I will talk about our recent progress on bootstrapping critical gauge theories. In specific, I will first introduce the current understanding that why bootstrap works, for example, why a CFT can sit at a kink of bootstrap bounds and why CFT can be isolated as an island. Then, I will apply these idea to a prototypical critical gauge theory--the scalar QED (i.e. SU(N) deconfined phase transition), and demonstrate it can be isolated in a bootstrap island when the matter flavour is large.

Considering the scale dependent effective spacetimes implied by the functional renormalization group in d-dimensional Quantum Einstein Gravity, we discuss the representation of entire evolution histories by means of a single, (d+1)-dimensional manifold furnished with a fixed (pseudo-) Riemannian structure.

We propose a universal form of the higher dimensional metric and discuss its properties. We show that, under precise conditions, this metric is always Ricci flat; if the evolving spacetimes are maximally symmetric, their (d+1)-dimensional representative has a vanishing Riemann tensor even. The non-degeneracy of the higher dimensional metric is linked to a monotonicity requirement for the running of the cosmological constant, which we test in the case of Asymptotic Safety.

Furthermore, we allow the higher dimensional manifold to be an arbitrary Einstein space, admitting the possibility that the spacetimes to be embedded have a Lorentzian signature, a prime example being a stack of de Sitter spaces. We “derive” the (A)dS/CFT correspondence by applying the gravitational Effective Average Action approach, by solving the corresponding functional RG and the effective Einstein equations, and finally embedding the 4D metrics into the one single 5-dimensional one. It is an intriguing possibility that in this way one might find a specific solution to the general equations which coincides with the 5D kinematic setting which forms the basis of the conjectured (A)dS/CFT correspondence.

Zoom Link: https://pitp.zoom.us/j/92268060878?pwd=M2E1S1RxcHBFbzBiblhpSUJCMWIzUT09

I will discuss how spontaneous breaking of time reversal symmetry in multiband superconductors leads quite generally to the formation of small Fermi surfaces of Bogoliubov excitations, irrespective of whether inversion symmetry is absent or present in the superconducting state. In the latter case the inversion symmetry is susceptible to being dynamical broken at low temperatures by the residual interactions. A lattice model of this process will be discussed. Its final result is a reduced, but still finite Bogoliubov-Fermi surface.

One of the central themes of quantum many-body physics and quantum field theory is the emergence of universality classes. In general, determining which universality class emerges in a quantum many-body system is a highly complex problem. I will argue that the perspective of quantum anomaly provides powerful insights to the understanding of the landscape of universality classes that can emerge in a quantum matter, and I will present some interesting applications.

Rydberg atom arrays are programmable quantum simulators capable of preparing interacting qubit systems in a variety of quantum states. However, long experimental state preparation times limit the amount of measurement data that can be generated at reasonable timescales, posing a challenge for the reconstruction and characterization of quantum states. Over the last years, neural networks have been explored as a powerful and systematically tuneable ansatz to represent quantum wavefunctions. These models can be efficiently trained from projective measurement data or through Hamiltonian-guided variational Monte Carlo. In this talk, I will compare the data-driven and Hamiltonian-driven training procedures to reconstruct ground states of two-dimensional Rydberg atom arrays. I will discuss the limitations of both approaches and demonstrate how pretraining on a small amount of measurement data can significantly reduce the convergence time for a subsequent variational optimization of the wavefunction.

Artificial neural networks have been widely adopted as ansatzes to study classical and quantum systems. However, some notably hard systems such as those exhibiting glassiness and frustration have mainly achieved unsatisfactory results despite their representational power and entanglement content, thus, suggesting a potential conservation of computational complexity in the learning process. We explore this possibility by implementing the neural annealing method with autoregressive neural networks on a model that exhibits glassy and fractal dynamics: the two-dimensional Newman-Moore model on a triangular lattice. We find that the annealing dynamics is globally unstable because of highly chaotic loss landscapes. Furthermore, even when the correct ground state energy is found, the neural network generally cannot find degenerate ground-state configurations due to mode collapse. These findings indicate that the glassy dynamics exhibited by the Newman-Moore model caused by the presence of fracton excitations in the configurational space likely manifests itself through trainability issues and mode collapse in the optimization landscape.

