Perimeter Institute Graduate Students' Conference 2024

What types of differences among causal structures with latent variables are impossible to distinguish by statistical data obtained by probing each visible variable? If the probing scheme is simply passive observation, then it is well-known that many different causal structures can realize the same joint probability distributions. Even for the simplest case of two visible variables, for instance, one cannot distinguish between causal influence of one variable on the other and the two variables sharing a latent common cause. However, it is possible to distinguish between these two causal structures if we have recourse to more powerful probing schemes, such as the possibility of intervening on one of the variables and observing the other. Herein, we address the question of which causal structures remain indistinguishable even given the most informative types of probing schemes on the visible variables. We find that two causal structures remain indistinguishable if and only if they are both associated with the same mDAG structure (as defined by Evans (2016)). We also consider the question of when one causal structure dominates another in the sense that it can realize all of the joint probability distributions that can be realized by the other using a given probing scheme. (Equivalence of causal structures is the special case of mutual dominance.) Finally, we investigate to what extent one can weaken the probing schemes implemented on the visible variables and still have the same discrimination power as a maximally informative probing scheme.

Violations of Bell’s inequality have been studied for spin-1/2 systems in much detail. Turns out that one can show Bell violation for systems that are expressed in terms of continuous variables such as position and momentum. The most ubiquitous examples of such systems are Gaussian states, notably the two-mode squeezed vacuum state. I will talk about how one can quantify violations of local realism in such states. I will discuss the dependence of Bell violation on temperature as well as the result that entanglement is not a monotonic function of Bell's inequality.

We present a study of the relationship between energy and entanglement in finite regions of possibly arbitrary shape in QFT. We show how one can quantify the entanglement avoiding divergences by using techniques inspired by the formalism of particle detectors in relativistic quantum information. We also show how the energy cost of entanglement extraction varies with the shape and size of the regions, as well as analyze the energy density of the quantum field after this entanglement has been extracted.

The dynamics of closed quantum systems undergoing unitary processes has been well studied, leading to notions of measures for the expressive power of parameterized quantum circuits, relative to the unique, maximally expressive, average behaviour of ensembles of unitaries. Such unitary expressivity measures have further been linked to concentration phenomena known as barren plateaus. However, existing quantum hardware are not isolated from their noisy environment, and such non-unitary dynamics must therefore be described by more general trace-preserving operations. To account for hardware noise, we propose several, non-unique measures of expressivity for quantum channels and study their properties, highlighting how average non-unitary channels differ from average unitary channels. In the limit of large composite system and environments, average noisy quantum channels are shown to be maximally globally depolarizing, with next-leading-order non-unital perturbative behaviour. Furthermore, we rigorously prove that highly-expressive parameterized quantum channels will suffer from barren plateaus, thus generalizing explanations of noise-induced phenomena. This work is based on forthcoming work with Diego Martin, Zoe Holmes, and Marco Cerezo, in affiliation with Los Alamos National Laboratory.

This talk will be based on SciPost Phys. 17, 021 (2024). Defects are common in physical systems with boundaries, impurities or extensive measurements. The interaction between bulk and defect can lead to rich physical phenomena. Defects in gapless phases of matter with conformal symmetry usually flow to a defect conformal field theory (dCFT). Understanding the universal properties of dCFTs is a challenging task. In this talk, we propose a computational strategy applicable to a line defect in arbitrary dimensions. Our main assumption is that the defect has a UV description in terms of a local modification of the Hamiltonian so that we can compute the overlap between low-energy eigenstates of a system with or without the defect insertion. We argue that these overlaps contain a wealth of conformal data, including the $g$-function, which is an RG monotonic quantity that distinguishes different dCFTs, the scaling dimensions of defect creation operators $\Delta^{+0}_\alpha$ and changing operators $\Delta^{+-}_\alpha$ that live on the intersection of different types of line defects, and various OPE coefficients. We apply this method to the fuzzy sphere regularization of 3D CFTs and study the magnetic line defect of the 3D Ising CFT. Using exact diagonalization and DMRG, we report the non-perturbative results $g=0.602(2),\Delta^{+0}_0=0.108(5)$ and $\Delta^{+-}_0=0.84(5)$ for the first time. We also obtain other OPE coefficients and scaling dimensions. Our results have significant physical implications. For example, they constrain the possible occurrence of spontaneous symmetry breaking at line defects of the 3D Ising CFT. Our method can be potentially applied to various other dCFTs, such as plane defects and Wilson lines in gauge theories.

In this work, we propose a systematic method to obtain the effective field theory of the quantum dissipative systems which nonlinearly realize symmetries. We focus on the high temperature or Brownian limit, in which the effective action of the dissipative dynamics is localized in time. We first introduce a microscopic model at the linear response level, which shows how the dissipative dynamics on Lie group emerges effectively through the reduced dynamics of a system interacting with a thermal bath. The model gives a systematic method to give the Langevin equation which is covariant with respect to the symmetries of the system. In addition, the model shows a systematic way to go beyond the Gaussian white noise and the interaction between the noise and dissipation. Then, using the dynamical KMS symmetry, without any reference to the microscopic structure of the bath, we obtain the most general effective action of the nonlinearly realized dissipative dynamics at high temperature. The universal dissipative coefficients are larger than the case of the linear response approximation. Then, we focus on the case of Ohmic friction where the corresponding dissipative coefficients are more restricted; we suggest an alternative model, the bulk model, to describe any Ohmic dissipative system at high temperature. The Bulk model provides a geometrical picture for the noise in the case of Ohmic friction.

