Quantum Simulation of the Universal Features of the Polyakov Loop.

Lattice gauge theories are fundamental to our understanding of high-energy physics. Nevertheless, the search for suitable platforms for their quantum simulation has proven difficult. We show that the Abelian Higgs model in 1+1 dimensions is a prime candidate for an experimental quantum simulation of a lattice gauge theory. To this end, we use a discrete tensor reformulation to smoothly connect the space-time isotropic version used in most numerical lattice simulations to the continuous-time limit corresponding to the Hamiltonian formulation. The eigenstates of the Hamiltonian are neutral for periodic boundary conditions, but we probe the nonzero charge sectors by introducing either a Polyakov loop or an external electric field. In both cases we obtain universal functions relating the mass gap, the gauge coupling, and the spatial size, which are invariant under the deformation of the temporal lattice spacing. We propose to use a physical multileg ladder of atoms trapped in optical lattices and interacting with Rydberg-dressed interactions to quantum simulate the model and check the universal features. Our results provide a path to the analog quantum simulation of lattice gauge theories with atoms in optical lattices.

Fine structure of the entanglement entropy in the O(2) model.

We compare two calculations of the particle density in the superfluid phase of the O(2) model with a chemical potential µ in 1+1 dimensions. The first relies on exact blocking formulas from the Tensor Renormalization Group (TRG) formulation of the transfer matrix. The second is a worm algorithm. We show that the particle number distributions obtained with the two methods agree well. We use the TRG method to calculate the thermal entropy and the entanglement entropy. We describe the particle density, the two entropies and the topology of the world lines as we increase µ to go across the superfluid phase between the first two Mott insulating phases. For a sufficiently large temporal size, this process reveals an interesting fine structure: the average particle number and the winding number of most of the world lines in the Euclidean time direction increase by one unit at a time. At each step, the thermal entropy develops a peak and the entanglement entropy increases until we reach half-filling and then decreases in a way that approximately mirrors the ascent. This suggests an approximate fermionic picture.

B→πll Form Factors for New Physics Searches from Lattice QCD.

The rare decay B→πℓ^{+}ℓ^{-} arises from b→d flavor-changing neutral currents and could be sensitive to physics beyond the standard model. Here, we present the first ab initio QCD calculation of the B→π tensor form factor f_{T}. Together with the vector and scalar form factors f_{+} and f_{0} from our companion work [J. A. Bailey et al., Phys. Rev. D 92, 014024 (2015)], these parametrize the hadronic contribution to B→π semileptonic decays in any extension of the standard model. We obtain the total branching ratio BR(B^{+}→π^{+}µ^{+}µ^{-})=20.4(2.1)×10^{-9} in the standard model, which is the most precise theoretical determination to date, and agrees with the recent measurement from the LHCb experiment [R. Aaij et al., J. High Energy Phys. 12 (2012) 125].

Tensor renormalization group study of classical XY model on the square lattice.

Using the tensor renormalization group method based on the higher-order singular value decomposition, we have studied the thermodynamic properties of the continuous XY model on the square lattice. The temperature dependence of the free energy, the internal energy, and the specific heat agree with the Monte Carlo calculations. From the field dependence of the magnetic susceptibility, we find the Kosterlitz-Thouless transition temperature to be 0.8921(19), consistent with the Monte Carlo as well as the high temperature series expansion results. At the transition temperature, the critical exponent δ is estimated as 14.5, close to the analytic value by Kosterlitz.

Refining new-physics searches in B→Dτν with lattice QCD.

The semileptonic decay channel B→Dτν is sensitive to the presence of a scalar current, such as that mediated by a charged-Higgs boson. Recently, the BABAR experiment reported the first observation of the exclusive semileptonic decay B→Dτ(-)ν, finding an approximately 2σ disagreement with the standard-model prediction for the ratio R(D)=BR(B→Dτν)/BR(B→Dℓν), where ℓ = e,µ. We compute this ratio of branching fractions using hadronic form factors computed in unquenched lattice QCD and obtain R(D)=0.316(12)(7), where the errors are statistical and total systematic, respectively. This result is the first standard-model calculation of R(D) from ab initio full QCD. Its error is smaller than that of previous estimates, primarily due to the reduced uncertainty in the scalar form factor f(0)(q(2)). Our determination of R(D) is approximately 1σ higher than previous estimates and, thus, reduces the tension with experiment. We also compute R(D) in models with electrically charged scalar exchange, such as the type-II two-Higgs-doublet model. Once again, our result is consistent with, but approximately 1σ higher than, previous estimates for phenomenologically relevant values of the scalar coupling in the type-II model. As a by-product of our calculation, we also present the standard-model prediction for the longitudinal-polarization ratio P(L)(D)=0.325(4)(3).

