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Motivated by recent experiments on twisted van der Waals materials, we perform an analytical and numerical study of the effects of strong on-site and short-range interactions in fractionally filled ideal Chern bands. We uncover an extensive non-trivial ground state manifold within the band filling range $0 < \nu < 1$ and introduce a general principle, the ''three-rule'', for combining flatband wave functions, which governs their zero-energy property on the torus geometry. Based on the structure of these wave functions, we develop a variational approach that reveals distinct phases under different perturbations: metallic behavior emerges from a finite dispersion, and superconductivity is induced by attractive Cooper channel interactions. Our approach, not reliant on the commonly applied mean-field approximations, provides an analytical expression for the macroscopic wave function of the off-diagonal long-range order correlator, attributing pairing susceptibility to the set of non-trivial zero-energy ground state wave functions. Extending to finite screening lengths and beyond the ideal limit using exact diagonalization simulations, we demonstrate the peculiar structure in the many-body wave function's coefficients to be imprinted in the low-energy spectrum of the topologically ordered Halperin spin-singlet state. Our findings also make connections to frustration-free models of non-commuting projector Hamiltonians, potentially aiding the future construction of exact ground states for various fractional fillings., Comment: 21 pages, 9 figures, 1 table

We study a model of spinless fermions on the honeycomb lattice with nearest-neighbor exclusion and extended repulsive interactions that exhibits `lattice supersymmetry' [P. Fendley, K. Schoutens, and J. de Boer, Phys. Rev. Lett. 90, 120402 (2003)]. Using a combination of exact diagonalization of large ($N\leq56$ site) systems, mean-field numerics, and symmetry analysis, we establish a rich phase structure as a function of fermion density, that includes non-Fermi liquid behavior, resonating charge stripes, domain-wall and bubble physics, and identify a finite range of fillings with extensive ground state degeneracy and both gapped and gapless spectra. We comment on the stability of our results to relaxing the stringent requirements for supersymmetry, and on their possible broader relevance to systems of strongly-correlated electrons with extended repulsive interactions., Comment: 15 pages, 12 figures, 1 table

We show that Hubbard models with nearest-neighbor hopping and a nearest-neighbor hardcore constraint exhibit `maximal' Hilbert space fragmentation in many lattices of arbitrary dimension $d$. Focusing on the $d=1$ rhombus chain and the $d=2$ Lieb lattice, we demonstrate that the fragmentation is strong for all fillings in the thermodynamic limit, and explicitly construct all emergent integrals of motion, which include an extensive set of higher-form symmetries. Blockades consisting of frozen particles partition the system in real space, leading to anomalous dynamics. Our results are potentially relevant to optical lattices of dipolar and Rydberg-dressed atoms., Comment: 5+11 pages

Observations of CH$^+$ are used to trace the physical properties of diffuse clouds, but this requires an accurate understanding of the underlying CH$^+$ chemistry. Until this work, the most uncertain reaction in that chemistry was dissociative recombination (DR) of CH$^+$. Using an electron-ion merged-beams experiment at the Cryogenic Storage Ring, we have determined the DR rate coefficient of the CH$^+$ electronic, vibrational, and rotational ground state applicable for different diffuse cloud conditions. Our results reduce the previously unrecognized order-of-magnitude uncertainty in the CH$^+$ DR rate coefficient to $\sim \pm 20\%$ and are applicable at all temperatures relevant to diffuse clouds, ranging from quiescent gas to gas locally heated by processes such as shocks and turbulence. Based on a simple chemical network, we find that DR can be an important destruction mechanism at temperatures relevant to quiescent gas. As the temperature increases locally, DR can continue to be important up to temperatures of $ \sim 600\,\mathrm{K} $ if there is also a corresponding increase in the electron fraction of the gas. Our new CH$^+$ DR rate coefficient data will increase the reliability of future studies of diffuse cloud physical properties via CH$^+$ abundance observations., Comment: Main paper: PDFLaTeX with 7 pages, 3 figures. Appendix starting on page 7: PDFLaTeX with 11 pages, 2 figures, 4 tables. This article has been accepted by The Astrophysical Journal

