2026 Simons Collaboration on Ultra Quantum Matter Annual Meeting

The 7th annual meeting of the Simons Collaboration on Ultra-Quantum Matter (UQM) was held January 22–23, 2026, with 120 in-person participants. In addition to the speakers, the PIs and postdoctoral fellows of the UQM Collaboration, and other students and postdocs, the meeting was attended by over 40 other faculty members working on various aspects of UQM.

The first day emphasized advances in the theory of ultra-quantum matter. The meeting opened with a talk from Ashvin Vishwanath, who surveyed work across the Collaboration and proceeded to introduce a new mechanism for superconductivity, dubbed topological criticality. He also explored connections between universal quantum computation and the complexity of topological phases of matter, in particular of two related states: the S₃ quantum double, which was recently realized experimentally and used to demonstrate a complete gate set, and a novel charge‑4 superconductor related to a Read–Rezayi quantum Hall state. Michael Levin covered recent progress in understanding entanglement-based probes of two-dimensional topological phases, in particular the topological entanglement entropy and the modular commutator. Xie Chen’s talk introduced a notion of “emergent symmetry” in gapped phases, focusing on the example of a two-dimensional Z₂ symmetry-protected topological (SPT) state placed on a Klein bottle. Michael Hermele followed with a survey of the complex landscape of fracton phases of matter, presenting the first classifications of certain types of fracton order, and introducing the related problem of classification and characterization of subsystem symmetries. The day concluded with a talk by Shu-Heng Shao on chiral anomalies and CPT symmetry in lattice systems. Focusing on a massless Dirac fermion in 1+1 dimensions, he demonstrated that lattice realizations of vector and axial U(1) symmetries form a non-Abelian algebra and enforce gaplessness, providing a striking example of anomaly constraints in discrete systems.

The second day broadened the scope of the meeting to include materials discovery and novel routes to superconductivity. Dogus Cubuk described work at Periodic Labs that combines automated experimentation, large language models, and theoretical insight to accelerate the discovery of quantum materials. A particular emphasis was placed on the search for superconductors with higher critical temperatures, illustrating how modern machine-learning tools can interface with experimental and theoretical physics. Senthil Todadri then discussed superconductivity emerging from doped fractional quantum Hall states realized in lattice systems at zero magnetic field. Upon doping, such states host a mobile fluid of anyons whose collective behavior can give rise to metallic and superconducting phases. The meeting concluded with a talk from Nathan Seiberg, in which he clarified the distinctions between “gauging a one-form symmetry” and “anyon proliferation.” He showed how these closely related but distinct operations can be used to analyze phase transitions out of a given topological order. His presentation tied together themes of symmetries and anomalies that resonated throughout the meeting.

Xie Chen
California Institute of Technology

SPT Transition on Klein Bottle and Emergent Symmetry

In this talk, we start from an observation about the 2D Z2 SPT when it is put on the Klein bottle: inserting a Z2 flux through the orientation-reversing cycle induces a Z2 symmetry charge. The role played by reflection symmetry in this example led us to define the notion of “emergent symmetry” in gapped phases. We comment on its connection to sequential circuit, the Symmetry TFT formalism, and potential implications on low energy excitations at critical points.

Dogus Cubuk
Periodic Labs

Combining Experiments, Large Language Models, and Theory to Discover Quantum Materials

TBA

Michael Hermele
University of Colorado Boulder

Navigating the Fracton Landscape

There are now many examples of gapped fracton models, which are defined by the presence of restricted-mobility excitations above the quantum ground state. This complex landscape of examples is far from being mapped out. In this talk, Michael Hermele will describe recent progress on characterization and classification of fracton orders, and on related problems for subsystem symmetries.

Michael Levin
University of Chicago

Entanglement Probes of Topological Phases of Matter
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Michael Levin will discuss recent progress in understanding entanglement-based probes of 2D topological phases of matter. These probes are supposed to extract universal topological information from a many-body ground state. Specifically, Levin will discuss (1) the topological entanglement entropy, which is supposed to give information about whether the ground state supports anyon exciations, and (2) the modular commutator and its variants, which are supposed to tell us the chiral central charge.

Nathan Seiberg
Institute for Advanced Study

Symmetry, Anomaly, Gauging, Proliferation, and Condensation

In the study of topological quantum field theories in 2+1 dimensions, it is common to perform an operation known as “anyon condensation.” This term is misleading. Two more appropriate terms for this operation are “gauging a one-form symmetry” or “anyon proliferation.” Interestingly, these two terms are similar but not identical. We will clarify these different notions and use this insight to analyze various phase transitions out of a given topological order.

Shu-Heng Shao
Massachusetts Institute of Technology

Chiral Anomalies and CPT

We discuss how the vector and axial U(1) symmetries of a massless Dirac fermion in 1+1d are realized in Hamiltonian lattice systems. Interestingly, these two lattice charges do not commute and form a non-abelian algebra, first discussed by Onsager. We prove that these symmetries force the low-energy phase to be gapless, reminiscent of consequences from perturbative anomalies of continuous global symmetries in quantum field theory. This lattice anomaly is of order 2, but when a lattice CPT symmetry is further imposed, the anomaly becomes of infinite order (i.e., torsion-free).

Senthil Todadri
Massachusetts Institute of Technology

Superconductivity from the Fractional Quantum Hall Effect

The fractional quantum Hall effect was discovered in lattice systems in zero magnetic field in 2023. Doping such a state leads naturally to a realization of a mobile fluid of anyons. Senthil Todadri will describe some possible ground states of such a fluid refining old ideas on anyon-induced superconductivity. Todadri will show that a variety of conducting states, either metallic or superconducting, can arise. For the prominent 2/3 state seen in experiments, Todadri will show that the anyon-induced mechanism provides a possible explanation of the superconductivity observed very recently. Finally, Senthil will show that, in the presence of disorder, the first superconductor to form in the doped state is an “anomalous vortex glass” with randomly pinned spontaneous vortices despite the absence of an external magnetic field. He will discuss the implications for the phenomenology of the observed superconducting state.

Ashvin Vishwanath
Harvard University

What Is Ultra-Quantum Matter?

TBA2

Watch a playlist of all presentations from this meeting here.