Scientific Series

We consider the one dimensional, periodic spin chain with $N$ sites, similar to the one studied by Haldane \cite{hal}, however in the opposite limit of very large anisotropy and small nearest neighbour, anti-ferromagnetic exchange coupling between the spins, which are of large magnitude $s$.  For a  chain with an even number of sites we show that actually the ground state is non degenerate and given by a superposition of the two Néel states, due to quantum spin tunnelling.  With an odd number of sites, the Néel state must necessarily contain a soliton. The position of the soliton is arbitrary thus the  ground state is $N$-fold degenerate.  This set of  states reorganizes into a band. We show that this occurs at order $2s$ in perturbation theory.  The ground state is non-degenerate for integer spin, but degenerate for half-odd integer spin as is required by Kramer's theorem \cite{kram}. arXiv:1404.6706 , Phys.Lett. A378 (2014) 3066-3069; arXiv:1304.3734 Phys.Rev. B88 (2013) 22, 220403 

In this talk, I will prove the Landau-Ginzburg mirror symmetry conjecture for general quasi-homogenous singularities, i.e., the FJRW theory (LG A-model) of such polynomials is equivalent to the Saito-Givental theory (LG B-model) of the mirror polynomial. This is joint work with Weiqiang He, Rachel Webb and Yefeng Shen. 

If dark matter is asymmetric, fermionic, and self-interacting, it may form black holes in pulsars at the galactic center. In this case, a measurable maximum attainable pulsar age would track the density of the dark matter halo, with the oldest pulsars being allowed in the least dense parts of the halo. This could explain a recent observation, that there are not as many pulsars in the galactic center as expected.

Models such as Natural Inflation that use Pseudo-Nambu-Goldstone bosons (PNGB's) as the inflaton are attractive for many reasons. However, they typically require trans-Planckian field excursions $\Delta \Phi>M_{\rm Pl}$, due to the need for an axion decay constant $f>M_{\rm Pl}$ to have both a sufficient number of e-folds {\em and} values of $n_s,\ r$ consistent with data.  Such excursions would in general require the addition of all other higher dimension operators consistent with symmetries, thus disrupting the required flatness of the potential and rendering the theory non-predictive. We show that in the case of Natural Inflation, the existence of spinodal instabilities (modes with tachyonic masses) can modify the inflaton equations of motion to the point that versions of the model with $f<M_{\rm Pl}$ can still inflate for the required number of e-folds. The instabilities naturally give rise to two separate phases of inflation with different values of the Hubble parameter $H$ one driven by the zero mode, the other by the unstable fluctuation modes. The values of $n_s$ and $r$ typically depend on the initial conditions for the zero mode, and, at least for those examined here, the values of $r$ tend to be unobservably small.

Everything around us, everything each of us has ever experienced, and virtually everything underpinning our technological society and economy is governed by quantum mechanics. Yet this most fundamental physical theory of nature often feels as if it is a set of somewhat eerie and counterintuitive ideas of no direct relevance to our lives. Why is this? One reason is that we cannot perceive the strangeness (and astonishing beauty) of the quantum mechanical phenomena all around us by using our own senses. I will describe the recent development of techniques that allow us to image electronic quantum matter directly at the atomic scale. As examples, we will visually explore the previously unseen and very beautiful forms of quantum matter making up electronic liquid crystals [1,2]; hybridized heavy-fermions [3,4]; topological-insulator surface states [5]; and high temperature superconductors [6,7]. We will discuss the implications for fundamental research, and also for advanced materials and new technologies, arising from the development and application of these novel techniques .

We explore the brightness frontier in time domain radio astronomy and its possible usefulness for cosmology.  It is argued that the brightest known source of emission, Crab nanoshots, are caused by Schwinger pair production.  The same mechanism may be the source of Fast Radio Bursts (FRBs) if this emission is form coalescing neutron stars.  It is then shown how using FRBs as triggers can extend the reach of gravitational radiation and neutrino telescopes.  Finally we discuss how combining FRB monitoring, large neutrino telescopes, combined with preexisting galaxy catalogs could provide an accurate cosmological distance estimator.

