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We identify ground states of one-dimensional fermionic systems subject to competing repulsive interactions of finite range, and provide phenomenological and fundamental signatures of these phases and their transitions. Commensurable particle densities admit multiple competing charge-ordered insulating states with various periodicities and internal structure. Our reference point are systems with interaction range $p=2$, where phase transitions between these charge-ordered configurations are known to be mediated by liquid and bond-ordered phases. For increased interaction range $p=4$, we find that the phase transitions can also appear to be abrupt, as well as being mediated by re-emergent ordered phases that cross over into liquid behavior. These considerations are underpinned by a classification of the competing charge-ordered states in the atomic limit for varying interaction range at the principal commensurable particle densities. We also consider the effects of disorder, leading to fragmentization of the ordered phases and localization of the liquid phases.
Analysis of neutron diffraction, dc magnetization, ac magnetic susceptibility, heat capacity, and electrical resistivity for DyRuAsO in an applied magnetic field are presented at temperatures near and below those at which the structural distortion (T
Using Quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with $N$ flavors of fermions per site for $N=1,2$ and $3$. The models have an extensive number of conserved quantities b
We present a fully many-body formulation of topological invariants for various topological phases of fermions protected by antiunitary symmetry, which does not refer to single particle wave functions. For example, we construct the many-body $mathbb{Z
FeGa$_3$ is an unusual intermetallic semiconductor that presents intriguing magnetic responses to the tuning of its electronic properties. When doped with Ge, the system evolves from diamagnetic to paramagnetic to ferromagnetic ground states that are
There has been a great interest in magnetic field induced quantum spin liquids in Kitaev magnets after the discovery of neutron scattering continuum and half quantized thermal Hall conductivity in the material $alpha$-RuCl$_3$. In this work, we provi