B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine Kharkiv 61103, Ukraine
Received March 15, 2021, published online July 26, 2021
We review one-dimensional lattice models and the corresponding results that describe the low-temperature properties of quasi-one-dimensional lattice systems with long-range interaction. A widely known example is narrow-band low-dimensional conductors with long-range interelectron repulsion. The models deal with particles that live on the one-dimensional host lattice (chain), translation invariant or disordered, and interact via the long-range repulsive potential. The results are presented concerning the translation invariant host chain, in particular: the low-temperature thermodynamics incommensurable ground states and related devil-staircase form of various characteristics as functions of pertinent parameters, the self-localization of particles, a new branch of elementary excitations, etc. In the disordered case, where the sites of the host chain fluctuate randomly around the sites of the periodic chain, the low-temperature thermodynamics and the structure of the ground state are discussed in the framework of a certain model, which we call the cluster model and which seems to be a fairly reasonable approximation for low temperatures and small concentration of particles. Using analytical and numerical tools we analyze the thermodynamics and the ground state of the model. The latter proves to be a sequence of random domains and we study in detail their distribution.