New applications of the renormalization group method in physics: a brief introduction.

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

Fisher's zeros as the boundary of renormalization group flows in complex coupling spaces.

We propose new methods to extend the renormalization group transformation to complex coupling spaces. We argue that Fisher's zeros are located at the boundary of the complex basin of attraction of infrared fixed points. We support this picture with numerical calculations at finite volume for two-dimensional O(N) models in the large-N limit and the hierarchical Ising model. We present numerical evidence that, as the volume increases, the Fisher's zeros of four-dimensional pure gauge SU(2) lattice gauge theory with a Wilson action stabilize at a distance larger than 0.15 from the real axis in the complex ß=4/g{2} plane. We discuss the implications for proofs of confinement and searches for nontrivial infrared fixed points in models beyond the standard model.

Small numerators cancelling small denominators of the high-temperature scaling variables: a systematic explanation in arbitrary dimensions.

We describe a method to express the susceptibility and higher derivatives of the free energy in terms of the scaling variables (Wegner's nonlinear scaling fields) associated with the high-temperature (HT) fixed point of the Dyson hierarchical model in arbitrary dimensions. We give a closed form solution of the linearized problem. We check that up to order 7 in the HT expansion, all the poles ("small denominators") that would naively appear in some positive dimension are canceled by zeros ("small numerators"). The requirement of continuity in the dimension can be used to lift ambiguities which appear in calculations at fixed dimension. We show that the existence of a HT phase in the infinite volume limit for a continuous set of values of the dimension, requires that this mechanism works to all orders. On the other hand, most poles at negative values of the dimensional parameter [where the free energy density is not well-defined, but renormalization group (RG) flows can be studied] persist and reflect the fact that for special negative values of the dimension, finite-size corrections become leading terms. We show that the inverse problem is also free of small denominator problems and that the initial values of the scaling variables can be expressed in terms of the infinite volume limit of the susceptibility and higher derivatives of the free energy. We discuss the existence of an infinite number of conserved quantities (RG invariants) and their relevance for the calculation of universal ratios of critical amplitudes.

Simple method to make asymptotic series of Feynman diagrams converge.

We show that, for two nontrivial lambda phi(4) problems (the anharmonic oscillator and the Landau-Ginzburg hierarchical model), improved perturbative series can be obtained by cutting off the large field contributions. The modified series converge to values exponentially close to the exact ones. For lambda larger than some critical value, the method outperforms Padé's approximants and Borel summations. The method can also be used for series which are not Borel summable such as the double-well potential series. We show that semiclassical methods can be used to calculate the modified Feynman rules, estimate the error, and optimize the field cutoff.

Small numerators canceling small denominators: is Dyson's hierarchical model solvable?

We present an analytical method to solve Dyson's hierarchical model, involving the scaling variables near the high-temperature fixed point. The procedure seems plagued by small denominators as in perturbative expansions near integrable systems in Hamiltonian mechanics. However, in 36 cases considered, a zero denominator always comes with a zero numerator. We conjecture that these cancellations occur in general, allowing the application of the analytical method and suggesting that the model has remarkable features reminiscent of the integrable systems.

Nonuniversal quantities from dual renormalization group transformations.

Using a simplified version of the renormalization group (RG) transformation of Dyson's hierarchical model, we show that one can calculate all the nonuniversal quantities entering into the scaling laws by combining an expansion about the high-temperature fixed point with a dual expansion about the critical point. The magnetic susceptibility is expressed in terms of two dual quantities transforming covariantly under an RG transformation and has a smooth behavior in the high-temperature limit. Using the analogy with Hamiltonian mechanics, the simplified example discussed here is similar to the anharmonic oscillator, while more realistic examples can be thought of as coupled oscillators, allowing resonance phenomena.