New theoretical framework to describe how certain quantum systems avoid equilibrium

When many quantum particles evolve over time, they typically end up reaching an equilibrium state through a process called thermalization. Something similar happens in many classical systems. For example, if you place an ice cube in a thermos with water, the ice melts and the final (equilibrium) state is simply colder water than before.

In classical physics, complex systems eventually reach equilibrium (if you wait long enough, the ice always melts, in cases like the example). However, certain quantum many-body systems challenge this norm. For them, thermalization does not occur and the system remains out of equilibrium. This is the case for a large class of strongly disordered systems, where characteristics such as interactions between particles or individual energies exhibit a certain degree of randomness. This behavior is due to many-body localization (MBL), a mechanism that preserves the initial conditions of the system over time.

Local integrals of motion (LIOMs) constitute a widely used theoretical framework to study MBL. However, a recent study, carried out by an international team led by Adith Sai Aramthottil, from the Jagiellonian University of Krakow in Poland, and in which Piotr Sierant and Maciej Lewenstein, from the Institute of Photonic Sciences (ICFO) in Castelldefels, collaborated, Barcelona, ​​shows that LIOMs are insufficient to describe the behavior of a broad class of systems, particularly those with more complex types of disorder. The authors of the study propose a new theoretical framework, the real-space renormalization group for excited states (RSRG-X), that can explain MBL in a larger number of quantum many-body systems.

The team knew that LIOMs can capture the behavior of the MBL when the disorder of the system affects individual properties of the particles (localized disorder). However, they suspected that LIOMs could not describe systems where randomness influences interactions between particles (binding disorder).

To test this hypothesis, the researchers applied RSRG-X to a chain disordered by spin particle bonds (i.e., particles that behave like small magnets). The results showed that, indeed, the RSRG-X provides a theoretical description of the MBL in these systems, where LIOMs do not even exist. Their theoretical framework reveals new features of MBL in many-body quantum systems, including energy levels with anomalously small separations, the emergence of non-trivial entanglement structures, and the presence of observable quantities that allow experimental demonstration of the phenomenon. The description obtained turned out to be qualitatively accurate and, in this way, the researchers demonstrated the validity of the procedure.

In classical physics, the temperature difference between a mass of ice and its hot surroundings disappears over time. In quantum physics, there are systems in which this generic process towards a final state of equilibrium does not occur. (Image: Amazings/NCYT)

“We have provided a framework applicable to a broader range of systems and, thanks to this, we have shown that the physics of the MBL is richer than previously thought,” explains Piotr Sierant. Furthermore, the novel approach has implications that can be tested in experiments, for example, with ultracold atom gases or superconducting qubits. Sierant adds: “Rydberg atoms are just one platform, among many others, where the systems we have in mind could be realized. “That’s very convenient because, as theorists, we would love to see our framework implemented in a real-world scenario.”

The study is titled “Phenomenology of Many-Body Localization in Bond-Disordered Spin Chains.” And it has been published in the academic journal Physical Reviews Letters. (Source: ICFO)