In the final talk of the series, I will discuss some fundamental aspects of the physics of interacting electrons in 1D that go beyond the conventional Luttinger-liquid phenomenology. Strongly- interacting low-density electrons form a Wigner-crystal arrangement on finite length scales. Finite wires are experimentally shown to undergo a transition from a Luttinger-liquid order at high electron densities to a crystal-like state below some critical density, which blocks the two-terminal wire conductivity. But even infinite 1D systems cannot be described as Luttinger liquids at low densities and finite temperatures, since nearest-neighbor exchange coupling is exponentially suppressed in the strongly-interacting limit, and electrons are likely to enter an effectively free-spin regime. This has a dramatic effect on electron spectral properties and, in particular, may have an intricate connection to the “0.7 anomaly” in point contacts.

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