MPS Conference on Ultra Quantum Matter

The MPS Conference on Ultra Quantum Matter focused on recent progress describing states of matter that are inherently quantum mechanical on the macro scale — hence ‘ultra quantum’ — featuring long-range quantum entanglement. The conference was divided into four sessions on (i) gapped or topological phases, (ii) gapless phases including novel metals, (iii) out of equilibrium phases and (iv) routes to realize and probe these new states. Each session included a pedagogical overview to bring everyone up to speed, complemented by longer talks and concluding with a panel of short talks that focused on future directions. This format generated substantial discussion that carried over into the breaks.

Hermele opened with an overview of topological phases of matter reviewing recent progress in classifying and characterizing topological matter, and identified frontier areas crystalline topological phases, fracton states and non-equilibrium topology, with the latter two areas being developed further in other talks (Chen, Galitski, Potter). Connections between topological and gapless ultra-quantum matter, such as that discussed in the ‘ultra-quantum metals’ session, were also drawn. Anomalies play an important role in topological phases, with surface properties often connected to different kinds of anomaly cancellation between the surface and the bulk. Witten explained a new type of anomaly cancellation, whereby the anomaly of the Kitaev chain model for a topological superconductor can be canceled by coupling it to topological gravity. On the experimental front, Andrea Young reported on studies of fractional quantum Hall physics in a new regime, where a lattice potential plays a key role, leading to fractional Chern insulator states. These states offer the prospect to control non-Abelian excitations by making and manipulating defects in the lattice potential.

In the session on gapless phases and ultra-quantum metals, Sachdev and Balents presented an exciting new paradigm for a tractable theoretical description of the ‘bad,’ ‘strange’ or ‘incoherent’ metal phenomenology common to many strongly correlated materials. This paradigm, whose implications — including possible connections with dual gravity theories — are only beginning to be explored, is based on models with a solvable large-N limit, constructed by coupling Sachdev-Ye-Kitaev (SYK) quantum dots together into a lattice. Kapitulnik described measurements of the thermal diffusivity in strongly correlated materials that provide a new window into non-quasiparticle transport in these systems. Son’s talk focused on a classic ultra-quantum metal system, the composite Fermi liquid in the half-filled Landau level, and presented his theory of the composite fermion as a Dirac particle. This theory is closely connected to a series of new quantum field theory dualities and to the boundary physics of topological phases, tying together the two sessions of the day.

In the session on realizing and probing novel phases in hybrid and synthetic matter, Barkeshli described a theoretical proposal to physically implement modular transformations, long believed to be beyond the scope of experiment, in two-dimensional topologically ordered phases. Lukin reported on experiments in a promising new synthetic matter platform of arrays of Rydberg atoms, which are driven across a variety of order-disorder quantum phase transitions with an exciting degree of control.

Further into the realm of non-equilibrium quantum matter, Fisher presented results on the surprising possibility of quantum effects in finite-temperature fluids, both hidden partly entangled phases and chemical consequences. Galitski and Potter discussed Floquet topological states of matter, where theory predicts new forms of topological order that are impossible in equilibrium settings, enabled by periodic external drive.

Defining New Directions:
A goal of the meeting was to define research directions that were both exciting and tractable in light of recent scientific advances, and this goal was fostered by panel discussions featuring short talks, where the speakers were asked to present what they saw as the most interesting open questions and potential angles of attack.

1. Can we construct and solve models that describe transport in ultra-quantum metals?
   The talks of Sachdev, Balents, Senthil, McGreevy and Georges drove home the remarkable similarities of SYK-based models to existing experiments in ‘bad’ metals. They are now challenged to make predictions for a new generation of measurements as discussed in Kapitulnik’s talk. A key open question that will be pursued by them is to derive these models starting from more conventional ingredients such as random impurity spins. Tantalizing connections to two-dimensional black holes and earlier holographic models of non-Fermi liquids, highlighted by Kachru, Sachdev and McGreevy, should also be understood and exploited.
2. How do we probe novel phases and engineer Hamiltonians to realize them?
   Talks by Dalmonte and Gurarie discussed new probes of topological and gapless phases, including measurement of the entanglement Hamiltonian. The model of these feasible near-term experiments will be pursued by Galitski. Talks by Gurarie and Vishwanath highlighted the inverse problem of finding Hamiltonians for target states, with constructions whose potential caveats were pointed out by Levin.
3. How do topological phases constrain the dynamics of their gapless surfaces?
   Son’s and Metlitiski’s talks related topological phases, anomalies and gapless phases, like the composite Fermi liquid, and showed the potential to realize anomalous phases in unexpected ways. Clear-cut signatures for experiments like that described by Andrea Young are an important open problem, as are other applications to quantum critical systems like deconfined critical points.
4. Can we achieve a full understanding of topological order in 3+1 dimensions?
   As described by Wen, Chen and Levin, there has been substantial progress with the identification of `quantum volume’ and three-loop braiding, and a complete solution appears within reach. Important exceptions are ‘fracton’ topological phases, which seem to defy intuitions of spatial dimensionality and evade a conventional field theory description, which were flagged for future research.
5. What are the limits of quantum coherence in ‘hot’ or driven systems, and what new phenomena can arise?
   Stimulating talks by Potter and Fisher emphasized Floquet topological phases, sparking new efforts by Chen using tensor network methods and by Gurarie using the Chalker-Coddington approach. The role of disorder and the possibility of defining driven quantum phases in its absence was identified as a promising direction for future work by Galitski and Vishwanath.