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1. Lieb-Schultz-Mattis, Luttinger, and 't Hooft - anomaly matching in lattice systems

   https://doi.org/10.21468/SciPostPhys.15.2.051  

   Cheng, Meng; Seiberg, Nathan (January 2023, SciPost Physics)

   We analyze lattice Hamiltonian systems whose global symmetries have ’t Hooft anomalies. As is common in the study of anomalies, they are probed by coupling the system to classical background gauge fields. For flat fields (vanishing field strength), the nonzero spatial components of the gauge fields can be thought of as twisted boundary conditions, or equivalently, as topological defects. The symmetries of the twisted Hilbert space and their representations capture the anomalies. We demonstrate this approach with a number of examples. In some of them, the anomalous symmetries are internal symmetries of the lattice system, but they do not act on-site. (We clarify the notion of “on-site action.”) In other cases, the anomalous symmetries involve lattice translations. Using this approach we frame many known and new results in a unified fashion. In this work, we limit ourselves to 1+1d systems with a spatial lattice. In particular, we present a lattice system that flows to the c=1 compact boson system with any radius (no BKT transition) with the full internal symmetry of the continuum theory, with its anomalies and its T-duality. As another application, we analyze various spin chain models and phrase their Lieb-Shultz-Mattis theorem as an ’t Hooft anomaly matching condition. We also show in what sense filling constraints like Luttinger theorem can and cannot be viewed as reflecting an anomaly. As a by-product, our understanding allows us to use information from the continuum theory to derive some exact results in lattice model of interest, such as the lattice momenta of the low-energy states. 

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2. Lattice Hamiltonian for adjoint QCD2

   https://doi.org/10.1007/JHEP08(2024)009  

   Dempsey, Ross; Klebanov, Igor R; Pufu, Silviu S; Søgaard, Benjamin T (August 2024, Journal of High Energy Physics)

   A<sc>bstract</sc> We introduce a Hamiltonian lattice model for the (1 + 1)-dimensional SU(N_c) gauge theory coupled to one adjoint Majorana fermion of massm. The discretization of the continuum theory uses staggered Majorana fermions. We analyze the symmetries of the lattice model and find lattice analogs of the anomalies of the corresponding continuum theory. An important role is played by the lattice translation by one lattice site, which in the continuum limit involves a discrete axial transformation. On a lattice with periodic boundary conditions, the Hilbert space breaks up into sectors labeled by theN_c-alityp= 0, …N_c− 1. Our symmetry analysis implies various exact degeneracies in the spectrum of the lattice model. In particular, it shows that, form= 0 and evenN_c, the sectorspandp′ are degenerate if |p−p′| =N_c/2. In theN_c= 2 case, we explicitly construct the action of the Hamiltonian on a basis of gauge-invariant states, and we perform both a strong coupling expansion and exact diagonalization for lattices of up to 12 lattice sites. Upon extrapolation of these results, we find good agreement with the spectrum computed previously using discretized light-cone quantization. One of our new results is the first numerical calculation of the fermion bilinear condensate. 

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3. Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices

   https://doi.org/10.22331/q-2020-02-10-228  

   Daniel, Austin K.; Alexander, Rafael N.; Miyake, Akimasa (February 2020, Quantum)

   What kinds of symmetry-protected topologically ordered (SPTO) ground states can be used for universal measurement-based quantum computation in a similar fashion to the 2D cluster state? 2D SPTO states are classified not only by global on-site symmetries but also by subsystem symmetries, which are fine-grained symmetries dependent on the lattice geometry. Recently, all states within so-called SPTO cluster phases on the square and hexagonal lattices have been shown to be universal, based on the presence of subsystem symmetries and associated structures of quantum cellular automata. Motivated by this observation, we analyze the computational capability of SPTO cluster phases on all vertex-translative 2D Archimedean lattices. There are four subsystem symmetries here called ribbon, cone, fractal, and 1-form symmetries, and the former three are fundamentally in one-to-one correspondence with three classes of Clifford quantum cellular automata. We conclude that nine out of the eleven Archimedean lattices support universal cluster phases protected by one of the former three symmetries, while the remaining lattices possess 1-form symmetries and have a different capability related to error correction. 

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4. Analysis of a 3D nonlinear moving boundary problem describing fluid-mesh-sell interaction

   Suncica Canic, Marija Galic (January 2020, Transactions of the American Mathematical Society)

   Abstract. We consider a nonlinear, moving boundary, fluid-structure interaction problem between a time dependent incompressible, viscous fluid flow, and an elastic structure composed of a cylindrical shell supported by a mesh of elastic rods. The fluid flow is modeled by the time-dependent Navier- Stokes equations in a three-dimensional cylindrical domain, while the lateral wall of the cylinder is modeled by the two-dimensional linearly elastic Koiter shell equations coupled to a one-dimensional system of conservation laws defined on a graph domain, describing a mesh of curved rods. The mesh supported shell allows displacements in all three spatial directions. Two-way coupling based on kinematic and dynamic coupling conditions is assumed between the fluid and composite structure, and between the mesh of curved rods and Koiter shell. Problems of this type arise in many ap- plications, including blood flow through arteries treated with vascular prostheses called stents. We prove the existence of a weak solution to this nonlinear, moving boundary problem by using the time discretization via Lie operator splitting method combined with an Arbitrary Lagrangian-Eulerian approach, and a non-trivial extension of the Aubin-Lions-Simon compactness result to problems on moving domains. 

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5. A simplified coaxial ion trap mass analyzer: Characterization of the simplified toroidal ion trap with a rectilinear ion guide

   Sirbescu-Stanley, DV; Lemmer, KM; Austin, DE; Taylor, NR (October 2024, International journal of mass spectrometry)

   A new miniature coaxial ion trap mass analyzer with a rectilinear ion guide has been constructed using a combination of planar and cylindrical electrodes. The results reported here focus on characterizing the performance of the rectilinear ion guide and simplified toroidal ion trap components. The simplified toroidal ion trap was found to have an ion capacity in excess of 105 ions and mass spectral resolution of 0.5–0.6 when used as a mass analyzer. The ion storage efficiency within the toroidal trapping region was evaluated and found the stored ion population decreased exponentially with storage time. Ion losses depended slightly on the stored βz condition. Ion losses within the toroidal region are attributed primarily to field instabilities at the intersection point of the two components while charge exchange reactions were observed but considered a minor loss mechanism. The ability to mass selectively ejection ions of a specific mass from the toroidal trapping region was characterized and found to approach 100 % efficiency under appropriate ejection conditions. 

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