Scientific Series

This talk concerns a family of special functions common to the study of quantum conformal blocks and hypergeometric solutions to q-KZB type equations.  In the first half, I will explain two methods for their construction -- as traces of intertwining operators between representations of quantum affine algebras and as certain theta hypergeometric integrals we term Felder-Varchenko functions.  I will then explain our proof by bosonization the first case of Etingof-Varchenko's conjecture that these constructions are related by a simple renormalization.

The second half of the talk will concern applications to affine Macdonald theory.  I will present refinements of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof-Kirillov Jr.  I will then explain how to prove the first non-trivial cases of these conjectures by combining the methods of the first half and well-chosen applications of the elliptic beta integral.   The second half of this talk is joint work with E. Rains and A. Varchenko.

Topological phases of matter serve as one of the most striking examples of the richness and novelty of quantum systems with many degrees of freedom.  In contrast to conventional matter, they are characterized by both non-local properties and non-classical notions such as entanglement.  I will discuss two broad categories of topological phases, distinguished by whether or not they possess fractionalized “anyon” excitations that are neither bosons nor fermions.  I will demonstrate that entanglement not only provides an understanding of such phases but also enables the transmutation between these two categories of topological phases. 

What is the essence of quantum theory? In the present talk I want to approach this question from a particular operationalist perspective. I take advantage of a recent convergence between operational approaches to quantum theory and axiomatic approaches to quantum field theory. Removing anything special to particular physical models, including underlying notions of space and (crucially) time, what remains is what I shall call "abstract quantum theory". This embeds into a more general framework that also includes classical theory, with classical and quantum theory representing two extremes in a spectrum of possible theories. I shall present this within a "hierarchy of abstraction", where adding structure leads to more specialized frameworks. In particular, adding topological spacetime and locality leads to the recently proposed positive formalism and recovers quantum field theory. Further rigidifying time and adding causality recovers the standard formulation of quantum theory. There are other promising specializations such as Hardy's proposal to work in op-space.

We normally think of large accelerators and large-scale cosmic events when we consider the frontiers of elementary particle physics, pushing to understand the universe at higher and higher energy scales. However, several tabletop low-energy experiments are posed to discover a wide range of new physics beyond the Standard model, where feeble interactions require precision measurements rather than high energies.  In our experiments, high-Q resonant sensors enable ultra-sensitive force and field detection. In this talk I will describe two applications of these sensors in searches for new physics, based on techniques in atomic-molecular-and optical (AMO) physics. First, I will discuss an experiment which uses laser-cooled optically trapped silica nanospheres to search for corrections to Newtonian gravity at micron distances with zeptonewton sensitivity.  Finally, I will discuss the Axion Resonant InterAction Detection Experiment (ARIADNE), a new precision magnetometry experiment using laser-polarized 3-He gas to search for a notable dark-matter candidate: the QCD axion.  

We prove that constant-depth quantum circuits are more powerful than their classical counterparts. We describe an explicit (i.e., non-oracular) computational problem which can be solved with certainty by a constant-depth quantum circuit composed of one- and two-qubit gates. In contrast, we prove that any classical probabilistic circuit composed of bounded fan-in gates that solves the problem with high probability must have depth logarithmic in the input size. This is joint work with Sergey Bravyi and Robert Koenig (arXiv:1704.00690).

Recent studies of highly frustrated antiferromagnets (AFMs) have demonstrated the qualitative impact of virtual, longer-range singlet excitations on the effective RVB tunneling parameters of the low energy sector of the problem [1,2]. Here, I will discuss the current state of affairs on the RVB description of the spin-1/2 kagome AFM, and present new results that settle a number of issues in this problem [3].

[1] I. Rousochatzakis, Y. Wan, O. Tchernyshyov, and F. Mila, PRB 90,

100406(R) (2014)

[2] A. Ralko and I. Rousochatzakis, PRL 115, 167202 (2015) [3] in preparation.