Predicting the fate of an interacting system in the limit where the electronic bandwidth is quenched is often highly non-trivial. The complex interplay between interactions and quantum fluctuations driven by the band geometry can drive a competition between various ground states, such as charge density wave order and superconductivity. In this work, we study an electronic model of topologically-trivial flat bands with a continuously tunable Fubini-Study metric in the presence of on-site attraction and nearest-neighbor repulsion, using numerically exact quantum Monte Carlo simulations. By varying the electron filling and the spatial extent of the localized flat-band Wannier wavefunctions, we obtain a number of intertwined orders. These include a phase with coexisting charge density wave order and superconductivity, i.e., a supersolid. In spite of the non-perturbative nature of the problem, we identify an analytically tractable limit associated with a `small' spatial extent of the Wannier functions, and derive a low-energy effective Hamiltonian that can well describe our numerical results.

Thermodynamics has shed light on engines, efficiency, and time’s arrow since the Industrial Revolution. But the steam engines that powered the Industrial Revolution were large and classical. Much of today’s technology and experiments are small-scale, quantum, far from equilibrium, and processing information. Nineteenth-century thermodynamics needs re-envisioning for the 21st century. Guidance has come from the mathematical toolkit of quantum information theory. Applying quantum information theory to thermodynamics sheds light on fundamental questions (e.g., how does entanglement spread during quantum thermalization? How can we distinguish quantum heat from quantum work?) and practicalities (e.g., quantum engines and the thermodynamic value of coherences). I will overview how quantum information theory is being used to revolutionize thermodynamics in quantum steampunk, named for the steampunk genre of literature, art, and cinema that juxtaposes futuristic technologies with 19th-century settings.

Zoom Link: https://pitp.zoom.us/j/92454766615?pwd=QzZXMnYwN3ZZOTE5RzZEcHp6TkhMdz09

The sign structure of quantum states is closely connected to quantum phases of matter, yet detecting such fine-grained properties of amplitudes is subtle. We employ as a diagnostic measurement-induced entanglement (MIE)-- the average entanglement generated between two parties after measuring the rest of the system. We propose that for a sign-free state, the MIE upon measuring in the sign-free basis decays no slower than correlations in the state before measurement. Concretely, we prove that MIE is upper bounded by mutual information for sign-free stabilizer states (essentially CSS codes), which establishes a bound between scaling dimensions of conformal field theories describing measurement-induced critical points in stabilizer systems. We also show that for sign-free qubit wavefunctions, MIE between two qubits is upper bounded by a simple two-point correlation function, and we verify our proposal in several critical ground states of one-dimensional systems, including the transverse field and tri-critical Ising models. In contrast, for states with sign structure, such bounds can be violated, as we illustrate in critical hybrid circuits involving both Haar or Clifford random unitaries and measurements, and gapless symmetry-protected topological states.

Two-dimensional gapless Dirac fermions emerge in various condensed-matter settings. In the presence of interactions such Dirac systems feature critical points and the precision determination of their exponents is a prime challenge for quantum many-body methods. In a field-theoretical language, these critical points can be described by Gross-Neveu-Yukawa-type models and in my talk I will show some results on Gross-Neveu critical behavior using field theoretical approaches beyond the leading order. To that end, I will first present higher-loop perturbative RG calculations for generic Gross-Neveu-Yukawa models and compare estimates for the exponents with recent corresponding results from Quantum Monte Carlo simulations and the conformal bootstrap. Then, I will discuss a more exotic variant of Gross-Neveu-Yukawa models which describes the interacting fractionalized excitations of two-dimensional frustrated spin-orbital magnets. Here, we have provided field-theoretical estimates for the critical exponents employing higher-order epsilon expansion, large-N calculations, and functional renormalization group.