Physicists have come closer to detecting unusual quasiparticles

Scientists have developed a quantum model of a solid body, which shows signs of the existence of fractons, unusual quasi—particles that are practically unable to move singly. It is assumed that this property can be used in the future for more reliable storage of quantum information. A study by an international group of physicists has been published in Nature Communications. About what fractons are, why they have not yet been detected in quantum spin liquids, and what exactly the new calculations have shown, see the Izvestia article.

What are fractons?

A fracton cannot be considered a new elementary particle like an electron or a photon. It is a quasi-particle, that is, a collective excitation resulting from the coordinated behavior of a multitude of interacting particles within a substance.

Such objects exist only in a certain environment. For example, the vibrations of atoms in a crystal lattice are described by physicists as quasi—particles - phonons. They are able to transfer energy inside the material, although there is no separate phonon outside it.

Fractons arise according to a similar principle, but they are characterized by extremely limited mobility. If the usual excitation can move between neighboring parts of the system, then a single fracton is practically unable to move. To move it, it is necessary to simultaneously change the position of other fractons.

In some cases, connected pairs of such excitations can move, but only in a certain direction. More complex groups get more freedom of movement. Thus, the mobility depends not only on the properties of the quasiparticle itself, but also on what other excitations it is associated with.

Why fractons hardly move

The immobility of fractons is not related to a physical obstacle inside the material, but to the conservation laws in force in the system. In an ordinary physical system, when a particle moves, its charge must be preserved. In theories describing fractons, the dipole moment is additionally preserved, which is an indicator that takes into account the distribution of charge in space. Independent movement of one fracton would change this distribution and violate the established rule.

Therefore, solitary arousal remains in place. Movement becomes possible only when several fractons change position in concert and the total dipole moment of the system is preserved.

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This behavior is described using gauge theories of rank 2 type U(1). A similar mathematical approach is used in electrodynamics, but in the case of fractons, the field has a more complex structure. It creates additional restrictions, due to which individual arousals lose the ability to move freely.

Previously, fractonic states could be described mainly using such abstract theories. The main difficulty was to transfer their rules into a fairly simple model of interacting spins, which could be experimentally reproduced in the future.

What is a quantum spin liquid?

Quantum spin fluids are considered to be one of the possible environments for the existence of fractons. Despite the name, we are not talking about a liquid in the usual sense, but about a special magnetic state of a solid.

Collective excitations with unusual properties may occur within such a system. In ordinary quantum spin liquids, quasiparticles are able to move through the material. In the fractonic phase, additional restrictions are imposed on their movement.

What model did the scientists create?

The authors of the new work considered a two-dimensional square lattice, the nodes of which correspond to quantum variables with spin 1. This means that each element of the model can be in one of three states, conventionally designated as -1, 0 and +1. A special scheme of interactions was set between the spins, reproducing the rules of the gauge theory of rank 2. Then the scientists calculated the behavior of the system using the Monte Carlo method based on the Green's function.

It is used to study complex quantum systems in which it is impossible to directly iterate through all possible configurations. The number of such variants increases rapidly with each new element of the grid, so researchers use probabilistic calculations and gradually approach the lowest-energy state of the system.

The scientists paid special attention to the influence of quantum effects. In previous models, a problem arose: with too weak quantum interactions, fractons were preserved, but in fact remained classical objects. As these effects intensified, the desired phase collapsed or gave way to the usual magnetic order.

Using spin 1 gave each node of the lattice an additional state compared to the spin 1/2 model. As a result, the system has received more possible ways to rebuild itself without violating the restrictions responsible for the existence of fractons.

Calculations have shown that with a certain ratio of parameters, the usual magnetic order is not formed in the model. Instead, a quantum phase appears, the properties of which correspond to a fractonic spin liquid.

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How physicists found signs of fractons

Because the study was conducted on a computer, the scientists did not observe individual quasiparticles directly. They were looking for characteristic features that should appear in the magnetic response of the system when a fractonic phase occurs.

One of these indicators was the magnetic structural factor. It reflects how the spin states in different parts of the lattice are related to each other. The result is usually depicted as a map in a pulsed space, where different types of magnetic behavior create characteristic patterns.

The so-called suppressed compression points appeared in the calculated picture. These are special elements of the magnetic correlation distribution predicted by the gauge theory of rank 2. Their shape practically coincided with the theoretical picture expected for a fractonic quantum spin liquid.

Another sign was the appearance of gapless collective excitations, which the authors call emergent photons. They are not particles of light and do not represent ordinary electromagnetic radiation.

Such "photons" arise only inside a quantum system as a result of the collective behavior of spins. Their properties are described by equations similar to those used for ordinary photons. In the new model, they exist in two spatial dimensions and time, so the researchers are talking about a space-time of dimension 2+1. Scientists have found signs of a fractonic phase not only in the ground state of the system with minimal energy, but also in a number of nearby low-energy states. This shows that the result is not limited to one specially selected configuration.

Why do quantum technologies need fractons?

Modern quantum systems are extremely sensitive to external influences. Heat, electromagnetic noise and imperfect equipment can change the state of the qubit and lead to the loss of recorded information.

In many systems, a local disturbance creates an excitation capable of moving freely and spreading the error to neighboring areas. This is more difficult to do with fractons: a single excitation remains in place, and in order to move it, several elements must be changed in concert.

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Theoretically, such limited mobility can make it difficult for some errors to propagate and make quantum information more stable. For this reason, fracton systems are considered as one of the possible approaches to creating quantum memory.

However, the practical application is still a hypothesis. In the new study, the researchers did not create an information storage device, record data, or measure its retention time. The work is devoted to the existence of the quantum phase itself, on the properties of which appropriate technologies can potentially be based in the future.

Even after the experimental detection of fractons, researchers will have to learn how to control them, write and read information, and check whether limited mobility really provides protection in real conditions.

When will fractons be able to be detected in an experiment

The fractons predicted specifically for quantum spin liquids have not yet been observed directly in the experiment. The system developed by the authors also remains a theoretical model, not a ready-made material. The next task will be to create a physical platform capable of reproducing a given pattern of interactions between spins.

A Rydberg atom is an atom whose one of the electrons has been transferred to a high energy level. Such atoms have a strong interaction, and their states can be controlled using lasers.

By placing Rydberg atoms in a given order, the researchers create programmable lattices and simulate the processes occurring in complex quantum materials inside them. This allows us to verify the theoretical model, even if the appropriate natural substance is still unknown.

To find the fractonic phase, it will be necessary to reproduce the necessary geometry of interactions, prepare the system in a low-energy state, and measure correlations between its elements. The coincidence of the obtained picture with the calculations will be an argument in favor of the experimental implementation of a fractonic quantum spin liquid.