Disorder by disorder and flat bands in the kagome transverse field Ising model

We study the transverse field Ising model on a kagome and a triangular lattice using high-order series expansions about the high-field limit. For the triangular lattice our results confirm a second-order quantum phase transition in the 3d XY universality class. Our findings for the kagome lattice indicate a notable instance of a disorder by disorder scenario in two dimensions. The latter follows from a combined analysis of the elementary gap in the high- and low-field limit which is shown to stay finite for all fields h. Furthermore, the lowest one-particle dispersion for the kagome lattice is extremely flat acquiring a dispersion only from order eight in the 1/h limit. This behaviour can be traced back to the existence of local modes and their breakdown which is understood intuitively via the linked cluster expansion.Comment: 11 pages, 11 figrue

Comparison of Relativistic Nucleon-Nucleon Interactions

We investigate the difference between those relativistic models based on interpreting a realistic nucleon-nucleon interaction as a perturbation of the square of a relativistic mass operator and those models that use the method of Kamada and Gl\"ockle to construct an equivalent interaction to add to the relativistic mass operator. Although both models reproduce the phase shifts and binding energy of the corresponding non-relativistic model, they are not scattering equivalent. The example of elastic electron-deuteron scattering in the one-photon-exchange approximation is used to study the sensitivity of three-body observables to these choices. Our conclusion is that the differences in the predictions of the two models can be understood in terms of the different ways in which the relativistic and non-relativistic $S$-matrices are related. We argue that the mass squared method is consistent with conventional procedures used to fit the Lorentz-invariant cross section as a function of the laboratory energy.Comment: Revtex 13 pages, 5 figures, corrected some typo

Translationally-invariant coupled-cluster method for finite systems

The translational invariant formulation of the coupled-cluster method is presented here at the complete SUB(2) level for a system of nucleons treated as bosons. The correlation amplitudes are solution of a non-linear coupled system of equations. These equations have been solved for light and medium systems, considering the central but still semi-realistic nucleon-nucleon S3 interaction.Comment: 16 pages, 2 Postscript figures, to be published in Nucl. Phys.

Transverse Deformation of Parton Distributions and Transversity Decomposition of Angular Momentum

Impact parameter dependent parton distributions are transversely distorted when one considers transversely polarized nucleons and/or quarks. This provides a physical mechanism for the T-odd Sivers effect in semi-inclusive deep-inelastic scattering. The transverse distortion can also be related to Ji's sum rule for the angular momentum carried by the quarks. The distortion of chirally odd impact parameter dependent parton distributions is related to chirally odd GPDs. This result is used to provide a decomposition of the quark angular momentum w.r.t. quarks of definite transversity. Chirally odd GPDs can thus be used to determine the correlation between quark spin and quark angular momentum in unpolarized nucleons. Based on the transverse distortion, we also suggest a qualitative connection between chirally odd GPDs and the Boer-Mulders effect.Comment: 12 pages, 1 figure, version to appear in PR

An extension of the coupled-cluster method: A variational formalism

A general quantum many-body theory in configuration space is developed by extending the traditional coupled cluter method (CCM) to a variational formalism. Two independent sets of distribution functions are introduced to evaluate the Hamiltonian expectation. An algebraic technique for calculating these distribution functions via two self-consistent sets of equations is given. By comparing with the traditional CCM and with Arponen's extension, it is shown that the former is equivalent to a linear approximation to one set of distribution functions and the later is equivalent to a random-phase approximation to it. In additional to these two approximations, other higher-order approximation schemes within the new formalism are also discussed. As a demonstration, we apply this technique to a quantum antiferromagnetic spin model.Comment: 15 pages. Submitted to Phys. Rev.

A light-front coupled cluster method

A new method for the nonperturbative solution of quantum field theories is described. The method adapts the exponential-operator technique of the standard many-body coupled-cluster method to the Fock-space eigenvalue problem for light-front Hamiltonians. This leads to an effective eigenvalue problem in the valence Fock sector and a set of nonlinear integral equations for the functions that define the exponential operator. The approach avoids at least some of the difficulties associated with the Fock-space truncation usually used.Comment: 8 pages, 1 figure; to appear in the proceedings of LIGHTCONE 2011, 23-27 May 2011, Dalla

Unbounded lower bound for k-server against weak adversaries

We study the resource augmented version of the $k$-server problem, also known as the $k$-server problem against weak adversaries or the $(h,k)$-server problem. In this setting, an online algorithm using $k$ servers is compared to an offline algorithm using $h$ servers, where $h\le k$. For uniform metrics, it has been known since the seminal work of Sleator and Tarjan (1985) that for any $\epsilon>0$, the competitive ratio drops to a constant if $k=(1+\epsilon) \cdot h$. This result was later generalized to weighted stars (Young 1994) and trees of bounded depth (Bansal et al. 2017). The main open problem for this setting is whether a similar phenomenon occurs on general metrics. We resolve this question negatively. With a simple recursive construction, we show that the competitive ratio is at least $\Omega(\log \log h)$, even as $k\to\infty$. Our lower bound holds for both deterministic and randomized algorithms. It also disproves the existence of a competitive algorithm for the infinite server problem on general metrics.Comment: To appear in STOC 202

Nuclear Structure Calculations with Coupled Cluster Methods from Quantum Chemistry

We present several coupled-cluster calculations of ground and excited states of 4He and 16O employing methods from quantum chemistry. A comparison of coupled cluster results with the results of exact diagonalization of the hamiltonian in the same model space and other truncated shell-model calculations shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei, with much less computational effort than traditional large-scale shell-model approaches. Unless truncations are made, for nuclei like 16O, full-fledged shell-model calculations with four or more major shells are not possible. However, these and even larger systems can be studied with the coupled cluster methods due to the polynomial rather than factorial scaling inherent in standard shell-model studies. This makes the coupled cluster approaches, developed in quantum chemistry, viable methods for describing weakly bound systems of interest for future nuclear facilities.Comment: 10 pages, Elsevier latex style, Invited contribution to INPC04 proceedings, to appear in Nuclear Physics

Coupled-cluster theory of a gas of strongly-interacting fermions in the dilute limit

We study the ground-state properties of a dilute gas of strongly-interacting fermions in the framework of the coupled-cluster expansion (CCE). We demonstrate that properties such as universality, opening of a gap in the excitation spectrum and applicability of s-wave approximations appear naturally in the CCE approach. In the zero-density limit, we show that the ground-state energy density depends on only one parameter which in turn may depend at most on the spatial dimensionality of the system.Comment: 7 figure

Vacuum Structures in Hamiltonian Light-Front Dynamics

Hamiltonian light-front dynamics of quantum fields may provide a useful approach to systematic non-perturbative approximations to quantum field theories. We investigate inequivalent Hilbert-space representations of the light-front field algebra in which the stability group of the light-front is implemented by unitary transformations. The Hilbert space representation of states is generated by the operator algebra from the vacuum state. There is a large class of vacuum states besides the Fock vacuum which meet all the invariance requirements. The light-front Hamiltonian must annihilate the vacuum and have a positive spectrum. We exhibit relations of the Hamiltonian to the nontrivial vacuum structure.Comment: 16 pages, report \# ANL-PHY-7524-TH-93, (Latex