*This Simons Collaboration will bring together successful theorists – both established and young leaders in complementary areas of condensed matter, mathematical physics, atom**ic, molecular, and optical physics, and string theory. Each member of the team delivers a unique capability and set of tools to study the cornerstone concepts of quantum physics, and strong collaborations already exist within this group, while new ones were formed recently in the course of the Simons Ultra QuantumMatter meetings.*

** Leon Bale****nts** (Kavli Institute) is a leading figure in condensed matter theory, where he has made fundamental contributions to the theory of low-dimensional conductors, spin liquids, quantumcritical phenomena, and topological phases of matter. He co-authored the first paper on topological insulators in three dimensions and coined the term“topological insulator.”

**Xie Chen** (Caltech) is an associate professor of theoretical physics at the California Institute of Technology. She received her Ph.D. from MIT in 2012, and prior to joining Caltech, she was a Miller research fellow at the University of California, Berkeley. Chen’s research bridges quantum information theory and condensed matter physics. She uses quantum information techniques and tools to study emergent phenomena in quantum many-body systems, especially topological phases in strongly interacting systems. Her contribution includes the classification of symmetry protected topological phases and the proposal of anomaly detection methods for symmetry enriched topological phases. More recently, she is interested in a new class of quantum models — the fracton models — with deep connection to both quantum codes and field theory. Chen has revealed a hidden “foliation” structure in a large class of fracton models and used it to formulate the notion of “fracton order”.

**Matthew Fisher** (UCSB) is universally recognized as a leader in theory of condensed matter, who has also been a celebrated mentor of several generations of theorists (including three members of this Collaboration). He pioneered the application of field-theoretic duality in quantum condensed matter systems, and has made many other important discoveries in the nascent field of UQM. His recent work includes continued contributions to the theory of gapped and gapless UQM, in addition to examining the non-equilibrium dynamics of quantum entanglement.

**Victor Galitski** (Joint Quantum Institute, UMD) works broadly across the fields of atomic, molecular, and optical physics and condensed matter physics. He is known for his ability to connect sophisticated mathematical constructions and concepts to concrete experiments. To wit, he introduced and predicted topological Kondo insulators (subsequently discovered in heavy-fermion materials), Floquet topological insulators (experimentally realized in photonic systems), and spin-orbit-coupled Bose-Einstein condensates (subsequently engineered in the cold atom laboratory). These examples are among the most promising platforms for UQM.

**Victor Gurarie** (CU Boulder). Originally known for seminal work in conformal field theory, Gurarie’s work spans the areas of topological states ofmatter, disordered systems, and ultra-cold atoms. His work onUQMincludes contributions to the theory of non-Abelian statistics in the fractional quantum Hall effect, topological p-wave superfluids in quantum gases, the characterization of topological order using Green’s functions, and, with Hermele, exotic phases of alkaline earth atoms.

**Michael Hermele** (CU Boulder) is a young but established leader in the field of strongly correlated quantum matter. Early in his career, he made seminal contributions to the theory of quantum spin liquids. His recent work spans from UQM in both ultra-cold atomic gases and solid state materials, to topics in topological UQM, especially the role of crystalline symmetries, and fracton UQM (some with Chen).

**Shamit Kachru** (Stanford) has done foundational work on quantum field theory, string theory, and their interconnections. His recent work explores deep mathematics connecting automorphic forms, black holes, and string vacua, and develops quantum field theories describing ‘non-Fermi liquids’ and other novel phases in condensed matter physics.

**Andreas Karch** (University of Washington) is a high-energy theorist and a leader in the formal study of strongly correlated systems. He has successfully used dualities to map out interesting physical properties of gauge theories with potential applications to real world physical problems. Among his accomplishments in this area are the study of energy loss in strongly correlated systems and the analytic treatment of non-linear conductivities. He is a co-inventor of the web of dualities in 2+1 dimensions that is at the heart of the recent resurgence in research in this area.

