[Physics]Viewpoint: Theory for 1D Quantum Materials Tested with Cold Atoms and Superconductors
The Tomonaga-Luttinger theory describing one-dimensional materials has been tested with cold atoms and arrays of Josephson junctions.
coupled degrees of freedom (the approximate number of electrons in a cubic centimeter of material) is an intractable problem. Simplifying approaches exist in 2 and 3 dimensions for both bosonic and fermionic systems. For bosonic systems, mean-field approximations convert a many-body problem into a one-body one: each boson interacts with the averaged field of the others. And fermionic systems can be described by Lev Landau’s Fermi-liquid theory, which recasts the problem of strongly interacting particles in terms of excitations (called Landau quasiparticles) that are nearly free, bringing us back to the more comfortable case of free particles. Unfortunately, the game changes in 1D, as all of the above descriptions break down.
The key difference between 1D systems and higher-dimensional systems is that the former are governed by collective excitations, not individual ones. This fact can be illustrated by the queuing of people in a line: an individual can only move together with his or her neighbors. The TLL formalism rests on the fact that only two parameters are sufficient to describe the system: the speed of collective excitations (such as oscillations of the density of particles, or sound waves propagating through the system) and the TLL parameter (which measures the degree of quantum fluctuations inside the material). TLL theory predicts certain hallmark features: superconductivity, quasi-long-range order at zero temperature, and the tendency of the system to undergo instabilities—such as charge- or spin-density waves .
However, the observation of TTL features has been a long-standing challenge, with the first hints found in condensed-matter systems. With the advent of cold atoms as condensed-matter simulators, researchers had hoped to find easier ways to observe TLL physics. But there are complications due to the finite size of the systems, the difficulty of reaching sufficiently low temperatures to reach quantum regimes and, most importantly, the challenge of realizing homogeneous 1D systems—the confining potential of the traps used to hold the atoms leads to an atomic density varying from point to point. Such an inhomogeneity enormously complicates the theoretical description of the system. (See Refs.  and  for a review of TLL studies in both condensed matter and cold atoms.)
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