Scientific Series

In the second lecture, I will extend the previous discussion to gravity, and show that the conformal trace anomaly must play a special role in the effective field theory of low energy gravity. Classical General Relativity receives an infrared relevant modification from the conformal trace anomaly of the energy-momentum tensor of massless, or nearly massless, quantum fields, which implies the existence of a new long range massless scalar degree of freedom, not present in the classical Einstein theory, that contributes to gravitational scattering processes and has long range gravitational effects. Similar to the axial anomaly, the local form of the effective action associated with the conformal anomaly is expressible in terms of a dynamical scalar field that couples to the conformal factor of the spacetime metric, allowing it to propagate over macroscopic distances. Among the significant implications of this effective field theory of gravity are the prediction of scalar gravitational wave solutions—a spin-0 breather mode— in addition to the transversely polarized tensor waves of the classical Einstein theory. Astrophysical sources for scalar gravitational waves are considered, with the excited gluonic condensates in the interiors of neutron stars in merger events with other compact objects likely to provide the strongest burst signals. The conformal anomaly also implies generically large quantum back reaction effects and conformal correlators in the vicinity of black hole horizons which are relevant to the formation of a non-singular interior, as well as an additional scalar degree of freedom in cosmology, providing a theoretical foundation for dynamical dark energy.

Applying a chemical potential bias to a conductor drives the system out of equilibrium into a current carrying non-equilibrium state.  This current flow is associated with entropy production in the leads, but it remains poorly understood under what conditions the system is driven to local equilibrium by this process.  We investigate this problem using two toy models for coherent quantum transport of diffusive fermions:  Anderson models in the conducting phase and a class of random quantum circuits acting on a chain of qubits, which exactly maps to an interacting fermion problem. Under certain conditions, we find that the long-time states in both models exhibit volume-law mutual information and entanglement, in striking violation of local equilibrium.  Extending this analysis to Anderson metal-insulator transitions, we find that the volume-law entanglement scaling persists at the critical point up to mobility edge effects.  This work points towards a broad class of examples of physical systems where volume-law entanglement can be sustained, and potentially harnessed, despite strong coupling of the system to its surrounding environment. 

Ubiquitous in the behavior of physical systems is the competition between an energy term E and an entropy term S of their free energy F = E - beta S. These concepts are also relevant for error correction, where the `energy` E is the number of qubits afflicted by an error, the `entropy' S(E) is the logarithm of the number of energy-E failing errors, and beta relates to the probability of each qubit's error. Error-correction schemes with larger minimum free energy have better performance. Often distance d (which correct all errors with energy less than d/2) is used as a proxy for a code's performance since it increases the minimal E and therefore tends to increases the minimal F. However, a sufficiently large entropy S can counteract a large d and reduce the free energy (negatively impacting a code's performance). A great example of these principles is the surface code, which is at present the leading architecture for fault tolerant quantum computing. Rotating a square lattice geometry over the surface of the torus can increase the distance of the code by a factor of root two, but at the cost of increased entropy. We obtain exact expressions for this entropic effect in the low error regime, and introduce an analytical model that qualitatively describes the behavior for error rates all the way up to threshold. Our predictions are corroborated by numerical estimates of the low error failure rate, using the splitting method algorithm introduced by Bravyi et al. We find that although the rotated lattice outperforms the non-rotated lattice with the same number of qubits for low error rates, the two codes have very similar performance for error rates which are an appreciable fraction of the threshold error rate. Surprisingly, we also find some system sizes and error rates for which the non-rotated lattice has marginally better performance. 

I will discuss the status and future of numerical lattice Quantum Chromodynamics (QCD) calculations for nuclear physics. With advances in supercomputing, we are beginning to quantitatively understand nuclear structure and interactions directly from the fundamental quark and gluon degrees of freedom of the Standard Model. Recent studies provide insight into the neutrino-nucleus interactions relevant to long-baseline neutrino experiments, double beta decay, and nuclear sigma terms needed for theory predictions of dark matter cross-sections at underground detectors. I will also address new work constraining `exotic glue’ in nuclei, which will be measurable for the first time at a future electron-ion collider, and explain how machine learning tools are providing new possibilities in this field.

In this first of two lectures, intended to be a pedagogical introduction, I will review the quantum field theory origin of anomalies starting with the more familiar example of the axial anomaly in QED, emphasizing the infrared effects and the appearance of a two-particle massless state, similar to a Cooper pairing in superconductor, associated with both the axial and conformal anomalies in two and four dimensions. In both cases the effective action of the anomaly is non-local, but may be expressed in a local form by the introduction of a bosonic field, which one can verify becomes a bona fide propagating quantum field in its own right. At finite chiral chemical potential this boson is a chiral density wave, a gapless pseudo-scalar collective excitation of the Fermi surface of a dissipationless chiral superfluid, analogous to the Goldstone-Nambu boson of spontaneous symmetry breaking. In the limit of vanishing chiral background the boson is a chiral collective mode of the Dirac vacuum itself, which therefore supports an axion-like boson excitation with a two-photon coupling, arising directly from the axial anomaly.

