Supersymmetric quantum mechanics on the lattice: II. Exact results

Simulations of supersymmetric field theories with spontaneously broken supersymmetry require in addition to the ultraviolet regularisation also an infrared one, due to the emergence of the massless Goldstino. The intricate interplay between ultraviolet and infrared effects towards the continuum and infinite volume limit demands careful investigations to avoid potential problems. In this paper – the second in a series of three – we present such an investigation for N=2 supersymmetric quantum mechanics formulated on the lattice in terms of bosonic and fermionic bonds. In one dimension, the bond formulation allows to solve the system exactly, even at finite lattice spacing, through the construction and analysis of transfer matrices. In the present paper we elaborate on this approach and discuss a range of exact results for observables such as the Witten index, the mass spectra and Ward identities.

Supersymmetric quantum mechanics on the lattice: III. Simulations and algorithms

In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a fluctuating open fermion string. It guarantees sufficient tunnelling between the topological sectors, and hence provides a solution to the fermion sign problem affecting systems with broken supersymmetry. Moreover, the algorithm shows no critical slowing down even in the massless limit and can hence handle the massless Goldstino mode emerging in the supersymmetry broken phase. In this paper – the third in a series of three – we present the details of the simulation algorithm and demonstrate its efficiency by means of a few examples.

Compactified N = 1 supersymmetric Yang-Mills theory on the lattice: continuity and the disappearance of the deconfinement transition

Fermion boundary conditions play a relevant role in revealing the confinement mechanism of N=1 supersymmetric Yang-Mills theory with one compactified space-time dimension. A deconfinement phase transition occurs for a sufficiently small compactification radius, equivalent to a high temperature in the thermal theory where antiperiodic fermion boundary conditions are applied. Periodic fermion boundary conditions, on the other hand, are related to the Witten index and confinement is expected to persist independently of the length of the compactified dimension. We study this aspect with lattice Monte Carlo simulations for different values of the fermion mass parameter that breaks supersymmetry softly. We find a deconfined region that shrinks when the fermion mass is lowered. Deconfinement takes place between two confined regions at large and small compactification radii, that would correspond to low and high temperatures in the thermal theory. At the smallest fermion masses we find no indication of a deconfinement transition. These results are a first signal for the predicted continuity in the compactification of supersymmetric Yang-Mills theory.

From doubled Chern–Simons–Maxwell lattice gauge theory to extensions of the toric code

We regularize compact and non-compact Abelian Chern–Simons–Maxwell theories on a spatial lattice using the Hamiltonian formulation. We consider a doubled theory with gauge fields living on a lattice and its dual lattice. The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link. The two electric field operators associated with the link-pair do not commute. In the non-compact case with gauge group R, each local Hilbert space is analogous to the one of a charged “particle” moving in the link-pair group space R2 in a constant “magnetic” background field. In the compact case, the link-pair group space is a torus U(1)2 threaded by k units of quantized “magnetic” flux, with k being the level of the Chern–Simons theory. The holonomies of the torus U(1)2 give rise to two self-adjoint extension parameters, which form two non-dynamical background lattice gauge fields that explicitly break the manifest gauge symmetry from U(1) to Z(k). The local Hilbert space of a link-pair then decomposes into representations of a magnetic translation group. In the pure Chern–Simons limit of a large “photon” mass, this results in a Z(k)-symmetric variant of Kitaev’s toric code, self-adjointly extended by the two non-dynamical background lattice gauge fields. Electric charges on the original lattice and on the dual lattice obey mutually anyonic statistics with the statistics angle . Non-Abelian U(k) Berry gauge fields that arise from the self-adjoint extension parameters may be interesting in the context of quantum information processing.

Hierarchical self-assembly of the DNA-grafted supramolecular polymers

Conjugation of functional entities with a specific set of optical, mechanical or biological properties to DNA strands allows engineering of sophisticated DNA-containing architectures. Among various hybrid systems, DNA-grafted polymers occupy an important place in modern materials science. In this contribution we present the non-covalent synthesis and properties of DNA-grafted linear supramolecular polymers (SPs), which are assembled in a controllable manner from short chimeric DNA-pyrene oligomers. The synthetic oligomers consist of two parts: a 10 nucleotides long DNA chain and a covalently attached segment of variable number of phosphodiester-linked pyrenes. The temperature-dependent formation of DNA-grafted SPs is described by a nucleation-elongation mechanism. The high tendency of pyrenes to aggregate in water, leads to the rapid formation of SPs. The core of the assemblies consists of stacked pyrenes. They form a 1D platform, to which the DNA chains are attached. Combined spectroscopic and microscopic studies reveal that the major driving forces of the polymerization are π-stacking of pyrenes and hydrophobic interactions, and DNA pairing contributes to a lesser extent. AFM and TEM experiments demonstrate that the 1D SPs appear as elongated ribbons with a length of several hundred nanometers. They exhibit an apparent helical structure with a pitch-to-pitch distance of 50±15 nm. Since DNA pairing is a highly selective process, the ongoing studies are aimed to utilize DNA-grafted SPs for the programmable arrangement of functional entities. For example, the addition of non-modified complementary DNA strands to the DNA-grafted SPs leads to the cooperative formation of higher-order assemblies. Also, our experiments suggest that the fluorescent pyrene core of 1D ribbons serves as an efficient donor platform for energy transfer applications.

