This week a paper was published in Nature about the observation via Raman scattering of a particular excitation in the charge density wave materials RTe3 (R = La, Gd) that is mathematically an example of an "amplitude mode" that carries angular momentum that the authors identify as an axial Higgs mode. (I'm not going to get into the detailed physics of this.)

The coverage of this paper elicited a kerfuffle on blogs (e.g here and here) for two main reasons that I can discern. First, there is disagreement in the community about whether calling a mode like this "Higgs" is appropriate, given the lack of a gauge field in this system (this is in the comments on the second blog posting). That has become practice in the literature, but there are those who strongly disapprove. Second, some people are upset because some of the press coverage of the paper, with references to dark matter, hyped up the result to make it sound like this was a particle physics discovery, or at least has implications for particle physics.

This does give me the opportunity, though, to talk about an implication that I see sometimes from our high energy colleagues in discussions of condensed matter, that "quasiparticles" are somehow not "real" in the way of elementary particles.

What are quasiparticles? In systems with many degrees of freedom built out of large numbers of constituents, amazingly it is often possible to look at the low energy excitations above the ground state and find that those excitations look particle-like - that is, there are discrete excitations that, e.g., carry (crystal) momentum \(\hbar \mathbf{k}\), have an energy that depends on the momentum in a clear way \(\epsilon(\mathbf{k})\), and also carry spin, charge, etc. These excitations are "long lived" in the sense that they propagate many of their wavelengths (\(2 \pi/|\mathbf{k}|\)) before scattering and have lifetimes \(\tau\) such that their uncertainty in energy is small compared to their energy above the ground state, (\(\hbar/\tau << \epsilon(\mathbf{k})\)). The energy of the many-body system can be well approximated as the sum of the quasiparticle excitations: \(E \approx \Sigma n(\mathbf{k})\epsilon(\mathbf{k})\).

There are many kinds of quasiparticles in condensed matter systems. There are the basic ones like (quasi)electrons and (quasi)holes in metals and semiconductors, phonons, magnons, polarons, plasmons, etc. While it is true that quasiparticles are inherently tied to their host medium, these excitations are "real" in all practical ways - they can be detected experimentally and their properties measured. Indeed, I would argue that it's pretty incredible that complicated, many-body interacting systems so often host excitations that look so particle-like. That doesn't seem at all obvious to me *a priori*.

What has also become clear over the last couple of decades is that condensed matter systems can (at least in principle) play host to quasiparticles that act mathematically like a variety of ideas that have been proposed over the years in the particle physics world. You want quasiparticles that mathematically look like massless fermions described by the Dirac equation? Graphene can do that. You want more exotic quasiparticles described by the Weyl equation? TaAs can do that. You want Majorana fermions? These are expected to be possible, though challenging to distinguish unambiguously. Remember, the Higgs mechanism started out in superconductors, and the fractional quantum Hall system supports *fractionally charged* quasiparticles. (For a while it seemed like there was a cottage industry on the part of a couple of teams out there: Identify a weird dispersion relation \(\epsilon(\mathbf{k})\) predicted in some other context; find a candidate material whose quasiparticles might show this according to modeling; take ARPES data and publish on the cover of a glossy journal.)

Why are quasiparticles present in condensed matter, and why to they "look like" some models of elementary particles? Fundamentally, both crystalline solids and free space can be usefully described using the language of quantum field theory. Crystalline solids have lower symmetry than free space (e.g. the lattice gives discrete rather than continuous translational symmetry), but the mathematical tools at work are closely related. As Bob Laughlin pointed out in his book, given that quasiparticles in condensed matter can be described in very particle-like terms and can even show fractional charge, maybe its worth wondering whether everything is in a sense quasiparticles.