Exploring Phases of Matter With Restrictive Conservation Laws: Anomalies, Topology, and Dynamics

NONTECHNICAL SUMMARY

This award supports theoretical research with a general goal to understand how constraints in many-particle quantum systems can lead to novel phases of matter and physical phenomena. During the last decade, new experiments have enabled the study of regimes of physics, in which many particles conspire to behave collectively in ways that are very different from the behaviors exhibited by individual atoms.

This has allowed physicists to explore a wide range of intriguing phenomena, from synthesizing exotic new kinds of particles, to realizing states of matter that can remember their initial state for an arbitrarily long time (in sharp contrast to the predictions of the laws of thermodynamics).

These new experimental capabilities have renewed efforts to understand what kinds of collective behaviors can emerge in quantum many-body systems. Understanding these possibilities has both fundamental implications for expanding our understanding of the world around us, and the potential for practical implications in advancing quantum computing. One part of this project focuses on exploring a new class of such behaviors, that can arise when the microscopic particles undergo motion that is restricted in some way, with the aim of developing new mathematical tools and frameworks to describe them.

Such frameworks will enable a more general exploration of what new kinds of physical effects these mobility restrictions can lead to, including their potential for storing quantum information in protected quantum states that are spatially localized near their boundaries. A major challenge in pushing the frontiers of this new generation of experiments is noise: random processes that couple a quantum system to its environment, ultimately destroying the delicate quantum information stored therein.

As such, understanding noise in complex, many-body quantum systems has become an increasingly important problem. The second part of this project focuses on understanding how restrictions on particle mobility, as well as related constraints that can be imposed on quantum systems, affect the impact of certain types of noise. The goal of this study is to understand whether, and when, such constraints can lead to quantum phenomena that are unexpectedly robust to noise.

This award will also support the PI's education and outreach activities, which consist of (i) modernizing the undergraduate quantum mechanics curriculum and transitioning a special topics course on quantum computation and quantum information designed by the PI to a regular course, (ii) training graduate students in both basic analytical and numerical skills, and (iii) helping coordinate events aimed at attracting women and minorities to the physics major.

TECHNICAL SUMMARY

This award supports theoretical research with a general goal to understand how constraints in many-particle quantum systems can lead to novel phases of matter and physical phenomena. Two classes of problems will be investigated. The first consists of understanding the interplay between topology and highly constraining symmetries, such as subsystem symmetry, which requires particle motion to conserve all multipole moments.

The PI will (i) explore how anomalies in subsystem symmetries can be used to understand different classes of gapless boundary modes that are known in the literature, and (ii) apply new mathematical tools to study a general construction, known as a topological defect network, that can produce a wide array of subsystem-symmetric models in 2 dimensions. This research may also have implications for understanding phases with less stringent symmetry constraints, such as conserved dipole (but not higher multipole) moments, that may lead to experimentally verifiable predictions, as global dipole symmetry arises naturally, for example, in some cold atomic systems.

The second class of questions to be explored is how constraints impact the dynamics of open quantum systems. A particular focus is on understanding when slow dynamics can arise, such that quantum coherence can be preserved for an unexpectedly long time. Here, the PI will explore the impact of constraints on dynamics by developing a modified Lindblad formalism for Hilbert spaces with local constraints.

This formalism can be used to study open system dynamics in a variety of cases where constraints are known to lead to atypical Hamiltonian dynamics, such as Hilbert space shattering and approximate quantum scars.

This award will also support the PI's education and outreach activities, which consist of (i) modernizing the undergraduate quantum mechanics curriculum and transitioning a special topics course on quantum computation and quantum information designed by the PI to a regular course, (ii) training graduate students in both basic analytical and numerical skills, and (iii) helping coordinate events aimed at attracting women and minorities to the physics major.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.