Related papers: Low-lying excitations in one-dimensional lattice e…
We obtain a closed form expression for the energy spectrum of $\mathcal{P}\mathcal{T}$-symmetric superlattice systems with complex potentials of periodic sets of two $\delta$-potentials in the elementary cell. In the presence of periodic…
We extend the Lieb-Schupp theorem to the Heisenberg models with higher order interactions on non-frustrated or frustrated finite lattices. These lattices are constructed by even numbered rings with or without crossing bonds and have…
We consider the overdamped dynamics of a paradigmatic long-range system of particles residing on the sites of a one-dimensional lattice, in the presence of thermal noise. The internal degree of freedom of each particle is a periodic…
The properties of a dilute electron gas, coupled to the lattice degrees of freedom, are studied and compared with the properties of an electron gas at half-filling, where spinless fermions with two orbitals per lattice site are considered.…
Atomic-scale helices exist as motifs for several material lattices. We examine a tight-binding model for a single one-dimensional monatomic chain with a p-orbital basis coiled into a helix. A topologically nontrivial phase emerging from…
Examples of one-dimensional lattice systems are considered, in which patterns of different spatial scales arise alternately, so that the spatial phase over a full cycle undergo transformation according to expanding circle map that implies…
We show how the area law for the entanglement entropy may be violated by free fermions on a lattice and look for conditions leading to the emergence of a volume law. We give an explicit construction of the states with maximal entanglement…
We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where $N \gg 1$ lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper…
Pure gauge theories are rather different from theories with pure scalar and fermionic matter, especially in terms of the nature of excitations. For example, in scalar and fermionic theories, one can create ultra-local excitations. For a…
On the grounds of a Feynman-Kac--type formula for Hamiltonian lattice systems we derive analytical expressions for the matrix elements of the evolution operator. These expressions are valid at long times when a central limit theorem…
We study quantum many-body systems in the presence of an exotic antiunitary translation or inversion symmetry involving time reversal. Based on a symmetry-twisting method and spectrum robustness, we propose that a half-integer spin chain…
We prove that a quantum spin chain with half-odd-integral spin cannot have a unique ground state with a gap, provided that the interaction is short ranged, translation invariant, and possesses time-reversal symmetry or ${\mathbb Z}_2 \times…
We discuss quantum many-body systems with lattice translation and discrete onsite symmetries. We point out that, under a boundary condition twisted by a symmetry operation, there is an exact degeneracy of ground states if the unit cell…
Using an exactly solvable model, we study low-energy properties of a one-dimensional spinless electron fluid contained in a quantum-mechanically moving wire located in a static magnetic field. The phonon and electric current are coupled via…
We analyse the antiferromagnetic spin-1/2 Heisenberg model on a depleted kagome lattice, where some bonds have been reduced to exchange integral J_2 << J_1. The fully depleted system consists of 1D chains, each with a doubly degenerate…
A Hubbard-like model with SU(4) symmetry for electrons with two-fold orbital degeneracy is studied extensively. Exact solution in one dimension is derived by means of Bethe ansatz, where the sites are supposed to be occupied by at most two…
We consider the antiferromagnetic Heisenberg model and the repulsive Hubbard model for a class of frustrated lattices with a completely dispersionless (flat) lowest one-particle (either one-magnon or one-electron) band. We construct exact…
For quantum lattice systems with local interactions, the Lieb-Robinson bound acts as an alternative for the strict causality of relativistic systems and allows to prove many interesting results, in particular when the energy spectrum…
A continuum of excitations in interacting one-dimensional systems is bounded from below by a spectral edge that marks the lowest possible excitation energy for a given momentum. We analyse short-range interactions between Fermi particles…
In the presence of a magnetic field and an external periodic potential, the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter's butterfly. In this…