What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a mathematical theory of the macroscopic fluctuations generated by ensembles of independent microscopic discrete systems. We provide algorithms to decide which multivariate gaussian distributions can be approximated by sums of finitely-valued random vectors. We study non-trivial cases where the microscopic variables have an unbounded range, as well as asymptotic scenarios with infinitely many macroscopic variables. From a foundational point of view, our results imply that bipartite gaussian states of light cannot be understood as beams of independent d-dimensional particle pairs. It is also shown that the classical description of certain macroscopic optical experiments, as opposed to the quantum one, requires variables with infinite cardinality spectra.

Since the Higgs, the LHC has offered no discoveries despite a sweeping hunt for new resonances. However, many well-motivated new physics models would not turn up in resonance searches, but could instead be uncovered in existing and forthcoming LHC data, by searching for novel angular distributions of Standard Model particles. I will show that in the upcoming years at the LHC, (1) through radiative corrections, dark matter can turn up in dilepton scattering angles in the parametric regions where it would elude conventional missing energy-based searches; the scattering patterns can reveal dark matter's mass, self-conjugation property, spin, and chirality of interactions, (2) through tree level interference, leptoquarks may emerge in dilepton scattering angles long before they would in dedicated direct searches; these angular measurements would also overtake the excellent sensitivities of low-energy precision measurements of atomic parity violation, and (3) Higgs Yukawa couplings to light quarks of the size of the bottom Yukawa could be measured using the Higgstrahlung scattering angle.

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects. This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions.

I present three possible non-standard additions to cosmology.  First I show that a very long early period of inflation could exist in which parameters evolve, or 'relax', to seemingly fine-tuned values.  Next, I show that even if cosmic inflation existed, a period after inflation with anisotropic stress can dramatically affect super-horizon modes and thus the imprint on the cosmic microwave background.  Finally, I show that cosmological singularities can be avoided by a bounce without using exotic matter that violates the Null Energy Condition, but by the addition of vorticity in compact extra dimensions.

We consider the problem of certifying entanglement and nonlocality in one-dimensional translation-invariant (TI) infinite systems when just averaged near-neighbor correlators are available. Exploiting the triviality of the marginal problem for 1D TI distributions, we arrive at a practical characterization of the near-neighbor density matrices of multi-separable TI quantum states. This allows us, e.g., to identify a family of separable two-qubit states which only admit entangled TI extensions. For nonlocality detection, we show that, when viewed as a vector in R^n, the set of boxes admitting an infinite TI classical extension forms a polytope, i.e., a convex set defined by a finite number of linear inequalities. Using DMRG, we prove that some of these inequalities can be violated by distant parties conducting identical measurements on an infinite TI quantum state. Both our entanglement witnesses and our Bell inequalities can be used to certify entanglement and nonlocality in large spin chains (namely, finite, and not TI chains) via neutron scattering.

Our attempts at generalizing our results to TI systems in 2D and 3D lead us to the virtually unexplored problem of characterizing the marginal distributions of infinite TI systems in higher dimensions. In this regard, we show that, for random variables which can only take a small number of possible values (namely, bits and trits), the set of nearest (and next-to-nearest) neighbor distributions admitting a 2D TI infinite extension forms a polytope. This allows us to compute exactly the ground state energy per site of any classical nearest-neighbor Ising-type TI Hamiltonian in the infinite square or triangular lattice. Remarkably, some of these results also hold in 3D.

In contrast, when the cardinality of the set of possible values grows (but remaining finite), we show that the marginal nearest-neighbor distributions of 2D TI systems are not described by a polytope or even a semi-algebraic set. Moreover, the problem of computing the exact ground state energy per site of arbitrary 2D TI Hamiltonians is undecidable.

The talk will review the computation of the three point function of gauge-invariant operators in the planar N=4 SYM theory using integrability-based methods. The structure constant can be decomposed, as proposed by Basso, Komatsu and Vieira, in terms of two form-factor-like objects (hexagons). The multiple sums and integrals implied by the hexagon decomposition can be performed in the large-charge limit, and be compared to the results obtained by semiclassics. I will discuss a method to perform these sums and the contributions currently accessible by this approach.