Talks

Conventional quantum processes are described by quantum circuits, that represent evolutions of states of systems from input to output. In this seminar we consider transformations of an input circuit to an output circuit, which then represent the transformation of quantum evolutions. At this level, all the processes complying to admissibility conditions have in principle a physical realization scheme. The construction of a hierarchy of transformations of transformations, however, can proceed arbitrarily far, and in the higher orders one encounters admissible functions that have indefinite causal structures. These give rise to questions about possible realization schemes. Still, many of the maps in the hierarchy can be proved to have a realistic physical interpretation. In order to study the hierarchy, we introduce a simple rule for constructing new types of maps from known ones, and show how the tensor product can be rephrased in terms of the new rule. We use the hierarchy of types to introduce a partial order, which allows us to prove properties of maps by induction. We will then use induction proofs to discuss the characterisation of mathematically admissible maps at every level. We show an important structural result for a subclass of higher-order maps, and we conclude with the open question of their physical achievability.

Quantum critical points (QCP) beyond the Landau-Ginzburg paradigm are often called unconventional QCPs. There are in general two types of unconventional QCP: type I are QCPs between ordered phases that spontaneously break very different symmetries, and type II involve topological (or quasi-topological) phases on at least one side of the QCP. Recently significant progress has been made in understanding (2+1)-dimensional unconventional QCPs, using the recently developed (2+1)d dualities, i.e., seemingly different theories may actually be identical in the infrared limit. One group of dualities between unconventional QCPs have attracted particular interests in the field of condensed matter theory. This group of dualities include the so called deconfined QCP between the Neel and valence bond solid phases, and the topological transition between a bosonic topological insulator and a trivial Mott insulator. Each of the transitions mentioned above is also "self-dual". This group of dualities make extremely powerful predictions for numerical test. We will review the theoretical aspects and most recent numerical evidences for these new results.

In this talk I prove that the standard notion of entanglement is not defined for gravitationally anomalous two-dimensional theories  because they do not admit a local tensor factorization of the Hilbert space into local Hilbert spaces.  I make this precise by combining two observations:

    First, a two-dimensional CFT admits a consistent quantization on a space with boundary only if it is not anomalous.

    Second, a local tensor factorization always leads to a definition of consistent, unitary, energy-preserving boundary condition.

    As a corollary we establish a generalization of the Nielsen--Ninomiya theorem to all two-dimensional unitary local QFT:

    No continuum quantum field theory in two dimensions can admit a lattice regulator unless its gravitational anomaly vanishes.

I also show that the conclusion can be generalized to six dimensions by dimensional reduction on a four-manifold of nonvanishing signature.  I will advocate that these points be used to reinterpret the gravitational anomaly quantum-information-theoretically, as a fundamental obstruction to the localization of quantum information.

Standard Model particles account for a small fraction of the matter content of the universe.  If the remaining dark matter (DM) was ever in thermal equilibrium  with itself or with the Standard Model (SM) sector, there must  exist interactions that allowed its number density to be depleted  to its present value.  An interesting possibility for achieving this arises in scenarios  where the DM is composed of ``pions'' of a QCD-like dark sector.  The leading number changing process in these theories is the annihilation of three pions into two pions, which heats the pion bath relative to the SM. Consistency with observations of large and small scale structure in the universe requires a non-zero coupling with SM states, suggesting a multitude of experimental probes. I will review the cosmological production of DM in these strongly interacting dark sectors and discuss the prospects for discovering them at fixed target experiments.

The Dark Energy Survey (DES) is a five-year, 5000 sq. deg. observing program using the Dark Energy Camera on the 4m Blanco telescope at CTIO. I will describe the cosmological analysis of large-scale structure in the Universe using 1321 sq. deg. of data taken in the first year of DES operations. The analysis combines unprecedented measurements of weak gravitational lensing and the clustering of galaxies over the redshift range 0.2 to 1.3 to derive the most precise such cosmological constraints to date. These DES results from the low-redshift Universe are consistent with those from the cosmic microwave background (CMB) and support the standard cosmological model, LCDM. In the coming years, DES will produce significantly tighter constraints on cosmology through similar and additional analyses using observations over more than three times the sky-area and more than twice the integrated exposure time per object as these results.

Motivated by the close relations of the renormalization group with both the holography duality and the deep learning, we propose that the holographic geometry can emerge from deep learning the entanglement feature of a quantum many-body state. We develop a concrete algorithm, call the entanglement feature learning (EFL), based on the random tensor network (RTN) model for the tensor network holography. We show that each RTN can be mapped to a Boltzmann machine, trained by the entanglement entropies over all subregions of a given quantum many-body state. The goal is to construct the optimal RTN that best reproduce the entanglement feature. The RTN geometry can then be interpreted as the emergent holographic geometry. We demonstrate the EFL algorithm on 1D free fermion system and observe the emergence of the hyperbolic geometry (AdS_3 spatial geometry) as we tune the fermion system towards the gapless critical point (CFT_2 point).

Talk is based on the joint work with Lev Rozansky. In my talk will outline a construction that provides  complex $C_b$ of coherent sheaves on the Hilbert scheme of $n$ points on the plane for every $n$-stranded braid $b$. The space of global sections of $C_b$ is a categorification of the HOMFLYPT polynomial of the closure $L(b)$ of the braid. I will also present a physical interpretation of our construction as a particular case of Kapustin-Saulina-Rozansky 3D topological field theory.