Scientific Series

Renormalization is a principled coarse-graining of space-time. It shows us how the small-scale details of a system may become irrelevant when looking at larger scales and lower energies. Coarse-graining is also crucial, however, for biological and cultural systems that lack a natural spatial arrangement. I introduce the notion of coarse-graining and equivalence classes, and give a brief history of attempts to tame the problem of simplifying and "averaging" things as various as algorithms and languages. I then present state-space compression, a new framework for understanding the general problem. At the end, I present recent empirical results, in an animal social system, that show evidence for the coupling of scales: the reaction of coarse-grained facts about a system "downwards" to influence the microphysics. 

I will present recent theoretical work on cluster Mott insulators (CMI) in which interesting physics such as emergent charge lattices, charge fractionalization and quantum spin liquids are proposed. For the anisotropic Kagome system like LiZn2Mo3O8, we find two distinct CMIs, type-I and type-II, can arise from the repulsive interactions. In type-I CMI, the electrons are localized in one half of the triangle clusters of the Kagome system while the electrons in the type-II CMI are localized in every triangle cluster. Both CMIs are U(1) quantum spin liquids (QSL) in the weak Mott regime with a spinon Fermi surface and gapped charge excitations. In type-II CMI, however, the charge fluctuations lead to a long-range plaquette charge order that breaks the lattice symmetry, gives rise to an emergent charge lattice and reconstructs the mean-field spinon band structure of the underlying U(1) QSL. Such a reconstruction gives a consistent prediction of the "fractional spin susceptibility" that is observed in LiZn2Mo3O8.  For the pyrochlore system, the CMI can further support a charge fractionalization with an emergent gauge photon in the charge sector in addition to the spin fractionalization in the spin sector.

The Truncated Conformal Space Approach (TCSA) is a method that allows for controlled calculations in strongly coupled quantum field theories. It can be used whenever a theory is conformally invariant at short distances, and allows infrared quantities to be calculated in terms of the CFT data of this UV theory.

As an example, I will discuss how the TCSA applies to phi^4 theory in D dimensions and I will show that the method reliably reproduces several nonperturbative phenomena.

In this talk, I will review the main ideas underlying stochastic inflation, by introducing the formalism in two independent ways. First I will start from the intuitive picture stemming from the equations of motion of the system. I will then introduce a more rigorous approach based on the in-in formalism, and show how the usual set of Langevin equations can emerge from a path integral formulation. With this understanding, I will then formulate a new, recursive method which allows to solve consistently both in slow-roll parameters and in quantum corrections. I will then discuss examples of how this method can be applied to derive corrected predictions for cosmological observables in the case of hybrid inflation, multi-field inflation, and inflation on modulated potentials.

> I talk about a method to determine the anomaly polynomials of genera 6d N=(2,0) and N=(1,0) SCFTs, in terms of the anomaly matching on their tensor branches. This method is almost purely field theoretical, and can be applied to all known 6d SCFTs. Green-Schwarz mechanism plays the crucial role.

One hallmark of topological phases with broken time reversal symmetry is the appearance of quantized non-dissipative transport coefficients, the archetypical example being the quantized Hall conductivity in quantum Hall states. Here I will talk about two other non-dissipative transport coefficients that appear in such systems - the Hall viscosity and the thermal Hall conductivity. In the first part of the talk, I will start by reviewing previous results concerning the Hall viscosity, including its relation to a topological invariant known as the shift. Next, I will show how the Hall viscosity can be computed from a Kubo formula. For Galilean invariant systems, the Kubo formula implies a relationship between the viscosity and conductivity tensors which may have relevance for experiment. In the second part of the talk, I will discuss the thermal Hall conductivity, its relation to the central charge of the edge theory, and in particular the absence of a bulk contribution to the thermal Hall current. I will do this by constructing a low-energy effective theory in a curved non-relativistic background, allowing for torsion. I will show that the bulk contribution to the thermal current takes the form of an "energy magnetization" current, and hence show that it does not contribute to heat transport.  

In AdS/CFT, the HRT prescription relates the entanglement entropy of a region of a CFT to the area of an extremal surface in the dual AdS spacetime.  But there exists a class of spacetimes in which the HRT prescription is ill-defined.  These spacetimes consist of planar AdS wormholes containing an inflating region.  I will introduce these so-called AdS-dS-wormholes, discuss how the HRT prescription fails in them, and suggest possible modifications to remedy the problem.

From Feynman diagrams via Penrose graphical notation to quantum circuits, graphical languages are widely used in quantum theory and other areas of theoretical physics. The category-theoretical approach to quantum mechanics yields a new set of graphical languages, which allow rigorous pictorial reasoning about quantum systems and processes. One such language is the ZX-calculus, which is built up of elements corresponding to maps in the computational and the Hadamard basis. This calculus is universal for pure state qubit quantum mechanics, meaning any pure state, unitary operation, and post-selected pure projective measurement can be represented. It is also sound, meaning any graphical rewrite corresponds to a valid equality when translated into matrices.

While the calculus is not complete for general quantum mechanics, I show that it is complete for stabilizer quantum mechanics and for the single-qubit Clifford+T group. This means that within those subtheories, any equality that can be derived using matrices can also be derived graphically.

The ZX-calculus can thus be applied to a wide range of problems in quantum information and quantum foundations, from the analysis of quantum non-locality to the verification of measurement-based quantum computation and error-correcting codes. I also show how to construct a ZX-like graphical calculus for Spekkens' toy bit theory and give its associated completeness proof.

Instead of formulating the state space of a quantum field theory over a single big Hilbert space, it has been proposed by Jerzy Kijowski to describe quantum states as projective families of density matrices over a collection of smaller, simpler Hilbert spaces. I will discuss the physical motivations for this approach and explain how it can be implemented in the context of LQG. While the resulting state space forms a natural extension of the Ashtekar-Lewandowski Hilbert space, it treats position and momentum variables on equal footing. This paves the way for the construction of semi-classical states beyond fixed graph level, and eventually for the derivation of LQC from full LQG.

In this talk I will present some results of an upcoming paper where we study four-dimensional N=2  superconformal field theories using the conformal bootstrap.
We focus on two different four-point functions, involving either the superconformal primary of the flavor current multiplet or the one of the chiral multiplet.
Numerical analysis of the crossing equations yields lower bounds on the allowed central charges, and upper bounds on the dimensions of unprotected operators (for unitary theories).

Two-dimensional interacting electron gas in strong transverse magnetic field forms a collective state -- incompressible electron liquid, known as fractional quantum Hall (FQH) state. FQH states are genuinely new states of matter with long range topological order. Their primary observable characteristics are the absence of dissipation and quantization of the transverse electro-magnetic response known Hall conductance. In addition to quantized electromagnetic response FQH states are characterized by quantized geometric responses such as Hall viscosity and thermal Hall conductance.
  I will show how to derive the effective action for various Abelian and non-Abelian FQH states on a curved space. In particular, I will derive the quantized universal responses to the changes in geometry of space. These responses are described by Chern-Simons-type terms. It will be shown that in order to obtain the responses in a self consistent way one has to take into account the framing anomaly of the quantum Chern-Simons(-Witten) theory. This peculiar phenomenon illustrates the failure of a classically topological theory to remain topological at the quantum level.
   If time permits I will comment on the coupling of non-relativistic systems to the space-time geometry. Using the appropriate geometry I will write an effective action describing the bulk energy and thermal Hall conductances. From this effective action it will be clear that these response functions are neither universal nor topologically protected.