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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.