Electron liquids and solids in one dimension

Abstract

Even though bulk metallic systems contain a very large number of strongly interacting electrons, their properties are well described within Landau's Fermi liquid theory of non-interacting quasiparticles. Although many higher-dimensional systems can be successfully understood on the basis of such non-interacting theories, this is not possible for one-dimensional systems. When confined to narrow channels, electron interaction gives rise to such exotic phenomena as spin-charge separation and the emergence of correlated-electron insulators. Such strongly correlated electronic behaviour has recently been seen in experiments on one-dimensional carbon nanotubes and nanowires, and this behaviour challenges the theoretical description of such systems.

Formation of defects in multirow Wigner crystals

“…It has been shown that at a critical density, a transition to a zigzag crystal takes place 7,11,23,25,26 . Though not for electrons, this zigzag transition has indeed been observed using 24 Mg + ions in a quadrupole storage ring 27 .…”

“…Three equivalent minima at N = 58, N = 116, and N = 174 can be clearly seen. These minima correspond to configurations with defects in the outer-most rows, i.e., the outer rows have less particles than the inner rows, namely N inner = 12 (24,36), and N outer = 11 (22,33), respectively. The corresponding defect density is n 4.85 def = 1 − 11/12 = 0.083.…”

Coulomb drag

“…In recent years, a lot of the attention was devoted to 1D liquids with nonlinear dispersion [for reviews on this topic see Deshpande et al (2010); Imambekov et al (2012);and Matveev (2013) ]. In the TLL theory, the curvature of the quasiparticle spectrum is described by an irrelevant operator (in the renormalization group sense).…”

Quench-induced entanglement and relaxation dynamics in Luttinger liquids

“…In the context of interacting 1D systems, it is well established that their low-energy equilibrium properties are described by the Luttinger liquid (LL) model [30][31][32]. They exhibit peculiar effects stemming from their non-Fermi liquid nature due to inter-particle interactions, such as charge and spin fractionalization [19,20,[32][33][34][35][36][37][38][39][40][41][42]. In recent years the LL model has also been proven to be a very powerful tool for studying the dynamics of 1D systems after a quench of the interaction strength.…”