Phase Transitions in Insulating 1D Electron Systems

Holger Fehske, Eric Jeckelmann

We discuss the Luttinger-liquid charge-density-wave and Peierls-insulator Mott-insulator quantum phase transitions in 1D electron-phonon systems.

Hiromi Otsuka, 博巳 大塚

Xin Wan

Ilya V. Krive, A. A. Nersesyan, M. Jonson +1 more

We study the influence of long-range Coulomb interactions on the properties of one-dimensional (1D) strongly correlated electron systems in the vicinity of the metal-insulator Mott-Hubbard phase transition. It is shown that, in the metallic phase, the standard square-root singularity of the compressibility at the transition point changes to a logarithmic one, due to the formation of a 1D Wigner crystal of solitons (holons). On increasing the soliton density in a finite-size chain, the behavior of the compressibilty reflects a sequence of crossovers between classical, low-density regimes of perfectly or nearly ordered Wigner-crystal states, and quantum regimes of a nearly free Fermi gas of solitons, followed (in the high-density limit) by a liquid phase of strongly correlated solitons. In a mesoscopic situation, where the screening length in a 1D chain is controlled by a massive electrode (gate) placed near the chain, there is a narrow region near the transition point where quantum fluctuations melt the Wigner crystal and recover the universal square-root singularity of the compressibility. Strong Coulomb interaction affects the formation of the charge excitations in the insulating phase, transforming the sine-Gordon solitons into quasiclassical Coulomb solitons. Multiplicative logarithmic renormalizations of the characteristic soliton size and rest energy are found.

Rafael Miksian Magaldi

Topological insulators are materials that behave as insulators in the bulk, but present conducting edge states.Despite the growing interest in such materials due to their possible applications on spintronic devices and quantum computing, several open questions still remain regarding the roles of both electronic interactions and dimensionality in these systems.The goal of this work is to tackle some of these questions.To do so, we study a quasi-1D system presenting a topologically non-trivial phase and electronic interactions: the so-called Kane-Mele-Hubbard ladders.Here, we apply the density matrix renormalization group (DMRG) algorithm in the tensor network formalism in order to calculate some physical properties of this system.The DMRG calculations allow us to reach the system's ground state and enable the efficient computation of observables and of the entanglement entropy.The Kane-Mele-Hubbard model is an interacting version of the Kane-Mele model, which displays topologically non-trivial phases.The interest on this system is due to the combination of effects caused by the spin-orbit coupling and the electronic interactions.For the non-interacting case we have a topological insulator, whereas in the highly interacting picture we have a Mott insulator with localized electrons.We explore the phase transition between these regimes, looking at the conditions needed for the appearance of spin-polarized edge states.We also propose the entanglement entropy between two halves of the system as an indicator of the topological phase transition, as it presents a particular pattern when the phase transition takes place.

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