The generalization of the multi-scale entanglement renormalization ansatz (MERA) to continuous systems, or cMERA [Haegeman et al., Phys. Rev. Lett, 110, 100402 (2013)], is expected to become a powerful variational ansatz for the ground state of strongly interacting quantum field theories. In this paper we investigate, in the simpler context of Gaussian cMERA for free theories, the extent to which the cMERA state |Ψ Λ with finite UV cut-off Λ can capture the spacetime symmetries of the ground state |Ψ . For a free boson conformal field theory (CFT) in 1+1 dimensions as a concrete example, we build a quasi-local unitary transformation V that maps |Ψ into |Ψ Λ and show two main results. (i) Any spacetime symmetry of the ground state |Ψ is also mapped by V into a spacetime symmetry of the cMERA |Ψ Λ . However, while in the CFT the stress-energy tensor Tµν (x) (in terms of which all the spacetime symmetry generators are expressed) is local, the corresponding cMERA stress-energy tensor(ii) From the cMERA, we can extract quasi-local scaling operators O Λ α (x) characterized by the exact same scaling dimensions ∆α, conformal spins sα, operator product expansion coefficients C αβγ , and central charge c as the original CFT. Finally, we argue that these results should also apply to interacting theories. The study and numerical simulation of interacting quantum many-body systems is an extremely challenging task. Making progress often requires the use of a simplifying variational ansatz, such as the multi-scale entanglement renormalization ansatz (MERA) [1], which aims to describe the ground state of lattice Hamiltonians. The MERA can be visualized as the result of a unitary evolution, running from large distances to short distances, that maps an initial unentangled state into a complex many-body wavefunction by gradually introducing entanglement into the system, scale by scale. The success of the MERA in a large class of lattice systems, including systems with topological order [2] or at a quantum critical point [1,[3][4][5], teaches us that this entangling evolution in scale picture is a valid -and computationally powerful!-way of thinking about ground states and their intricate structure of correlations. With a built-in notion of the renormalization group [6], MERA is also actively investigated in several other contexts, from holography [7][8][9] (as a discrete realization of the AdS/CFT correspondence [10]) to statistical mechanics [11], error correction [12], and machine learning [13].The MERA formalism can also be applied to a quantum field theory (QFT), after introducing a lattice as a UV regulator. For instance, when applied to a conformal field theory (CFT) [14][15][16], corresponding to a critical QFT, lattice MERA has been seen to accurately reproduce the universal properties of the corresponding quantum phase transition (as given by the conformal data) [4, 5]. However, introducing a lattice has a devastating effect on the spacetime symmetries of the original QFT, * qhu@perimeterinstitute.ca with e.g. translatio...

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The compression‐compression fatigue performance of carbon nanotube (CNT) reinforced aluminium matrix composite foams (AMCFs) were investigated. The ε‐N curves of AMCFs are composed of three stages (the elastic, strain hardening, and rapid accumulation stages), while the fatigue strain of AMCFs accumulates very rapidly in stage III compared with Al foams. The fatigue strength of AMCFs with CNT contents of 2.0, 2.5, and 3.0 wt% increases by 6%, 44%, and 102% than Al foams, respectively. Different from Al foams' deformation of layer‐by‐layer, the main failure modes of AMCFs are the brittle fracture and collapse of pores within significant shear deformation bands under fatigue loading. The uniform distribution of CNTs and good interfacial bonding of CNTs and Al matrix is the important factor for the improvement of fatigue properties of AMCFs.

On the lattice, a renormalization group (RG) flow for two-dimensional partition functions expressed as a tensor network can be obtained using the tensor network renormalization (TNR) algorithm [G. Evenbly, G. Vidal, Phys. Rev. Lett. 115 (18), 180405 (2015)]. In this work we explain how to extend TNR to field theories in the continuum. First, a short-distance length scale 1/Λ is introduced in the continuum partition function by smearing the fields. The resulting object is still defined in the continuum but has no fluctuations at distances shorter than 1/Λ. An infinitesimal coarse-graining step is then generated by the combined action of a rescaling operator L and a disentangling operator K that implements a quasi-local field redefinition. As demonstrated for a free boson in two dimensions, continuous TNR exactly preserves translation and rotation symmetries and can generate a proper RG flow. Moreover, from a critical fixed point of this RG flow one can then extract the conformal data of the underlying conformal field theory.

The overall mechanical performance of modular steel structure buildings are largely determined by the mechanical performance of the connection joints between the adjacent modules. In this paper, a novel connection joints between the adjacent modules is taken as research object, which has the advantages of convenient construction and assembly. By means of FEA, three models including the joint model, the model of adding ribs and the model of increasing beam height are calculated, and the experimental results were compared. The finite element model uses solid elements to simulate the detail structure of joints and contact elements to the contact relationship between components. The research results show that the results of finite element analysis are in good agreement with the experimental results in terms of deformation state and bearing capacity, and the accuracy of the finite element model is verified. The finite element model established in this paper can simulate the stress state of various parts of the joint which can make up for the shortage of the experimental measurement.

This paper assumes that a row of the frame, shear wall structure as affected by lateral bending and torsion modules coupling effect of thin-walled members, through the floor to work together to establish a collaborative analysis of structural bias of the Hamiltonian on the dual system, with precise integration method for the numerical solution of high-precision systems, analysis of bias is given a set of construction the structure of collaborative work. The results make the structure more in line with the actual deformation.

Based on the quantum renormalization group, we derive the bulk geometry that emerges in the holographic dual of the fermionic U(N ) vector model at a nonzero charge density. The obstruction that prohibits the metallic state from being smoothly deformable to the direct product state under the renormalization group flow gives rise to a horizon at a finite radial coordinate in the bulk. The region outside the horizon is described by the Lifshitz geometry with a higher-spin hair determined by microscopic details of the boundary theory. On the other hand, the interior of the horizon is not described by any Riemannian manifold, as it exhibits an algebraic non-locality. The non-local structure inside the horizon carries the information on the shape of the filled Fermi sea.

Deformation microstructures and micro-orientations of columnar grains with different orientations in a polycrystalline high purity Al cold-rolled up to 65% (thickness reduction) were investigated using electron backscatter diffraction (EBSD) technique. It was found that rotations were Inhomogeneous within the individual grains, the rotation angles of the parts close to the initial boundaries (BPs) were smaller than those remote from the boundaries (IPs), e.g. the deviation angles between the BPs and the IPs were 5-6° in the grains with <001>//RD orientation, leading to the rotation along the α-fiber, while the deviation angles were 5-12° in the grains with <121>//ND orientation rotating toward the β-fiber. These results demonstrated that the microstructures and local rotations of various parts within the rolled individual columnar grains were influenced by their initial orientations and boundaries.