Influence of polymers on microstructure and adhesive strength of cementitious tile adhesive mortars

The impact of polymer modification on the physical properties of cementitious mortars is investigated using a multimethod approach. Special emphasis is put on the identification and quantification of different polymer components within the cementitious matrix. With respect to thin-bed applications, particularly tile adhesives, the spatial distributions of latex, cellulose ether (CE), polyvinyl alcohol (PVA), and cement hydration products can be quantified. It is shown that capillary forces and evaporation induce water fluxes in the interconnected part of the pore system, which transport CE, PVA, and cement ions to the mortar interfaces. In contrast, the distribution of latex remains homogeneous. In combination with results from qualitative experiments, the quantitative findings allow reconstruction of the evolution from fresh to hardened mortar, including polymer film formation, cement hydration, and water migration. The resulting microstructure and the failure modes can be correlated with the final adhesive strength of the tile adhesive. The results demonstrate that skinning prior to tile inlaying can strongly reduce wetting properties of the fresh mortar and lower final adhesive strength.

From Ribbons to Networks: Hierarchical Organization of DNA-Grafted Supramolecular Polymers

DNA-grafted supramolecular polymers (SPs) allow the programmed organization of DNA in a highly regular, one-dimensional array. Oligonucleotides are arranged along the edges of pyrene-based helical polymers. Addition of complementary oligonucleotides triggers the assembly of individual nanoribbons resulting in the development of extended supramolecular networks. Network formation is enabled by cooperative coaxial stacking interactions of terminal GC base pairs. The process is accompanied by structural changes in the pyrene polymer core that can be followed spectroscopically. Network formation is reversible, and disassembly into individual ribbons is realized either via thermal denaturation or by addition of a DNA separator strand.

Interaction of the Trinuclear Triangular Secondary Building Unit [Cu 3 (μ 3 -OH)(μ-pz) 3 ] 2+ with 4,4′-Bipyridine. Structural Characterizations of New Coordination Polymers and Hexanuclear Cu II Clusters. 2°

By reacting 4,4′-bipyridine (bpy) with selected trinuclear triangular CuII complexes, [Cu3(μ3-OH)(μ-pz)3(RCOO)2(LL′)] [pz = pyrazolate anion; R = CH3, CH3CH2, CH2═CH, CH2═C(CH3); L, L′ = Hpz, H2O, MeOH] in MeOH, the substitution of monotopic ligands by ditopic bpy was observed. Depending on the stoichiometric reaction ratios, different compounds were isolated and structurally characterized. One- and two-dimensional coordination polymers (CPs), as well as two hexanuclear CuII clusters were identified. One of the hexanuclear clusters self-assembles into a supramolecular three-dimensional structure, and its crystal packing shows the presence of two intersecting channels, one of which is almost completely occupied by guest bpy, while in the second one guest water molecules are present. This compound also shows a reversible, thermally induced, single-crystal-to-single-crystal transition.

Synthesis and Structural Characterizations of New Coordination Polymers Generated by the Interaction Between the Trinuclear Triangular SBU [Cu 3 (μ 3 -OH)(μ-pz) 3 ] 2+ and 4,4′-Bipyridine. 3°

The reactions of 4,4′-bipyridine with selected trinuclear triangular copper(II) complexes, [Cu3(μ3-OH)(μ-pz)3(RCOO)2Lx], [pz = pyrazolate anion, R = CH3(CH2)n (2 ≤ n ≤ 5); L = H2O, MeOH, EtOH] yielded a series of 1D coordination polymers (CPs) based on the repetition of [Cu3(μ3-OH)(μ-pz)3] secondary building units joined by bipyridine. The CPs were characterized by conventional analytical methods (elemental analyses, ESI-MS, IR spectra) and single crystal XRD determinations. An unprecedented 1D CP, generated through the bipyridine bridging hexanuclear copper clusters moieties, two 1D CPs presenting structural analogies, and two monodimensional tapes having almost exactly superimposable structures, were obtained. In one case, the crystal packing makes evident the presence of small, not-connected pores, accounting for ca. 6% of free cell volume.

Smart Hybrid Polymers for Advanced Damascene Electroplating: Combination of Superfill and Leveling Properties

A successful bottom-up fill of single Damascene test features is achieved by using a two-component additive package consisting of bis-(sodium-sulfopropyl)-disulfide (SPS) and Imep polymers (polymerizates of imidazole and epichlorohydrin). In addition, a remarkable leveling effect is observed. Clearly, the Imep additive combines bottom-up fill capabilities with leveling characteristics in one single polymer component. These unique hybrid properties of the Imep are rationalized on the basis of an extended N-NDR (N-shaped negative differential resistance) being present in the linear-sweep voltammogram of the SPS/Imep additive system during Cu electrodeposition.

Supramolecular Polymers in DNA Nanotechnology

Creation of biocompatible functional materials is an important task in supramolecular chemistry. In this contribution, we report on noncovalent synthesis of DNA-grafted supramolecular polymers (SPs). DNA-grafted SPs enable programmed arrangement of oligonucleotides in a regular, tightly packed one-dimensional array. Further interactions of DNA-grafted SPs with complementary DNA strands leads to the formation of networks through highly cooperative G-C blunt-end stacking interactions. The structural changes in the polymeric core enable to monitor spectroscopically the stepwise formation of networks. Such stimuli-responsive supramolecular networks may lead to the development of DNA-based smart materials.

Standard model cross-over on the lattice

With the physical Higgs mass the standard model symmetry restoration phase transition is a smooth cross-over. We study the thermodynamics of the cross-over using numerical lattice Monte Carlo simulations of an effective SU(2)×U(1) gauge+Higgs theory, significantly improving on previously published results. We measure the Higgs field expectation value, thermodynamic quantities like pressure, energy density, speed of sound and heat capacity, and screening masses associated with the Higgs and Z fields. While the cross-over is smooth, it is very well defined with a width of only ∼5  GeV. We measure the cross-over temperature from the maximum of the susceptibility of the Higgs condensate, with the result Tc=159.5±1.5  GeV. Outside of the narrow cross-over region the perturbative results agree well with nonperturbative ones.