Phase transition of electron system in quasi-one dimensional metal with weak and strong interaction

Alexei M. Tsvelik

It is quite beyond the purpose of this book to give a comprehensive review of the modern theory of metals. I shall touch only on those topics which are related to the mainstream of this course: the problem of strong interactions. As I have noted before, strong interactions can appear as a result of renormalization, and from the aesthetic point of view this is, perhaps, the most interesting case. As we shall see in Part IV, such renormalizations are particularly strong in one-dimensional systems, where practically any interaction leads to quite dramatic effects. Therefore a one-dimensional electron gas neither undergoes a phase transition (this is forbidden due to the low dimensionality), nor behaves like a system of free electrons. On the contrary, in higher dimensions at low temperatures a system of electrons either undergoes a phase transition (superconductivity, magnetic ordering, etc.), or behaves like a free electron gas. When temperatures as low as several degrees became experimentally available, physicists discovered that an enormous amount of experimental data on normal metals can be described by the model where one neglects electron–electron interactions. This apparent miracle was explained by Landau who demonstrated that the interaction pattern drastically simplifies close to the Fermi surface. Provided the system does not undergo a symmetry breaking phase transition, all interactions except forward scattering effectively vanish on the Fermi surface and low-lying excitations carry quantum numbers of electrons. Therefore they are called quasi-particles . The meaning of the word quasi will become clear in a moment.

Hiromi Otsuka, 博巳 大塚

Jun‐ichiro Kishine, Kenji Yonemitsu

We study the interplay of randomness, electron correlation, and dimensionality effects in weakly coupled half-filled Hubbard chains with weak quenched random potentials, based on the renormalization-group (RG) approach. We perform a two-loop RG analysis of an effective action derived by using the replica trick, and examine the following crossovers and phase transitions from an incoherent metal regime: (1) a crossover to the Anderson localization regime, (2) an antiferromagnetic phase transition, and (3) a crossover to the quasi-one-dimensional weak-localization regime. The case of $d=1+\ensuremath{\epsilon}$ $(\ensuremath{\epsilon}\ensuremath{\ll}1)$ dimensions is also mentioned.

Xin Wan

S V Kravchenko, M P Sarachik

The interplay between strong Coulomb interactions and randomness has been a long-standing problem in condensed matter physics. According to the scaling theory of localization in two-dimensional systems of non-interacting or weakly interacting electrons, the ever-present randomness causes the resistance to rise as the temperature is decreased, leading to an insulating ground state. However, new evidence has emerged within the past decade indicating a transition from the insulating to metallic phase in two-dimensional systems of strongly interacting electrons. We review earlier experiments that demonstrate the unexpected presence of a metallic phase in two dimensions, and present an overview of recent experiments with emphasis on the anomalous magnetic properties that have been observed in the vicinity of the transition.

Ph. Brune, A. P. Kampf