New physics theory to study low-energy excitations in quantum quasicrystals

Quasicrystals, exotic states of matter characterized by an ordered structure with non-repeating spatial patterns, have been the focus of numerous recent physics studies due to their unique organization and resulting symmetries. Among the quasicrystals that have sparked significant interest among the physics community are so-called quantum quasicrystals, which are comprised of bosons (i.e., subatomic particles that have spin in integer values, such as 0, 1, 2, and so on, and can occupy the same quantum state simultaneously).

Researchers at the Max Planck Institute for the Physics of Complex Systems (MPIPKS) recently introduced a new theoretical framework that describes low-energy excitations in bosonic quantum quasicrystals. Their newly devised theory, outlined in a paper published in Physical Review Letters, is an extension of conventional theories of elasticity, which also accounts for the unique symmetries of quantum quasicrystals.

“This paper is part of an ongoing collaboration with two colleagues, Prof. Francesco Piazza and Dr. Mariano Bonifacio, which began in 2022 when I was a guest scientist at MPIPKS in Dresden, Germany,” Alejandro Mendoza-Coto, first author of the paper, told Phys.org.

“We were studying quantum self-assembled quasi-crystalline phases in cavity QED models, and at a certain point, we concluded that, considering future experimental verification of our results, the study of the low-energy excitations in these systems would be relevant.

“Another compelling reason to consider this problem was the existence in the literature of previous symmetry arguments predicting five gapless excitation modes for these systems, while a first-principles theory supporting this conclusion was still lacking.”

Initially, Mendoza-Coto, Bonifacio and Piazza tried to study the entire excitation spectrum of quasicrystals numerically, but when this proved challenging, they started conducting theoretical analyses. As they progressed in their analyses, they realized that a first-principles elastic theory for bosonic quantum quasicrystals was still lacking, and they set out to develop one.

“We drew inspiration from several different papers focusing on the construction of a low energy effective theory for supersolids,” said Mendoza-Coto.

“I believe that the main point to highlight here is the recognition that if we wanted to pursue a first-principles theory for modulated bosonic systems, we needed to include not only the expected fluctuations in the phases of the modulated pattern and the condensate itself but also the respective density field fluctuations conjugate to each phase fluctuation field introduced. This is a very important consideration that separates our work from others in the literature.”

The main idea behind the team’s theory is that to study low-energy fluctuations at the ground state of a quantum quasicrystal system, one needs to consider more than fluctuations in the phases of the density pattern and condensate wave functions that are already expected to occur. Specifically, they should also account for other conjugate fluctuations (i.e., which are mathematically linked to expected fluctuations).

“In my view, this is the most important detail that we recognized in order to build a first-principles theory with the appropriate number of degrees of freedom, which at the same time is consistent with the symmetry properties already expected for this system,” explained Mendoza-Coto.

“Once you know which kind of fluctuations need to be included and in which way they should be added to the ground state wave function, the calculations are quite straightforward, and our conclusions do not rely on further assumptions.”

After the researchers obtained the low-energy action for the simplest possible quasicrystal structure (i.e., the dodecagonal quasicrystal), Piazza suggested extending their study to other possible quasi-crystalline structures. This allowed them to better understand the extent to which their theory could be generalized across different quantum quasicrystals and thus make predictions about the physics observed in these systems.

“This later proved valuable, as we found that different kinds of quasicrystal structures display different hybridization features between modes and even anisotropic properties, certainly a nice finding of our work,” said Mendoza-Coto. “I believe that our results are, to a point, the analog for non-homogeneous phases of the well-known Bogoliubov excitation spectrum for homogeneous condensates.

“To obtain closed analytical expressions for the excitation energies at low momentum in quantum quasicrystals is, in my view, a very nice result, as the standard method to pursue this kind of calculation in the literature is a numerical one.”

The recent work by Mendoza-Coto, Bonifacio, and Piazza could inform future studies to better understand bosonic quantum quasicrystals and their underlying physics. In the future, the theory they introduced could help to understand phase transitions in quantum quasicrystals and potentially also in supersolids (i.e., states of matter with a crystalline order that combine some properties of solids and superfluids).

“I think that this work will help us in the search for novel exotic phases in systems hosting superfluidity and topological defects, such as the proposed super-hexatic or super-nematic phases,” added Mendoza-Coto. “I have several projects following up this research. We are already working on extending this work to one-dimensional quasicrystals in cavity QED conditions, as well as other projects related to the application of this formalism to supersolids.”

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