Chen Chun's research group of Shanghai Jiaotong University has made progress in the research of unconventional multi-body localization

Recently, Chen Chun's research group of Shanghai Jiao Tong University collaborated with Professor Wang Xiaoqun and Professor Chen Yan of Fudan University to present "Many-body localization in the infinite-interaction limit and the discontinuous eigenstate phase transition" at npj Quantum The latest theoretical research results
were published on Information (impact factor: 10.
758).
This work explores how to achieve a novel unconventional many-body localization phenomenon and its accompanying dynamic eigenstate phase transition by introducing quasi-periodic disorder in the strongly interacting Rydberg atomic system
.

The Lars Onsager Prize, the highest prize in statistical physics at the American Physical Society in 2022, was awarded to three condensed matter theoretical physicists for their pioneering foundational work
on multibody localization and multibody localization phase transitions.

So, what is multibody localization? Why is it important?

On the one hand, multibody localization, more precisely, should be called multibody Anderson localization
.
It is a generalization
of non-interacting Anderson localization, under conditions such as short-range, weak interaction, and strong disorder.

On the other hand , from the physical image analysis , the many-body localization can be seen as generalizing Landau 's Fermi liquid theory to the entire Hilbert space
.
Specifically, Landau Fermi liquid theory is based on concepts such as quasiparticles and adiabatic approximations, and the free energy describing the interacting fermion system is near the Fermi surface, and the symmetry and other requirements are expanded according to the distribution of quasiparticles in the momentum space, thus constituting Landau functionals
.

Similarly , many-body Anderson localization , from a phenomenological point of view, expands the effective Hamiltonians describing a system into a complete set of interactions between local integrals of motion
.
The difference is that Fermi liquid theory is only suitable for describing low-energy quasiparticle excitation near Fermi surfaces, so it can only be used to characterize low-temperature ground states and physical processes
within their neighborhoods.
The many-body Anderson localization theory based on the integrals of local motion is considered to be applicable to describe the properties of all eigenstates in the entire Hilbert space of localized systems , and therefore to any temperature range
.

So, in a broader sense and analogy, what theory will correspond to the extension and generalization of non-Fermi liquids in a multibody localization framework? In other words, is there multibody non-Anderson localization? Or, is there an unconventional multibody localization phenomenon, in which the phenomenological theory based on the integration of local motion is no longer complete? This is similar to the fact that in the non-Fermi liquid theory, the concept of quasiparticles or their definition is not fully valid
.

Figure 1: Kinetic phase diagram
of an out-of-disorder restricted Rydberg atomic chain.
a and b show the evolution of the possible discontinuities of the left and right phase transition points with the size of the system
.
c shows a schematic diagram
of the discontinuous phase transition between the limited local state and the restricted thermal state at the thermodynamic limit.
Here, the level-spacing ratio is
represented.

Inspired by these questions, in this work, by studying the spatiotemporal evolution and propagation law of quantum information, we systematically predicted another form of many-body localization, that is, the "many-body non-Anderson local state" when the interaction between particles in a disordered system is infinite, and further revealed from a numerical point of view that the quantum eigenstate phase transition between the restricted local state and the restricted extended state is likely to have peculiar discontinuity
.
See Figure 1
.

This discovery greatly reduces the interference of size effects on such eigenstate phase transitions, and provides a new way
to solve the debate on the existence of many-body local states and their phase transitions in the field.
More significantly, existing analytic theories usually start from the assumption of the continuity of the phase transition, so the proposed theory of the discontinuous phase transition we have discovered may be able to further enrich the important frontier research
field of many-body localized phase transition.

The first author of the paper is Chen Chun, assistant professor of the School of Physics and Astronomy, Shanghai Jiao Tong University, and the corresponding authors are Chen Chun, Wang Xiaoqun and Chen
Yan.
The work was supported by the Shanghai Jiao Tong University faculty start-up fund, MOST2022YFA1402701, and the National Natural Science Foundation of China No.
11974244、the SKP of China Grant No.
2022YFA1404204 and National Natural Science Foundation of China No.
12274086 support
.

Link to the paper: https://doi.
org/10.
1038/s41534-022-00654-9