investigation of highly tunable quantum systems, where anisotropic, long-range dipolar interactions play a prominent role at the many-body level. In this article we review recent theoretical studies concerning the physics of such systems. Starting from a general discussion on interaction design techniques and microscopic Hamiltonians, we provide a summary of recent work focused on many-body properties of dipolar systems, including: weakly interacting Bose gases, weakly interacting Fermi gases, multilayer systems, strongly interacting dipolar gases and dipolar gases in 1D and quasi-1D geometries. Within each of these topics, purely dipolar effects and connections with experimental realizations are emphasized.Comment: Review article; submitted 09/06/2011. 158 pages, 52 figures. This document is the unedited author's version of a Submitted Work that was subsequently accepted for publication in Chemical Reviews, copyright American Chemical Society after peer review. To access the final edited and published work, a link will be provided soo