There are now multiple direct probes of the region near black hole horizons, including direct imaging with the Event Horizon Telescope (EHT). As a result, it is now of considerable interest to identify what aspects of the underlying spacetime are constrained by these observations. For this purpose, we present a new formulation of an existing broad class of integrable, axisymmetric, stationary spinning black hole spacetimes, specified by four free radial functions, that makes manifest which functions are responsible for setting the location and morphology of the event horizon and ergosphere. We explore the size of the black hole shadow and high-order photon rings for polar observers, approximately appropriate for the EHT observations of M87*, finding analogous expressions to those for general spherical spacetimes. Of particular interest, we find that these are independent of the properties of the ergosphere, but does directly probe on the free function that defines the event horizon. Based on these, we extend the nonperturbative, nonparametric characterization of the gravitational implications of various near-horizon measurements to spinning spacetimes. Finally, we demonstrate this characterization for a handful of explicit alternative spacetimes.

We discuss the concept of spontaneous symmetry breaking and illustrate it with a general example. We consider Wigner-Weyl and Nambu-Goldstone realisations of symmetry in the quantum theory. Next, we state Goldstone’s theorem and sketch its proof. We discuss why quantum chromodynamics is not realised in the Wigner-Weyl mode.

The theory $S = \int\text{d}^{4-\epsilon}x\left(\frac{1}{2}|\partial\phi|^2 - \frac{m^2}{2}|\phi|^2-\frac{g}{16}|\phi|^4\right)$ exhibits a global $U(1)$ symmetry, and the operators $\phi^n$ ($\bar\phi^n$) have charge $n$ ($-n$) with respect to this symmetry. By rescaling the fields and the coupling constant, it is possible to work in a double limit $n\to\infty$, $g\to 0$ with $\lambda = gn$ kept constant. In this way, it is possible to compute 2-point functions of the form $\langle \phi^n(x) \bar\phi^n(0) \rangle$ in the large $n$ limit, either diagrammatically by a resummation of the leading contribution at all orders in $g$, or using semiclassical methods through the saddle point approximation. This second approach is particularly powerful because it can also be applied to the theory on a curved background. This allows obtaining the form of the 2-point function for an arbitrary metric, and by functionally differentiating with respect to it, it is also possible to obtain, in the flat theory, the 3-point function $\langle T^{ij}(z) \phi^n(x) \bar \phi^n(0) \rangle$ in which an energy-momentum tensor has been inserted. This allows for a non-trivial check of the conformal symmetry of this sector of the theory by verifying the Ward identities that this 3-point function should satisfy.

It may be the case that a spacetime exhibits no asymptotia where gauge invariant observables can be defined in a natural way. On such occasions the introduction of a timeline boundary may be helpful. We therefore discuss the initial boundary value problem in the context of General Relativity.

The black hole information paradox is a fundamental conflict between the quantum-mechanical and thermodynamic descriptions of black holes, specifically of their particle-emission process known as the Hawking radiation. The paradox concerns whether the radiation of a black hole is a unitary time evolution or a thermal process that erases most information about the initial state of the black hole. Multiple black hole models (e.g. [1,2]) were shown to exhibit the Page curve behavior, suggesting the unitarity of the Hawking radiation. However, without a verified theory of quantum gravity, the exact structure of black holes remains undetermined, and we need a model-independent way to test black hole unitarity. My project thus aims to develop a general framework for testing black hole unitarity by searching for its physical signatures. In particular, we employ the "hybrid" RST model [3], which possesses a Page-curve behavior, and study whether the unitarity is manifested in the transition rate of the Unruh-DeWitt particle detector. [1] Hong Zhe Chen, Robert C. Myers, Dominik Neuenfeld, Ignacio A. Reyes, Joshua Sandor. Quantum Extremal Islands Made Easy, Part II: Black Holes on the Brane". https://doi.org/10.48550/arXiv.2010.00018. [2] Yohan Potaux, Sergey N. Solodukhin, and Debajyoti Sarkar. "Spacetime Structure, Asymptotic Radiation, and Information Recovery for a Quantum Hybrid State.” Physical Review Letters 130, no. 26 (June 30, 2023): 261501. https://doi.org/10.1103/PhysRevLett.130.261501. [3] Yohan Potaux, Debajyoti Sarkar, and Sergey N. Solodukhin. "Quantum States and Their Back-Reacted Geometries in 2D Dilaton Gravity.” Physical Review D 105, no. 2 (January 12, 2022): 025015. https://doi.org/10.1103/PhysRevD.105.025015.

This work investigates the ferroelectric properties of γ − In₂Se₃, a material that uniquely retains its spontaneous polarization at the nano-scale, making it resistant to depolarizing fields. With a direct band gap of 1.8 eV and the ability to switch between insulating and semiconducting phases at room temperature, γ − In₂Se₃ holds promise for next-gen memory devices, where its stable ferroelectricity could revolutionize data storage and processing.