Calendar

We will briefly talk about recent developments on inequalities for infinite dimensional quantum symmetries.

Zoom: https://harvard.zoom.us/j/779283357

Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudo gap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wave functions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang).Quantum fluctuations are described by a gauge theory of ghost fermions that carry neither spin nor charge. I will also describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.

Zoom: https://harvard.zoom.us/j/977347126

Math Table/Open Neighborhood Seminar

You’ve probably seen pictures drawn on the chalkboard of a torus (the surface of a donut) or the Klein bottle, a torus with many holes, and perhaps other surfaces.  In this talk we will take up the question of whether or not it is possible to make a list of all of the possible pictures of surfaces. The question turns out to have a surprising and beautiful answer, but it takes some real insights to make it into an actual question in mathematics.  The story here is not only one of a striking theorem, but also one about mathematicians find, ask, and refine questions.

via Zoom Video Conferencing: https://harvard.zoom.us/j/96759150216

email vcollins@math.harvard.edu or deg@math.harvard.edu for the Password

We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.

Zoom: https://harvard.zoom.us/j/977347126

Discriminating between unknown objects in a given set is a fundamental task in experimental science. Suppose you are given a quantum system which is in one of two given states with equal probability. Determining the actual state of the system amounts to doing a measurement on it which would allow you to discriminate between the two possible states. It is known that unless the two states are mutually orthogonal, perfect discrimination is possible only if you are given arbitrarily many identical copies of the state.

In this talk we consider the task of discriminating between quantum processes, instead of quantum states. In particular, we discriminate between a pair of unitary operators acting on a quantum system whose underlying Hilbert space is possibly infinite-dimensional. We prove that in contrast to state discrimination, one needs only a finite number of copies to discriminate perfectly between the two unitaries. Furthermore, no entanglement is needed in the discrimination task. The measure of discrimination is given in terms of the energy-constrained diamond norm and one of the key ingredients of the proof is a generalization of the Toeplitz-Hausdorff Theorem in convex analysis. Moreover, we employ our results to study a novel type of quantum speed limits which apply to pairs of quantum evolutions. This work was done jointly with Simon Becker (Cambridge), Ludovico Lami (Ulm) and Cambyse Rouze (Munich).

Zoom: https://harvard.zoom.us/j/779283357