Quantum dynamics鈥攖he study of how particles behave and interact in a quantum system鈥攈as long fascinated physicists due to its puzzling and sometimes bizarre behaviors. Unlike classical systems, where particles follow predictable paths, quantum systems can act unpredictably, such as in superposition, where the particle is in multiple quantum states simultaneously.

As particles interact, these systems often evolve towards thermal equilibrium, where the system is equally likely to be found in any configuration with the same total energy. However, in some cases, quantum systems have been conjectured to resist this process and exhibit what鈥檚 known as many-body localization (MBL), where, even as particles are allowed to interact with each other, the energy and quantum information remain 鈥渢rapped鈥� in localized microscopic configurations rather than spreading out among all available configurations over time.

Understanding whether and why MBL happens can help scientists delve into the fundamental laws of nature and unlock new possibilities for technologies like quantum computing, where preventing the loss of quantum information is critical. For years, physicists have debated whether MBL could occur in systems with many interacting particles.

Now, in a published as an Editor鈥檚 Suggestion in Physical Review Letters, 兔子先生传媒文化作品 Physics Associate Professors Andrew Lucas and Rahul Nandkishore, along with graduate student Chao Yin, provide a first-of-its-kind mathematical proof showing how MBL can happen in a many-particle system.

鈥淪o I would say the basic result is that our work settles a critical point of principle,鈥� stated Nandkishore. 鈥淚 think it sort of settles it in a way that's a little more easily understandable and transparent.鈥�

The Mystery of Many-Body Localization

While most quantum systems typically show thermalization, where the energy and particles in the system tend to spread out over space and time evenly, some quantum systems can resist this process and get stuck in a state known as thermalization. Instead of a mouse in a maze exploring every nook and cranny of its new environment, a 鈥渓ocalized鈥� mouse becomes stuck and only stays in one part of the maze.

The idea of localization was initially proposed in 1958 by physicist Phillip Anderson, who showed that localization could occur in single particle systems. This work would later be cited in his 1977 Nobel Prize.

However, whether such localization can occur in many-body systems鈥攕ystems with many interacting particles鈥攈as been a topic of heated debate in physics for the last twenty years.

Andrew Lucas explained, 鈥淧eople are interested in understanding systems where this will not happen. Even at infinite times, you watch the system, and it just doesn鈥檛 [thermalize]. Conventional statistical mechanics cannot describe it.鈥�

Computer Science and Physics Meet to Study MBL

Previous studies on many-body localization mainly focused on simple, one-dimensional systems. At least one earlier proof claimed that localization can occur in such systems, but it was long and complex and relied on a plausible but unproven assumption.

The 兔子先生传媒文化作品 team approached the problem from a different angle, taking inspiration from computer science.  They studied a quantum system inspired by low-density parity check (LDPC) codes鈥攎athematical tools commonly used in error correction for digital communication, such as in 5G communications. Error-correcting codes store information in a redundant way among many bits, such that experts can detect and correct such errors if a low enough number of bits have been corrupted.

Studying quantum systems based on LDPC codes allowed the researchers to bypass some of the complications of the previous research and provide a more accessible and rigorous demonstration of MBL.

Lucas explained the crux of their approach: 鈥淲e are almost able to analyze this many-body problem as if it was a single-particle problem... because these error-correcting codes have a very complicated energy landscape.鈥�

This energy landscape acts as a sort of maze, where the quantum system remains stuck near one of many low-energy configurations (or 鈥渃ode words鈥�), much like how an error-correcting code helps data stay stable despite noise.

Using the LDPC code, the researchers showed that the system's quantum particles get 鈥渢rapped鈥� in specific configurations, unable to explore all possible states due to large energy barriers. Their proof demonstrated that for systems governed by LDPC-like structures, quantum particles remain trapped in localized states indefinitely, even in systems with many interactions.

Nandkishore highlighted this significance: 鈥淲hat we were able to do is rigorously establish this via a relatively short and understandable proof.鈥�

This is the first time a fully rigorous proof has shown that many-body localization can occur in a system with many interacting particles and extensive configurations. Currently, the proof only works in an infinite dimensional geometry.

