This series covers all areas of research at Perimeter Institute, as well as those outside of PI's scope.
Conformal Field Theory (CFT) describes the long-distance
dynamics of numerous quantum and statistical many-body systems. The
long-distance limit of a many-body system is often so complicated that
it is hard to do precise calculations. However, powerful new
techniques for understanding CFTs have emerged in the last few years,
based on the idea of the Conformal Bootstrap. I will explain how the
Bootstrap lets us calculate critical exponents in the 3d Ising Model
In this talk, I will focus on cosmologies that replace the big bang with a big bounce. I will explain how, in these scenarios, the large-scale structure of the universe is determined during a contracting phase before the bounce and will describe the recent development of the first well-behaved classical (non-singular) cosmological bounce solutions.
Non-Fermi liquids are exotic metallic states which do not support well defined quasiparticles. Due to strong quantum fluctuations and the presence of extensive gapless modes near the Fermi surface, it has been difficult to understand universal low energy properties of non-Fermi liquids reliably. In this talk, we will discuss recent progress made on field theories for non-Fermi liquids.
In recent years, precise cosmological measurements have provided strong evidence for new physics beyond the Standard Model, occurring both in the very early universe and also today. In the near future, large-scale galaxy surveys will open another window on many different areas of physics, including tests of gravity, probes of dark energy, and cosmic inflation. However, interpreting galaxy surveys presents new challenges, because galaxies are sensitive to astrophysics that are unimportant for the cosmic microwave background.
I will argue that the standard model contains a rather strong hint that -- instead of being simply an ordinary continuous 4D manifold -- spacetime is actually the product of a 4D manifold and a certain discrete/finite 6D space (i.e. there are 6D discrete/finite "extra dimensions"). I will introduce this idea and the evidence for it in simple way, and then discuss various outstanding puzzles and future directions.
Tensor networks offer an efficient representation of many-body wave-functions in an exponentially large Hilbert space by exploiting the area law of ground state quantum entanglement. I will start with a gentle introduction to the tensor network formalism. Then I will describe its application to realizing Wilson's renormalization group directly on quantum lattice models (e.g. quantum spin chains), with emphasis on the RG fixed points corresponding to conformal field theories.
Scale invariant transfer matrices and Hamiltonians Abstract We investigate the possibility of strictly scale invariant transfer matrices in quantum spin chains based on a certain planar algebra, both as operators and as quadratic forms.
Recent explorations of the space of quantum field theories have provided novel topological and geometric information about this space. This voyage has resulted in the solution of some long-standing questions: the computation of sought-after topological invariants (Gromov-Witten invariants) by a new physics-based approach, the first instance of exact correlation functions in a four-dimensional QFT and the unearthing of the action of dualities on the basic observables of three dimensional gauge theories.
Experimentalists are getting better and better at building qubits, but no matter how hard they try, their qubits will never be perfect. In order to build a large quantum computer, we will almost certainly need to encode the qubits using quantum error-correcting codes and encode the quantum circuits using fault-tolerant protocols. This will eventually allow reliable quantum computation even when the individual components are imperfect.