Twisted double- and mono-bilayer graphene are graphene-based moir\'e materials hosting strongly correlated fermions in a gate-tunable conduction band with a topologically non-trivial character. Using unbiased exact diagonalization complemented by unrestricted Hartree-Fock calculations, we find that the strong electron-electron interactions lead to a non-coplanar magnetic state, which has the same symmetries as the tetrahedral antiferromagnet on the triangular lattice and can be thought of as a skyrmion lattice commensurate with the moir\'e scale, competing with a set of ferromagnetic, topological charge density waves featuring an approximate emergent O(3) symmetry, "rotating" the different charge density wave states into each other. Direct comparison with exact diagonalization reveals that the ordered phases are accurately described within the unrestricted Hartree-Fock approximation. Exhibiting a finite charge gap and Chern number $|C|=1$, the formation of charge density wave order which is intimately connected to a skyrmion lattice phase is consistent with recent experiments on these systems., Comment: 35 pages, 12 figures

We present state-selected measurements of rotational cooling and excitation rates of CH$^+$ molecular ions by inelastic electron collisions. The experiments are carried out at the Cryogenic Storage Ring, making use of a monoenergetic electron beam at matched velocity in combination with state-sensitive laser-dissociation of the CH$^+$ ions for simultaneous monitoring of the rotational level populations. Employing storage times of up to 600 s, we create conditions where electron-induced cooling to the $J = 0$ ground state dominates over radiative relaxation, allowing for the experimental determination of inelastic electron collision rates to benchmark state-of-the-art theoretical calculations. On a broader scale, our experiments pave the way to probe inelastic electron collisions for a variety of molecular ions relevant in various plasma environments., Comment: Main paper: PDFLaTeX with 7 pages, 4 figures. Supplemental material: PDFLaTeX with 26 pages, 11 figures, 5 tables. This article has been accepted by Physical Review Letters

We perform an extensive exact diagonalization study of interaction driven insulators in spin- and valley-polarized moir\'{e} flat bands of twisted bilayer graphene aligned with its hexagonal boron nitride substrate. In addition to previously reported fractional Chern insulator phases, we provide compelling evidence for competing charge-density-wave phases at multiple fractional fillings of a realistic single-band model. A thorough analysis at different interlayer hopping parameters, motivated by experimental variability, and the role of kinetic energy at various Coulomb interaction strengths highlight the competition between these phases. The interplay of the single-particle and the interaction induced hole dispersion with the inherent Berry curvature of the Chern bands is intuitively understood to be the driving mechanism for the ground-state selection. The resulting phase diagram features remarkable agreement with experimental findings in a related moir\'{e} heterostructure and affirms the relevance of our results beyond the scope of graphene based materials., Comment: 16 pages, 18 figures

An electrostatic cryogenic storage ring, CSR, for beams of anions and cations with up to 300 keV kinetic energy per unit charge has been designed, constructed and put into operation. With a circumference of 35 m, the ion-beam vacuum chambers and all beam optics are in a cryostat and cooled by a closed-cycle liquid helium system. At temperatures as low as (5.5 $\pm$ 1) K inside the ring, storage time constants of several minutes up to almost an hour were observed for atomic and molecular, anion and cation beams at an energy of 60 keV. The ion-beam intensity, energy-dependent closed-orbit shifts (dispersion) and the focusing properties of the machine were studied by a system of capacitive pickups. The Schottky-noise spectrum of the stored ions revealed a broadening of the momentum distribution on a time scale of 1000 s. Photodetachment of stored anions was used in the beam lifetime measurements. The detachment rate by anion collisions with residual-gas molecules was found to be extremely low. A residual-gas density below 140 cm$^{-3}$ is derived, equivalent to a room-temperature pressure below 10$^{-14}$ mbar. Fast atomic, molecular and cluster ion beams stored for long periods of time in a cryogenic environment will allow experiments on collision- and radiation-induced fragmentation processes of ions in known internal quantum states with merged and crossed photon and particle beams., Comment: PDFLaTeX with 17 pages, 16 figures, 2 tables. This article has been accepted by Review of Scientific Instruments. After it is published, it will be found at http://scitation.aip.org/content/aip/journal/rsi