Generic binary black holes have spins that are misaligned with their orbital angular momentum. When the binary separation between the black holes is large compared to their gravitational radii, the timescale on which the spins precess is much shorter than the radiation-reaction time on which the orbital angular momentum decreases due to gravitational-wave emission. We use conservation of the total angular momentum and the projected effective spin on the precession time to derive an effective potential for BBH spin precession. This effective potential allows us to solve the orbit-averaged spin-precession equations analytically for arbitrary mass ratios and spins. These solutions are quasiperiodic functions of time: after a precessional period the spins return to their initial relative orientations. We classify black-hole spin precession into three distinct morphologies between which the black holes can transition during their inspiral. Our new solutions constitute fundamental progress in our understanding of black-hole spin precession and also have important applications to astrophysical black holes. We derive a precession-averaged evolution equation that can be numerically integrated on the radiation-reaction time, allowing us to statistically track black-hole spins from formation to merger. This will greatly help us predict the signatures of black-hole formation in the gravitational waves emitted near merger and the distributions of final spins and gravitational recoils.

With recent advancement of experimental physics, macroscopic objects, which are typically well-described by classical physics, can now be isolated so well from their environment, that their quantum uncertainties can be studied quantitatively. In the research field called “optomechanics”, mechanical motions of masses from picograms to kilograms are being prepared into nearly pure quantum states, and observed at time scales ranging from nanoseconds to milliseconds. In practice, optomechanics experiments have been constructed to measure extremely weak classical forces, e.g., due to gravitational waves, acting on macroscopic test objects. In this case, experiments must be designed in such a way that quantum uncertainties of the test objects are avoided as much as possible --- often by employing the quantum correlations between the state of light and the motion of the test object, which can build up during the measurement process.

Optomechanics experiments can also be used to search for possible deviations from standard quantum mechanics when macroscopic objects are involved. In this case, experiments are designed to highlight as much as possible the quantum-state evolution of the macroscopic objects. It is hoped that these macroscopic quantum mechanics experiments will either lead our way toward new physics, or at least put experimental constraints on how standard quantum mechanics might be modified.

The Ryu-Takayanagi formula relates the entanglement entropy in a conformal field theory to the area of a minimal surface in its holographic dual. I will show that this relation can be inverted to reconstruct the bulk stress-energy tensor near the boundary of the bulk spacetime, from the entanglement on the boundary. I will also show that the positivity and monotonicity of the relative entropy for small spherical domains between the reduced density matrices of an excited state and of the ground state of the CFT, translate to energy conditions in the bulk.

Renormalization is a principled coarse-graining of space-time. It shows us how the small-scale details of a system may become irrelevant when looking at larger scales and lower energies. Coarse-graining is also crucial, however, for biological and cultural systems that lack a natural spatial arrangement. I introduce the notion of coarse-graining and equivalence classes, and give a brief history of attempts to tame the problem of simplifying and "averaging" things as various as algorithms and languages. I then present state-space compression, a new framework for understanding the general problem. At the end, I present recent empirical results, in an animal social system, that show evidence for the coupling of scales: the reaction of coarse-grained facts about a system "downwards" to influence the microphysics. 

I will present recent theoretical work on cluster Mott insulators (CMI) in which interesting physics such as emergent charge lattices, charge fractionalization and quantum spin liquids are proposed. For the anisotropic Kagome system like LiZn2Mo3O8, we find two distinct CMIs, type-I and type-II, can arise from the repulsive interactions. In type-I CMI, the electrons are localized in one half of the triangle clusters of the Kagome system while the electrons in the type-II CMI are localized in every triangle cluster. Both CMIs are U(1) quantum spin liquids (QSL) in the weak Mott regime with a spinon Fermi surface and gapped charge excitations. In type-II CMI, however, the charge fluctuations lead to a long-range plaquette charge order that breaks the lattice symmetry, gives rise to an emergent charge lattice and reconstructs the mean-field spinon band structure of the underlying U(1) QSL. Such a reconstruction gives a consistent prediction of the "fractional spin susceptibility" that is observed in LiZn2Mo3O8.  For the pyrochlore system, the CMI can further support a charge fractionalization with an emergent gauge photon in the charge sector in addition to the spin fractionalization in the spin sector.

The Truncated Conformal Space Approach (TCSA) is a method that allows for controlled calculations in strongly coupled quantum field theories. It can be used whenever a theory is conformally invariant at short distances, and allows infrared quantities to be calculated in terms of the CFT data of this UV theory.

As an example, I will discuss how the TCSA applies to phi^4 theory in D dimensions and I will show that the method reliably reproduces several nonperturbative phenomena.