Scientific Series

Quantum many-body systems ranging from a many-electron atom to a solid material are described by effective Hamiltonians which are obtained from more accurate Hamiltonians by neglecting or treating weak interactions perturbatively. Quantum complexity theory asks about the quantum computational power of such quantum many-body models for both practical as well as fundamental purposes. Three distinct computational classes have emerged within this framework: namely (1) classical Hamiltonians such as the Ising model, (2) sign-free or stoquastic Hamiltonians such as the transverse field Ising model, and (3) fully quantum Hamiltonians such as the Heisenberg model. Each class can be characterized by certain prototype universal Hamiltonians which can encode the physics of any other Hamiltonian in that class. We will show how this encoding is established through the use of perturbation theory via perturbative gadgets. We will discuss the technical expression of this classification in terms of the complexity classes NP, Stoquastic MA and QMA and the power of these Hamiltonians for performing quantum adiabatic computation.

We present an analytic, gauge invariant tensor network ansatz for the ground state of lattice Yang-Mills theory for nonabelian gauge groups. It naturally takes the form of a MERA, where the top level is the strong coupling limit of the lattice theory. Each layer performs a fine-graining operation defined in a fixed way followed by an optional step of adiabatic evolution, resulting in the ground state at an intermediate coupling. The ansatz is very much in the spirit of Kogut and Susskind's Hamiltonian approach to understanding confinement by starting from the strong coupling limit and perturbing, but exploiting a tensor network structure to go beyond perturbative approaches.

We present a first principles approach to a probabilistic description of nature based on two guiding principles: spacetime locality and operationalism. No notion of time or metric is assumed, neither any specific physical model. Remarkably, the emerging framework converges with the recently proposed positive formalism of quantum theory, obtained constructively from known quantum physics. However, it also seems to embrace classical physics.

A new experiment called PTOLEMY (Princeton Tritium Observatory for Light, Early-Universe, Massive-Neutrino Yield) is under development at the Princeton Plasma Physics Laboratory with the goal of challenging one of the most fundamental predictions of the Big Bang – the present-day existence of relic neutrinos produced less than one second after the Big Bang.  Using a gigantic graphene surface to hold 100 grams of a single-atomic layer of tritium, low noise antennas that sense the radio waves of individual electrons undergoing cyclotron motion, and a massive array of cryogenic sensors that sit at the transition between normal and superconducting states, the PTOLEMY project has the potential to challenge one of the most fundamental predictions of the Big Bang, to potentially uncover new interactions and properties of the neutrinos, and to search for the existence of a species of light dark matter known as sterile neutrinos.

Velocity fields are a powerful probe of structure formation and the energy content of our Universe. Additionally, the motion of ionized gas on intermediate scales can be used to measure the clustering of baryons and shed light on galaxy formation and feedback mechanisms.  I will discuss techniques that can be used to both constrain cosmology and measure baryon properties. I will also present some preliminary results.

We exactly evaluate the partition function (index) of N=4 supersymmetric quiver quantum mechanics in the Higgs phase by using the localization techniques. We show that the path integral is localized at the fixed points, which are obtained by solving the BRST equations, and D-term and F-term conditions. We turn on background gauge fields of R-symmetries for the chiral multiplets corresponding to the arrows between quiver nodes, but the partition function does not depend on these R-charges. We give explicit examples of the quiver theory including a non-coprime dimension vector. The partition functions completely agree with the mathematical formulae of the Poincare polynomials and the wall crossing for the quiver moduli spaces. We also discuss exact computation of the expectation values of supersymmetric (Q-closed) Wilson loops in the quiver theory.

We will discuss our work on (1) the global food crisis and the implications for how we can address hunger and social unrest around the world, (2) the financial crisis and the implications for the role of regulation in economic market stability, and (3) the Ebola epidemic and the vulnerability of global civilization to pandemics. 

I will review recent work on tensorial group field theories (TGFTs). The renormalization methods being developed in this context provide more and more control over their field-theoretic structures, and for models which increasingly resemble loop quantum gravity. Perhaps surprisingly, some of these models are asymptotically free and can therefore be made sense of at arbitrary values of the (abstract) scale with respect to which they are organized. They define in this sense UV complete quantum field theories. I will focus on TGFTs with gauge invariance condition, which allow for such a behavior but also for more complicated scenarii involving non-trivial fixed points of the renormalization group flow. I will finally comment on the physical relevance of this notion of UV completion.

A modified gravity (MOG) theory is explored that can explain current observational data in the present universe without detectable dark matter. This data includes galaxy rotation curves, cluster dynamics, gravitational lensing, globular clusters, the Bullet Cluster and solar system experiments. A vector field in the MOG action is a hidden, dark and massive photon that acts as a collisionless particle in the early universe and explains structure growth. The vector field evolves to an ultralight hidden photon in the present universe after the formation of stars and galaxies, and it cannot play the role of detectable dark matter. The theory successfully describes the CMB data. The matter power spectrum is fitted without dark matter and can distinguish between modified gravity and dark matter scenarios in the present universe.

Gravity in 1+1 dimension is classically trivial but, as shown by A. Polyakov in 1981, it is a non-trivial quantum theory, in fact a conformal field theory (the Liouville theory), and also a string theory. In the last decades many important results and connexions with various areas of mathematics and theoretical physics have been established, but some important issues remain to be understood. In this colloquium I shall focus on some recent developments and new questions on the relation between discrete and continuous 2 dimensional gravity, probabilities and stochastic processes, random fractal geometries and SLE curves.

I will describe how to define a proper RG flow in the space of
tensor networks, with applications to the evaluation of classical
partition functions, euclidean path integrals, and overlaps of tensor
network states.

A featureless insulator is a gapped phase of matter that does not exhibit fractionalization or other exotic physics, and thus has a unique ground state. The classic albeit non-interacting example is an electronic band insulator. A standard textbook argument tells us that band insulators require an even number of electrons -- an integer number for each spin -- per unit cell. I will explore the converse question: given such an 'integer filling', is a featureless insulating state possible?  I will demonstrate that in most three-dimensional crystals, an insulating ground state cannot be unique -- and hence cannot be featureless -- except at certain special fillings fixed by the crystalline space group. This result, which remains valid more generally for interacting systems of fermions, bosons, or spins (as long as they have a conserved U(1) charge), relies on a combination of topological 'flux insertion' arguments and elementary crystallographic ideas. I will explore its implications through examples ranging from band theory, where it leads to the identification of protected semimetals, to frustrated magnetism, where it suggests new venues for spin liquid physics.

References: S.A. Parameswaran, A.M. Turner, D.P. Arovas and A. Vishwanath, Nature Physics 9, 299 (2013).
(see also related work in PNAS 110, 16378 (2013) and Phys. Rev. Lett. 110, 125301 (2013).)