MBL Can Advance Other Fields

Understanding the dynamics of MBL is significant for many fields, including quantum computing, where the goal is to keep quantum states stable long enough to perform calculations. In a thermalizing system, quantum information would be quickly lost as particles spread energy and interact. However, in a localized system, quantum information could be preserved much longer, making error correction more feasible.

鈥淭his is the first construction where we have a mathematical proof for this localization phenomenon,鈥� stated Lucas. 鈥淚t鈥檚 suggestive that we can use ideas from error correction to learn things about physics and push the limits of concepts like statistical mechanics and thermodynamics."

Off

The Anatoly Larkin Award, named after the renowned theoretical physicist, celebrates outstanding achievements in theoretical physics. The accolade is given annually to two researchers鈥攐ne senior and one junior鈥攚ho have made exceptional contributions to advancing the field. 

Nandkishore鈥檚 work, which spans various complex areas in theoretical physics, continues to shape our understanding of many-body quantum systems and their behavior in disordered environments. His recognition by the FTPI underscores the impact and significance of his research in the scientific community. 

As part of the recognition, Nandkishore will be invited to present a colloquium at the University of Minnesota's School of Physics and Astronomy.  

鈥淚 am honored and grateful to receive this award,鈥� Nandkishore stated. 鈥淏eing a theoretical physicist can be a lonely business 鈥� you work hard on problems that you think are important, but at the same time you can鈥檛 help but wonder if anyone cares. It鈥檚 nice to know that the community does care, and recognizes the importance of the work you鈥檝e been doing. I am also grateful for the unflagging efforts of the students and postdocs who have worked with me, and who helped establish many of my results, to the senior scientists who mentored me, and to my colleagues at CU who created such a supportive environment for my research.鈥� 

Off

"I feel honored to receive this prestigious award for my research in theoretical condensed matter physics鈥� Nandkishore said.

According to their web site, the Sloan Research Fellowships seek to stimulate fundamental research by early-career scientists and scholars of outstanding promise. This year, 126 researchers were recognized for their distinguished performance and a unique potential to make substantial contributions to their field.

Dr. Nandkishore is a theoretical condensed matter physicist working on disordered many body quantum systems. He has made important contributions to several areas of condensed matter physics, including the study of Dirac semimetals, the phenomenon of many body localization, and investigations of unconventional superconductivity.  

"I intend to use the award to continue exploring the behavior of quantum many body systems, both in and out of equilibrium,鈥� Nandkishore said. 鈥淣ew frontiers in equilibrium many body physics are constantly being opened up by advances in materials science. Meanwhile, the study of out of equilibrium many body quantum physics is one of the great open frontiers for theoretical physics research, progress on which has recently been revolutionizing our understanding of quantum statistical mechanics. I am extremely happy that I have the opportunity to do research on a topic that is relevant for so many different areas of physics, and which offers the opportunity to make foundational contributions to our understanding of quantum phenomena."

The award comes with a $60,000 prize that Professor Nandkishore will use to further research the behavior of quantum many body systems, both in and out of equilibrium.

Rahul Nandkishore earned a bachelor鈥檚 degree and Master of Science degree from University of Cambridge in 2008 and a doctorate degree from MIT in 2012. Prior to coming to University of Colorado in 2015, he was a post doctoral researcher at the Center for Theoretical Science at Princeton University.  Assistant Professor Nandkishore is a theoretical physicist working on some of the most important current topics in theoretical condensed matter physics with exciting implications for areas from quantum information to string theory. He has published thirty-five papers, including twenty since 2014, and he is first-author on nineteen published papers. He has two invited review papers.

Established in 1934 by Alfred Pritchard Sloan Jr., then-president and CEO of General Motors, the New York-based foundation is a philanthropic, nonprofit grant-making institution supporting original research and education in science, technology, engineering, mathematics, and economics.

Off