 

Despite much theoretical effort, there is no complete theory of the “strange” metal phase of the high temperature 

superconductors, and its linear-in-temperature resistivity. This phase is believed to be a strongly-interacting metallic 

phase of matter without fermionic quasiparticles, and is virtually impossible to model accurately using traditional

perturbative field-theoretic techniques. Recently, progress has been made using large-N techniques based on the 

solvable Sachdev-Ye-Kitaev (SYK) model, which do not involve expanding about any weakly-coupled limit. I will 

describe constructions of solvable models of strange metals based on SYK-like large-N limits, which can reproduce  

some of the experimentally observed features of strange metals and adjoining phases. These models, and further 

extensions, could possibly pave the way to developing a controlled theoretical understanding of the essential building 

blocks of the electronic state in correlated-electron superconductors near optimal doping.

Violations of Bell inequalities have traditionally been used to refute a local-realistic description of the world. Not surprisingly, under the assumption that the world is quantum, they can be used to certify quantum devices. What is surprising is that in some cases this characterisation turns out to be (almost) complete, i.e.~we can determine (almost) everything about the devices and this phenomenon is known as self-testing of quantum systems. Although the first self- testing results can be traced back to the works of Tsirelson published in the 80's, the topic has remained largely unknown until the seminal work of Mayers and Yao in 1998. It has received further exposure with the advent of device-independent quantum cryptography to which it is closely connected. In this talk I will give a brief introduction to the topic of self-testing and discuss some recent developments, e.g.~robust self-testing, weak self-testing, self-testing of entangled measurements, self-testing of high-dimensional systems or self-testing in prepare-and-measure scenarios.

A key prediction of the Lambda CDM framework of structure formation is that a host halo containing a Milky Way sized disk galaxy should contain hundreds of thousands of sub-dwarf galaxy mass dark matter subhalos. Devoid of stars, these substructures remain undetected. Detecting them will not only corroborate the existence of dark matter but also give crucial information on the particle nature of dark matter and how they cluster at small scale. Cold stellar streams originate when globular clusters are tidally disrupted in the Milky Way potential. Gravitational encounters with dark matter subhalos will perturb these streams' density. I will present a novel method of probing the fundamental nature of dark matter by statistically analyzing the power spectrum of the stream density. I will discuss the uncertainties that the known baryonic structures such as the Galactic bar, the spiral arms, the Galactic population of giant molecular clouds and globular clusters can impart. Understanding their effects will be crucial for deciding whether a particular stream can be used to probe dark matter substructures.  

We discuss some algebraic quantum field theory (AQFT) ingredients that should be useful in defining a tensor network describing a Lorentzian space-time.

We look into toy models that approximate Minkowski space and show how Lorentz boosts are approximately recovered, and obtain Rindler modes that can be compared with the entanglement spectrum. 

We make connections of these approximations of Lorentz boosts with the corner transfer matrices in integrable models, and comment on the discrete realization of the Reeh-Schlieder theorem that governs entanglement in a Hilbert space with lower bounded energy. 

One can associate to any finite graph Q the skew-symmetic Kac-Moody Lie algebra g_Q. While this algebra is always infinite, unless Q is a Dynkin diagram of type ADE, g_Q shares a lot of the nice features of a semisimple Lie algebra. In particular, the cohomology of Nakajima quiver varieties associated to Q gives a geometric representations of g_Q. Encouraged by this story, one could hope to define the Yangian of g_Q, for general Q, as a subalgebra of the algebra of endomorphisms of cohomology of quiver varieties. In fact there are two approaches to doing this: firstly via the stable envelope construction of Maulik and Okounkov, secondly via the preprojective Hall algebra of Schiffmann and Vasserot. Via another Hall algebra construction, due to Kontsevich and Soibelman, and work of myself and Meinhardt on BPS Lie algebras, these approaches turn out to be more or less the same. In showing this we show that the correct Lie algebra of endomorphisms associated to Q is cohomologically graded, with zeroeth piece the old Kac-Moody Lie algebra - the best way to build a (Borcherds) Lie algebra out of Q is directly from geometric representation theory.

I discuss the canonical degrees of freedom of metric Einstein gravity on a null surface. The constraints are interpreted as conservation equations of a boundary current. Gravitational fluxes are identified, and the Hamiltonians of diffeomorphism symmetry are discussed. Special attention is given to the role of a modification of the phase space at the boundary of the null surface. Based on 1802.06135 with Laurent Freidel.