**Michael Levin** (Chicago) is widely known for his deep and thoughtful research on topological matter. Together with Wen, he pioneered string-net condensation as a physical mechanism for topological phases, and introduced topological entanglement entropy. He has made some of the key contributions in symmetry-protected topological phases, braiding statistics of loops in three dimensions, and the fundamental understanding of the bulk-boundary correspondence.

**John McGreevy** (UCSD) is a uniquely broad young theorist, working at the interface of condensed matter physics, quantum field theory, and string theory. He has developed influential controlled models of non-Fermi liquids in both field theory and string theory. He found the first holographic duals of non-relativistic fixed points. And most recently, he has done ambitious work classifying gapped and gapless phases of quantummatter based on entanglement scaling.

**Subir Sachdev** (Harvard) has had a long-standing interest in the study of gapless systemswithout quasiparticles. His book, Quantum Phase Transitions, described the non-zero-temperature dynamics of many such systems. He proposed what is now called the SYK model in 1992, and it has since emerged as a fundamental solvable model of UQM in metals. He has also studied metallic states with topological order, and their phase transitions, in the context of applications to cuprate compounds.

**Nathan Seiberg** (Institute for Advanced Studies, Princeton) is a world leader in the study of quantum field theory and string theory. His discovery (with Moore) of the mathematical structure of modular tensor categories, and his full solution (with Witten) of the dynamics of a confining gauge theory in 3+1 dimensions were major breakthroughs with profound implications for both physics and mathematics. Several of the best established gauge theory dualities are due to him. In recent years he and his collaborators (including in condensed matter physics) have launched an ambitious program of discovering dualities in non-supersymmetric theories in 2+1 dimensions.

**Dam Thanh Son** (Chicago) has made profound contributions in areas ranging from nuclear physics and quantum chromodynamics, to ultra-cold atomic gases, to the quantumHall effect. Recently, he argued that the composite fermion in the half-filled Landau level is aDirac particle. This has led to a flurry of activity to establish dualities between seemingly unrelated strongly correlated states of matter.

**Senthil Todadri** (MIT) is known for his work on exotic phases/phase transitions of strongly correlated quantum matter. Together with Balents, Fisher, Sachdev and Vishwanath, he proposed an alternative to the Landau-Ginzburg-Wilson paradigm for criticality, in the context of their theory of deconfined quantum critical points. He has played a leading role in the field of non-Fermi liquids, in the classification of strongly interacting topological insulators and related topological phases, and in the development of field theory dualities with diverse applications in condensed matter physics.

**Ashvin Vishwanath** (Harvard), is a condensed matter theorist, known for his work on the gauge theory description of “beyond-Landau” quantum phase transitions, as well as the theoretical prediction of Fermi-arc surface states in Weyl semimetals. He has contributed to the theory of topological phases, in particular highlighting the special properties of defects such as dislocation and the role of crystal symmeties in protecting and diagnosing topological states. He, along with T. Senthil, introduced the concept of surface topological order and with Chen and Fidkowski used it to demonstrate the interaction reduction of 3D topological superconductors. These ideas led to his recent work on dualities between quantum field theories and their physical signatures.

**Xiao-Gang Wen** (MIT) was one of the founders of the field of topological phases of matter, long before it became mainstream. His contributions to the field are manifold, but in particular he introduced the notion of topological order in 1989, and its bulk-boundary correspondence in terms of anomalies. This opened up a new research direction in condensed matter physics. Wen’s research has often exposed mathematical structures that have not appeared before in condensed matter physics problems. He has mentored a number of successful theorists (including two members of this Collaboration).

** Peter Zoller** (University of Innsbruck) is a world leader in the fields of quantum optics, quantum information and AMO physics. He has made many seminal contributions to these fields, including the key contributions that brought the study of quantum matter to ultra- cold atom systems. He is particularly interested in developing new schemes to carry out non-local measurements in atomic systems – ideas which have been taken up with notable recent success experimentally.