Talks

Quantum adiabatic optimization (QAO) slowly varies an initial Hamiltonian with an easy-to-prepare ground-state to a final Hamiltonian whose ground-state encodes the solution to some optimization problem. Currently, little is known about the performance of QAO relative to classical optimization algorithms as we still lack strong analytic tools for analyzing its performance. In this talk, I will unify the problem of bounding the runtime of one such class of Hamiltonians -- so-called stoquastic Hamiltonians -- with questions about functions on graphs, heat diffusion, and classical sub-stochastic processes. I will introduce new tools for bounding the spectral gap of stoquastic Hamiltonians and, by exploiting heat diffusion, show that one of these techniques also provides an optimal and previously unknown gap bound for particular classes of graphs. Using this intuition and combining heat diffusion with classical sub-stochastic processes, I will offer a classical adiabatic algorithm that exhibits behavior typically considered "quantum", such as tunneling.

In the rst part of this talk I will give a brief introduction to the variational class of continuous
matrix product states (cMPS). Then I will present a time evolution algorithm for cMPS with periodic
boundary conditions. In the second part, I will explain how to apply this method to simulate
atomtronic circuits. In particular, I will show results for persistent currents in an interacting bose
gas rotating in a ring shaped trap in the presence of an arti cial U(1) gauge potential.

The BPS spectrum of d=4 N=2 field theories in general contains not only hyper and vector-multipelts but also short multiplets of particles with arbitrarily high spin. These BPS states of higher spin reveal quite a peculiar behavior, so sometimes they are called "wild"

states. In this talk we would try to discuss a small refinement of the asymptotic study (spectral network technique) of tt* equations arising in an effective theory on 2d defects in N=2 4d SYM theory capturing spin information and apply it to study some properties of wild BPS spectra.

The vacuum energy changes when cosmological phase transitions take place, or in environments with high temperatures or chemical potentials.  The propagation of primordial gravity waves is affected through the trace anomaly, and eras where the vacuum energy dominates can lead tofeatures in the gravity wave spectrum.  High density phases of QCD in neutron stars, where the vacuum is rearranged, are also a novel probe:  The mass-radius relationships for neutron stars is sensitive to the equation of state appearing in the Einstein equations, which may depend on new dynamics associated with vacuum energy.  Such observations could potentially rule out large classes of explanations for the smallness of the currently observed cosmological constant.

In this talk I derive the evolution equations for two scalar fields with non-canonical field space metric up to third order in perturbation theory, employing the covariant formalism. These equations can be used to calculate the local bi- and trispectra of the non-minimal ekpyrotic model. Remarkably, the nearly scale-invariant entropy perturbations have vanishing bi- and trispectra during the ekpyrotic phase. However, an efficient conversion process to curvature perturbations induces local non-Gaussianity parameters f_NL and g_NL at levels that should be detectable by near-future observations.
In the second part of the talk I construct a new kind of cosmological model – conflation. The universe undergoes accelerated expansion, but with crucial differences compared to ordinary inflation. In particular, the potential energy is negative, which is of interest for supergravity and string theory where both negative potentials and the required scalar-tensor couplings are rather natural. A distinguishing feature of the model is that it does not amplify adiabatic scalar and tensor fluctuations, and in particular does not lead to eternal inflation and the associated infinities.

I discuss a new proposal for nonperturbatively defining chiral gauge theories, something that has resisted previous attempts. The proposal is a well defined field theoretic framework that contains mirror fermions with very soft form factors, which allows them to decouple, as well as ordinary fermions with conventional couplings.  The construction makes use of an extra dimension, which localizes chiral zeromodes on the boundaries, and a four dimensional gauge field extended into the bulk via classical gradient flow.  After explaining how this setup works, I consider open questions concerning the flow of topological gauge configurations, as well as possible exotic phenomenology in the Standard Model lurking at the low energy frontier.

I will present a new area law in General Relativity. This new area law holds on local analogues of event horizons that have an independent thermodynamic significance due to the Bousso bound. I will also discuss a quantum generalization of this more local notion of thermodynamics.

We introduce the spectrum bifurcation renormalization group (SBRG) as an improvement of the excited-state real space renormalization group (RSRG-X) for qubit models. Starting from a disordered many-body Hamiltonian in the full many-body localized (MBL) phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local integrals of motion and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the full MBL phase. As a Hilbert-space preserving RG, the SBRG also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space.

In this talk, I present a new framework for topologically ordered gapped ground states in 2+1 spacetime dimensions (which generalizes to higher dimensions) using tensor networks. We will see that topological order can exist in tensor network states (TNS), if the local tensor satisfies certain axioms which we call MPO (matrix product operator)-injectivity and pulling through. We then continue with examples, and see how renormalization fixed point models in the literature (Levin-Wen models, etc.) can be covered in this framework. If time permits, we finish with a discussion of excitations and the generalization to higher dimensions.