Conference

We give an introduction to cMERA, a continuous tensor networks ansatz for ground states of QFTs. We also explore a particular feature of it: an intrinsic length scale that acts as an ultraviolet cutoff. We provide evidence for the existence of this cutoff based on the entanglement structure of a particular family of cMERA states, namely Gaussian states optimized for free bosonic and fermionic CFTs. Our findings reflect that short distance entanglement is not fully present in the ansatz states, thus hinting at ultraviolet regularization.

A canonical analysis for general relativity is performed on a null surface without fixing the diffeomorphism gauge, and the canonical pairs of configuration and momentum variables are derived. Next to the well-known spin-2 pair, also spin-1 and spin-0 pairs are identified. The boundary action for a null boundary segment of spacetime is obtained, including terms on codimension two corners. FH, Laurent Freidel arXiv:1611.03096, Phys. Rev. D 95, 104006 (2017)

I will introduce the idea that topological field theories describe the low-energy properties of gapped local quantum systems. This idea has proved fruitful in recent studies of gapped phases of matter.

Extracting low energy universal data of quantum critical systems is a task whose difficulty increases with decreasing dimension. The increasing strength of quantum fluctuations can be tamed by using renormalization group (RG) schemes based on dimensional regularization close to the upper critical dimension of the system. By presenting a non-perturbative approach that allows the reliable extraction of the low energy universal data for the antiferromagnetic quantum critical metal in $2 \leq d < 3$-spatial dimensions, I will exemplify how an emergent non-commutativity between the low-energy limit and the dimensional limit preempts RG schemes based on dimensional regularization to access the correct low-energy universal data in integer dimensions.

We describe the tunneling of a quantum mechanical particle with a Lorentzian (realtime) path integral. The analysis is made concrete by application to the inverted harmonic oscillator potential, where the path integral is known exactly. We apply Picard-Lefschetz theory to the time integral of the Feynmann propagator at fixed energy, and show that the Euclidean integration contour is obtained as a Lefschetz thimble, or a sum of them, in a suitable limit. Picard-Lefschetz theory is used to make the integral manifestly convergent and is also essential for the saddle point or semiclassical approximation. The very simple example of the inverted harmonic oscillator presents many interesting mathematical features, such as the Stokes phenomenon and multiple relevant complex saddles. We also attempt to construct a more realistic picture of the tunneling process, by allowing for spreading in energy and duration.

We investigate response functions near quantum critical points, allowing for finite temperature and a mild deformation by a relevant scalar. When the quantum critical point is described by a conformal field theory, we use conformal perturbation theory and holography to determine the two leading corrections to the scalar two-point function and to the conductivity. We build a bridge between the couplings fixed by conformal symmetry with the interaction couplings in the gravity theory. We construct a minimal holographic model that allows us to numerically obtain the response functions at all frequencies, independently confirming the corrections to the high-frequency response functions. In addition to probing the physics of the ultraviolet, the holographic model probes the physics of the infrared giving us qualitative insight into new physics scalings.

Quantum relative entropy is a measure of the indistinguishability of two quantum states in the same Hilbert space. I will discuss the relative entropy between a state with periodic boundary conditions and one with twisted boundary conditions for a free 1+1 CFT with c=1. I will also highlight the unresolved discrepancy between analytic and numeric results.

In this talk we present a study of the “breathing” pyrochlore compound Ba3Yb2Zn5O11. Due to the nearly decoupled nature of its tetrahedral units, this compound serves as an ideal testbed for exploring the nature of anisotropic exchange in a theoretically and experimentally tractable rare-earth system. The relevant low-energy model of the Yb3+ tetrahedra is parametrized by four anisotropic exchange constants and is capable of reproducing the inelastic neutron scattering data, specific heat, and magnetic susceptibility with high fidelity. Using this model, we predict the appearance of an unusual non-Kramers octupolar paramagnet at low temperatures. We further speculate on possible collective, inter-tetrahedron physics of these non-Kramers doublets and discuss applications to about anisotropic exchange in other rare-earth magnets.

The XY pyrochlore Er2Ti2O7 has garnered much attention due to the possibility that its ground state selection could originate from an order-by-disorder mechanism [1,2]. However, recently, theoretical work has exploited the fact that the symmetry breaking in this system is a rare case of high discrete symmetry (Z6) [3]. This work studied the effect of a magnetic field on the Z6 symmetry breaking and predicted rich and controllable magnetothermodynamic properties. Indeed, the authors predict numerous domains transitions in the low field regime that strongly depends on the field direction. In this talk, I will present neutron scattering data on Er2Ti2O7 with a magnetic field applied along different high symmetry directions which provides the first experimental evidence for this rich Z6 domain phase behavior [4].

In recent years, there has been a resurgence of interest in the study of chiral spin liquids (CSLs), topologically ordered states of matter that are closely related to the celebrated fractional quantum Hall states. This resurgence has been driven by the introduction of exact parent Hamiltonians and a number of numerical studies that have identified CSLs in local spin models. However, our understanding of how and why these states emerge is still lacking. I will discuss evidence supporting one particularly intuitive mechanism in which they arise as "quantum-disordered" descendants of certain non-coplanar magnetic parent states, uniting many of the CSLs found so far under a common framework.

Many-body quantum systems are often hard to simulate on a computer, due to the computational complexity generated by non-classical correlations or entanglement between parts of these systems. An alternate platform is to experimentally simulate non-trivial quantum models on synthetic quantum matter composed of cold atomic systems. These systems exhibit excellent quantum coherence properties due to their isolation from environment, and hence faithfully evolve in time under the prescribed quantum Hamiltonian. In this talk, I will focus on simulating models of quantum magnetism with laser-cooled trapped atomic ions. Two internal states of each ion represent a spin-1/2 system that can be initialized, manipulated, and detected with near perfection by laser beams. Precisely tuned optical dipole forces couple individual spins to the collective vibrational (phonon) states of the ions, which mediate effective spin-spin interactions. By suitably tailoring these couplings, the interactions can be tuned dynamically in magnitude, sign, and range, allowing for the investigation of a large class of problems in quantum many-body physics.