The amazing engineering of Fractons

A fracton is a collective quantized vibration on a substrate with a fractal structure.^[1][2]

Fractons are the fractal analog of phonons. Phonons are the result of applying translational symmetry to the potential in a Schrödinger equation. Fractal self-similarity can be thought of as a symmetry somewhat comparable to translational symmetry. Translational symmetry is symmetry under displacement or change of position, and fractal self-similarity is symmetry under change of scale. The quantum mechanical solutions to such a problem in general lead to a continuum of states with different frequencies. In other words, a fracton band is comparable to a phonon band. The vibrational modes are restricted to part of the substrate and are thus not fully delocalized, unlike phonon vibrational modes. Instead, there is a hierarchy of vibrational modes that encompass smaller and smaller parts of the substrate. Source Wiki

Theorists are in a frenzy over “fractons,” bizarre, but potentially useful, hypothetical particles that can only move in combination with one another.

Source: https://www.quantamagazine.org/fractons-the-weirdest-matter-could-yield-quantum-clues-20210726/

The theoretical possibility of fractons surprised physicists in 2011 (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.83.042330;

). Recently, these strange states of matter have been leading physicists toward new theoretical frameworks that could help them tackle some of the grittiest problems in fundamental physics.

Fractons are quasiparticles — particle-like entities that emerge out of complicated interactions between many elementary particles inside a material. But fractons are bizarre even compared to other exotic quasiparticles, because they are totally immobile or able to move only in a limited way. There’s nothing in their environment that stops fractons from moving; rather it’s an inherent property of theirs. It means fractons’ microscopic structure influences their behavior over long distances.

Partial Particles

In 2011, Jeongwan Haah, then a graduate student at Caltech, was searching for unusual phases of matter that were so stable they could be used to secure quantum memory, even at room temperature. Using a computer algorithm, he turned up a new theoretical phase that came to be called the Haah code. The phase quickly caught the attention of other physicists because of the strangely immovable quasiparticles that make it up.

They seemed, individually, like mere fractions of particles, only able to move in combination. Soon, more theoretical phases were found with similar characteristics, and so in 2015 Haah — along with Sagar Vijay and Liang Fu — coined the term “fractons” for the strange partial quasiparticles. (An earlier but overlooked paper by Claudio Chamon is now credited with the original discovery of fracton behavior.(This Letter presents solvable examples of quantum many-body Hamiltonians of systems that are unable to reach their ground states as the environment temperature is lowered to absolute zero. These examples, three-dimensional generalizations of quantum Hamiltonians proposed for topological quantum computing, (1) have no quenched disorder, (2) have solely local interactions, (3) have an exactly solvable spectrum, (4) have topologically ordered ground states, and (5) have slow dynamical relaxation rates akin to those of strong structural glasses.))

The resultant movement is that of a particle-antiparticle pair moving sideways in a straight line. In this world — an example of a fracton phase — a single particle’s movement is restricted, but a pair can move easily.

The Haah code takes the phenomenon to the extreme: Particles can only move when new particles are summoned in never-ending repeating patterns called fractals. Say you have four particles arranged in a square, but when you zoom in to each corner you find another square of four particles that are close together. Zoom in on a corner again and you find another square, and so on. For such a structure to materialize in the vacuum requires so much energy that it’s impossible to move this type of fracton. This allows very stable qubits — the bits of quantum computing — to be stored in the system, as the environment can’t disrupt the qubits’ delicate state.

The immovability of fractons makes it very challenging to describe them as a smooth continuum from far away. Because particles can usually move freely, if you wait long enough they’ll jostle into a state of equilibrium, defined by bulk properties such as temperature or pressure. Particles’ initial locations cease to matter. But fractons are stuck at specific points or can only move in combination along certain lines or planes. Describing this motion requires keeping track of fractons’ distinct locations, and so the phases cannot shake off their microscopic character or submit to the usual continuum description.

“Without a continuous description, how do we define these states of matter?”

Fractons have yet to be made in the lab, but that will probably change. Certain crystals with immovable defects have been shown to be mathematically similar to fractons. And the theoretical fracton landscape has unfurled beyond what anyone anticipated, with new models popping up every month.

“Probably in the near future someone will take one of these proposals and say, ‘OK, let’s do some heroic experiment with cold atoms and exactly realize one of these fracton models,’” said Brian Skinner, a condensed matter physicist at Ohio State University who has devised fracton models.

Fractons do not fit into [the quantum field theory] framework. So my take is that the framework is incomplete.

Nathan Seiberg

Even without their experimental realization, the mere theoretical possibility of fractons rang alarm bells for Seiberg, a leading expert in quantum field theory, the theoretical framework in which almost all physical phenomena are currently described.

Quantum field theory depicts discrete particles as excitations in continuous fields that stretch across space and time. It’s the most successful physical theory ever discovered, and it encompasses the Standard Model of particle physics — the impressively accurate equation governing all known elementary particles.

“Fractons do not fit into this framework. So my take is that the framework is incomplete,” said Seiberg.

There are other good reasons for thinking that quantum field theory is incomplete — for one thing, it so far fails to account for the force of gravity. If they can figure out how to describe fractons in the quantum field theory framework, Seiberg and other theorists foresee new clues toward a viable quantum gravity theory.

“Fractons’ discreteness is potentially dangerous, as it can ruin the whole structure that we already have,” said Seiberg. “But either you say it’s a problem, or you say it’s an opportunity.”

He and his colleagues are developing novel quantum field theories that try to encompass the weirdness of fractons by allowing some discrete behavior on top of a bedrock of continuous space-time (We discuss nonstandard continuum quantum field theories in 2+1 dimensions. They exhibit exotic global symmetries, a subtle spectrum of charged excitations, and dualities similar to dualities of systems in 1+1 dimensions. These continuum models represent the low-energy limits of certain known lattice systems. One key aspect of these continuum field theories is the important role played by discontinuous field configurations. In two companion papers, we will present 3+1-dimensional versions of these systems. In particular, we will discuss continuum quantum field theories of some models of fractons.).

“Quantum field theory is a very delicate structure, so we would like to change the rules as little as possible,” he said. “We are walking on very thin ice, hoping to get to the other side.”

1.  Alexander, S; C. Laermans; R. Orbach; H.M. Rosenberg (15 October 1983). “Fracton interpretation of vibrational properties of cross-linked polymers, glasses, and irradiated quartz”. Physical Review B. 28 (8): 4615–4619. Bibcode:1983PhRvB..28.4615A. doi:10.1103/physrevb.28.4615.
2. ^ Srivastava, G. P. (1990), The Physics of Phonons, CRC Press, pp. 328–329, ISBN 9780852741535.