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

Entanglement guided search for parent Hamiltonians

We introduce a method for the search of parent Hamiltonians of input wave-functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several non-trivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave-functions considerably simplifies the search for parent Hamiltonians.Comment: 5 pages, 5 figures, supplementary materia

Trimer liquids and crystals of polar molecules in coupled wires

We investigate the pairing and crystalline instabilities of bosonic and fermionic polar molecules confined to a ladder geometry. By means of analytical and quasi-exact numerical techniques, we show that gases of composite molecular dimers as well as trimers can be stabilized as a function of the density difference between the wires. A shallow optical lattice can pin both liquids, realizing crystals of composite bosons or fermions. We show that these exotic quantum phases should be realizable under current experimental conditions in finite-size confining potentials.Comment: 5 pages, 3 figures plus additional material; Accepted for publication in Phys. Rev. Let

Entanglement Hamiltonians of lattice models via the Bisognano-Wichmann theorem

The modular (or entanglement) Hamiltonian correspondent to the half-space bipartition of a quantum state uniquely characterizes its entanglement properties. However, in the context of lattice models, its explicit form is analytically known only for the two spin chains and certain free theories in one dimension. In this work, we provide a thorough investigation of entanglement Hamiltonians in lattice models obtained via the Bisognano-Wichmann theorem, which provides an explicit functional form for the entanglement Hamiltonian itself in quantum field theory. Our study encompasses a variety of one- and two-dimensional models, supporting diverse quantum phases and critical points, and, most importantly, scanning several universality classes, including Ising, Potts, and Luttinger liquids. We carry out extensive numerical simulations based on the density matrix renormalization group method, exact diagonalization, and quantum Monte Carlo. In particular, we compare the exact entanglement properties and correlation functions to those obtained applying the Bisognano-Wichmann theorem on the lattice. We carry out this comparison on both the eigenvalues and eigenvectors of the entanglement Hamiltonian, and expectation values of correlation functions and order parameters. Our results evidence that as long as the low-energy description of the lattice model is well captured by a Lorentz-invariant quantum field theory, the Bisognano-Wichmann theorem provides a qualitatively and quantitatively accurate description of the lattice entanglement Hamiltonian. The resulting framework paves the way to direct studies of entanglement properties utilizing well-established statistical mechanics methods and experiments

1D Quantum Liquids with Power-Law Interactions: a Luttinger Staircase with Polar Molecules

We study one dimensional fermionic and bosonic gases with repulsive power-law interactions $1/|x|^{\beta}$, with $\beta>1$, in the framework of Tomonaga-Luttinger liquid (LL) theory. We obtain an accurate analytical expression linking the LL parameter to the microscopic Hamiltonian, for arbitrary $\beta$ and strength of the interactions. In the presence of a small periodic potential, power-law interactions make the LL unstable towards the formation of a cascade of lattice solids with fractional filling, thus forming a "Luttinger staircase". Several of these quantum phases and phase transitions are realized with groundstate polar molecules and weakly-bound magnetic Feshbach molecules.Comment: 4 pages, 3 figures, one table, updated discussions in Pag 2,

Entanglement topological invariants for one-dimensional topological superconductors

Entanglement provides characterizing features of true topological order in two-dimensional systems. We show how entanglement of disconnected partitions defines topological invariants for one-dimensional topological superconductors. These order parameters quantitatively capture the entanglement that is possible to distill from the ground-state manifold and are thus quantized to 0 or log2. Their robust quantization property is inferred from the underlying lattice gauge theory description of topological superconductors and is corroborated via exact solutions and numerical simulations. Transitions between topologically trivial and nontrivial phases are accompanied by scaling behavior, a hallmark of genuine order parameters, captured by entanglement critical exponents. These order parameters are experimentally measurable utilizing state-of-the-art techniques

Supplementation of Boswellia serrata and Salix alba Extracts during the Early Laying Phase: Effects on Serum and Albumen Proteins, Trace Elements, and Yolk Cholesterol

Abstract: Extracts from Boswellia serrata (Bs) and Salix alba (Sa) are used as supplement in poultry feed. The aims of this research were to study possible effects of a dietary supplementation with Bs and Sa on serum and albumen proteins, zinc and iron, and yolk cholesterol content in Leg-horn hens during the critical phase of the onset of laying. A total of 120 pullets, 17 weeks of age, were assigned to 2 groups (Control (C) and Treated (T), n = 60 each). The T group received a diet supplemented with 0.3% of dry extracts of Bs (5%) and Sa (5%) for 12 weeks. The study lasted 19 weeks. Serum proteins were fractionated using agarose gel electrophoresis (AGE) and SDS-polyacrylamide gel electrophoresis (SDS-PAGE). Trace elements were determined in serum using atomic absorption spectrometry and yolk cholesterol was determined using a colorimetric test. No significant differences were observed between control and supplemented hens for ana-lyzed biochemical indices. Moreover, the supplementation with phytoextracts did not negative-ly affect the physiological variations of serum proteins therefore it can be safely used as a treatment to prevent inflammatory states at onset and during the early laying phase

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