Conference

Topological Quantum field theories(TQFTs) are a special class of QFTs. Their actions do not depend on the metric of the background space-time manifold. Thus, it is very natural to define TQFTs on an arbitrary triangulation of the space-time manifold and they are independent on the triangulation. More importantly, TQFTs defined on triangulations are always a finite theory associated with a well defined cut-off. A well known example is the Turaev-Viro states sum invariants. Essentially, the Turaev-Viro constructions are (local) tensor network representations of a special class of 1+2D TQFTs. In this talk, I will show a new class of TQFTs that can be derived based on the (local) tensor network representations in arbitrary dimensions. They can be regarded as the discrete analogy of topological Berry phase terms of (discrete) non-linear sigma models. The edge theory of such a new class of TQFTs can be regarded as the discrete analogy of WZW terms. This new class of TQFTs naturally classify (bosonic) symmetry protected topological orders in arbitrary dimensions. Finally, I will also discuss new classes of fermionic TQFTs based on the Grassmann tensor network representations and possible new route towards Quantum Gravity(QG).

The MERA offers a powerful variational approach to quantum field theory. While the continuous MERA may allow us to directly address field theories in the continuum, the MERA on the lattice has already demonstrated its ability to characterize conformal field theories. In this talk I will explain how to extract the conformal data (central charge, primary fields, and their scaling dimensions and OPE) of a CFT from a quantum spin chain at a quantum critical point. I will consider both homogeneous systems (translation invariant) and systems with an impurity (where translation invariance is explicitly broken). Key to the success of the MERA is the exploitation of both scale and translation invariance. I will show how translation invariance can still be exploited even in the presence of an impurity, even if the system is no longer translation invariant. This follows from an intriguing "causality principle" in the RG flow. I will also discuss the relation of these results with Wilson's famous resolution of the Kondo impurity problem.

One might be confused by the proliferation of tensor network states, such as MPS, PEPS, tree tensor networks [TTN], MERA, etc. What is the main difference between them? In this talk I will argue that the geometry of a tensor network determines several properties of the state that is being represented, such as the asymptotic scaling of correlations and of entanglement entropy. I will also describe the relation between the MERA and the Renormalization Group, and will review Brian Swingle

In 1987, Feynman devoted one of his last lectures to highlighting three serious objections against the usefulness of the variational principle in the theory of relativistic quantum fields. In that same year, in a different branch of physics, Affleck, Kennedy, Lieb and Tasaki devised a quantum state that resulted in the development of a handful of different variational ansätze for lattice models over the last two decennia. These quantum states are known as tensor network states and invalidate at least two of Feynman's arguments. They could thus be used in a variational study of relativistic quantum field theories on a lattice. However, two classes of tensor network states, namely the matrix product state and the multi-scale entanglement renormalization ansatz, have recently been ported to the continuous setting, so that we now have direct access to variational wave functions for quantum field theories and are no longer restricted to a lattice regularization.

In this talk, I will present a first principle construction of a holographic dual for gauged matrix models that include gauge theories. The dual theory is shown to be a closed string field theory coupled with an emergent two-form gauge field defined in one higher dimensional space. The bulk space with an extra dimension emerges as a well defined classical background only when the two-form gauge field is in the deconfinement phase. Based on this, it is shown that critical phases that admit holographic descriptions form a novel universality class with a non-trivial quantum order.

The study of fermionic and frustrated systems in two dimensions is one of the biggest challenges in condensed matter physics. Among the most promising tools to simulate these systems are 2D tensor networks, including projected entangled-pair states (PEPS) and the 2D multi-scale entanglement renormalization ansatz (MERA), which have been generalized to fermionic systems recently. In the first part of this talk I will present a simple formalism how to include fermionic statistics into 2D tensor networks. The second part covers recent simulation results showing that infinite PEPS (iPEPS) can compete with the best known variational methods. In particular, for the t-J model and the SU(4) Heisenberg model iPEPS yields better variational energies than obtained in previous variational- and fixed-node Monte Carlo studies. Future perspectives and open problems are discussed.

This introductory talk aims to answer a few basic questions (What is a tensor network? Under which circumstance is a tensor network useful?) and describe the tensor network states that will be discussed during the workshop (matrix product state [MPS], projected entangled pair states [PEPS], and the multi-scale entanglement renormalization ansatz [MERA]). I will then briefly describe the recent developments that motivated this workshop on

DEAP-3600 is a dark matter experiment using 3600 kg of liquid argon for direct WIMP search, with a target sensitivity to the spin-independent WIMP-nucleon cross-section of 10^{-46} cm^2. The detector is currently under construction at SNOLAB, located 2 km underground in Sudbury. In this single-phase liquid argon experiment, discrimination of beta/gamma backgrounds from the WIMP-induced nuclear recoil signal will be achieved by analyzing the pulse shape of scintillation light. A prototype 7-kg liquid argon detector has been taking data at SNOLAB since 2007 and has allowed extensive background studies, including significant radon and surface contamination reduction. The status of the experiment and of background reduction studies will be presented.

We describe a model of composite dark matter, bound by an asymptotically free gauge interaction. This leads to a novel relic history and to an enhancement of the present-day dark matter annihilation cross section. Potential indirect detection signals are discussed.

Many explanations have been proposed for the origin of dark matter and the creation of the baryon asymmetry, but very few of them address both cosmological puzzles at once. At the same time, the observed energy densities of dark matter and baryons are within a factor of five of each other hinting at a possible common origin. In this talk I will present a novel mechanism that generates both densities at once, with the dark matter species carrying a net baryon number. This gives rise to new and unusual dark matter signals such as the destruction of nucleons by dark matter scattering. I will describe some of these signals, and discuss how they might be detected in current and upcoming experiments and astrophysical observations.