We consider $N$-particle generalizations of $eta$-paring states in a chain of $N$-component fermions and show that these states are exact (high-energy) eigenstates of an extended SU($N$) Hubbard model. We compute the singlet correlation function of t
he states and find that its behavior is qualitatively different for even and odd $N$. When $N$ is even, these states exhibit off-diagonal long-range order in $N$-particle reduced density matrix. On the other hand, when $N$ is odd, the singlet correlation function decays exponentially toward the other end of the chain but shows a revival at the other end. Finally, we prove that these states are the unique ground states of suitably tailored Hamiltonians.
Few-magnon excitations in Heisenberg-like models play an important role in understanding magnetism and have long been studied by various approaches. However, the quantum dynamics of magnon excitations in a finite-size spin-$S$ $XXZ$ chain with single
-ion anisotropy remains unsolved. Here, we exactly solve the two-magnon (three-magnon) problem in the spin-$S$ $XXZ$ chain by reducing the few-magnons to a fictitious single particle on a one-dimensional (two-dimensional) effective lattice. Such a mapping allows us to obtain both the static and dynamical properties of the model explicitly. The zero-energy-excitation states and various types of multimagnon bound states are manifested, with the latter being interpreted as edge states on the effective lattices. Moreover, we study the real-time multimagnon dynamics by simulating single-particle quantum walks on the effective lattices.
Flat-band models have been of particular interest from both fundamental aspects and realization in materials. Beyond the canonical examples such as Lieb lattices and line graphs, a variety of tight-binding models are found to possess flat bands. Howe
ver, analytical treatment of dispersion relations is limited, especially when there are multiple flat bands with different energies. In this paper, we present how to determine flat-band energies and wave functions in tight-binding models on decorated diamond and pyrochlore lattices in generic dimensions $D geq 2$. For two and three dimensions, such lattice structures are relevant to various organic and inorganic materials, and thus our method will be useful to analyze the band structures of these materials.
A new kind of spin-1 chain Hamiltonian consisting of competing dimer and trimer projection operators is proposed. As the relative strengths and signs of the interactions are varied, the model exhibits a number of different phases including the gapped
dimer phase and the gapless trimer phase with critical correlations described by a conformal field theory with central charge $c=2$. A symmetry-protected topological phase also exists in this model, even though the microscopic interactions are not the simple adiabatic extensions of the well-known Heisenberg and the Affleck-Kennedy-Lieb-Tasaki model and contains both two- and three-particle permutations. A fourth phase is characterized by macroscopically degenerate ground states. While bearing almost a one-to-one resemblance to the phase diagram of the bilinear-biquadratic spin-1 chain Hamiltonian, our model is rooted on very different physical origin, namely the two competing tendencies of spin-1 particles to form singlets through either dimer or trimer formation.
A defining property of particles is their behavior under exchange. In two dimensions anyons can exist which, opposed to fermions and bosons, gain arbitrary relative phase factors or even undergo a change of their type. In the latter case one speaks o
f non-Abelian anyons - a particularly simple and aesthetic example of which are Fibonacci anyons. They have been studied in the context of fractional quantum Hall physics where they occur as quasiparticles in the $k=3$ Read-Rezayi state, which is conjectured to describe a fractional quantum Hall state at filling fraction $ u=12/5$. Here we show that the physics of interacting Fibonacci anyons can be studied with strongly interacting Rydberg atoms in a lattice, when due to the dipole blockade the simultaneous laser excitation of adjacent atoms is forbidden. The Hilbert space maps then directly on the fusion space of Fibonacci anyons and a proper tuning of the laser parameters renders the system into an interacting topological liquid of non-Abelian anyons. We discuss the low-energy properties of this system and show how to experimentally measure anyonic observables.
