The bulk-edge correspondence is a remarkable duality in condensed matter physics, relating the value of bulk topological invariants to the emergence of gapless edge modes. In the case of the integer quantum Hall effect, the value of the Hall conductivity is equal to the sum of signed edge modes, taking into account their chirality. For noninteracting systems, this fact is by now understood in full mathematical rigor. For interacting models, in the last years there has been progress in the rigorous understanding of bulk topological phases, but a lot less is known about interacting edge modes and about the bulk-edge duality. From the point of view of effective QFTs, the edge modes of 2d Hall systems are expected to be well described by the multichannel Luttinger model, a 1+1 dimensional integrable QFT. In this talk I will discuss how rigorous RG methods can be used to prove the emergence of the Luttinger liquid description from the 2d lattice model, and to control the deviations away from it at finite scales. The approach allows to exactly compute real-time edge transport coefficients, and in particular to prove the quantization of the edge conductance, thanks to the combination of lattice and emergent Ward identities. Joint work with Vieri Mastropietro.
*Marcello Porta, SISSA Trieste
Attention Unusual date, the seminar will take place on Friday
On 12th and 13th 2023 will be held the symposium on Nonequilibrium many-body dynamics in memory of our colleague and friend Marko Medenjak who passed away last year. All talks will be given in the F1 room on the ground floor of the Faculty of Physics building, Jadranska 19. The symposium is open to all interested. Please find the program here.
In talk I will show how to self-consistently couple the Einstein-inflaton equations to a strongly coupled quantum field theory (QFT) as described by holography. We show that this can lead to an inflating universe, a reheating phase and finally a universe dominated by the QFT in thermal equilibrium. Special attention will be given to technical details that could be of relevance for modelling of more general holographic set-ups that for instance include charge.
In quantum physics, topological properties usually emerge as a feature of equilibrium quantum states. We show that topological fingerprints can also manifest in the relaxation rates of open quantum systems. To demonstrate this we consider one of the simplest models that has two distinct topological phases in its ground state: the Kitaev model for the p-wave superconductor. After introducing dissipation to this model we estimate the Liouvillian gap in both strong and weak dissipative regimes. Our results show that a non-zero superconducting pairing opens a Liouvillian gap that remains open at large system sizes. At strong dissipation this gap is essentially unaffected by the topology of the underlying Hamiltonian ground state. In contrast, when dissipation is weak, the topological phase of the Hamiltonian ground state plays a crucial role in determining the character of the Liouvillian gap. We present the method used to extract this Liouvillian gap for a number of different dissipative processes.
I will discuss a semiclassical approach to form factors in the sinh-Gordon field theory in the background of a radial classical solution that describes a heavy exponential operator placed at the origin. I will introduce and study new special functions which generalize the Bessel functions and have a nice interpretation in the Tracy–Widom theory of the Fredholm determinant solutions of the classical sinh-Gordon model.
Unusual venue: F1 room, 1st floor
I will discuss the matrix quantum mechanics with potential corresponding to an arbitrary spectral curve. This can be seen as a generalization of the duality between JT gravity and a particular matrix integral. Using the recently developed techniques of quantum generalised hydrodynamics, the effective theory of the eigenvalue density fluctuations is a simple 2D free-boson BCFT on a curved background. The ensemble average over random matrices then corresponds to a quantum expectation value. Using this formalism we reproduce non-perturbative results for matrix integrals (the ramp and the plateau in the spectral form factor). We also compute the entanglement between eigenvalues, matching a previous result by Hartnoll and Mazenc for the c = 1 matrix model and extending it to the general case. The hydrodynamical theory provides a clear picture of the emergence of spacetime in two dimensional string theory.
*Giuseppe Policastro, Laboratoire de Physique Théorique, ENS, Paris
New ! Before the seminar, you are invited to have pizzas in the seminar room at 12:45 (unusual venue, F1 classroom, Physics building first floor)
In recent years dual-unitary circuits have emerged as minimal models for chaotic quantum many-body systems in which the dynamics of correlations and entanglement remains tractable. The building blocks of these circuits are gates that are unitary in both time and space. After an introduction to these circuits I will extend the notion of dual-unitarity to biunitarity, which allows for a richer variety of building blocks and circuit dynamics, as well as unifying different notions of ‘dual-unitarity’. The resulting interactions are governed by quantum combinatorial data, which I will precisely characterize using a graphical 2-categorical framework based on the ‘shaded calculus’. These generalized circuits remain exactly solvable and we show that they retain the attractive features of the original dual-unitary models, with exact results for correlations functions, maximal entanglement growth and exact thermalization.
* Pieter Claeys, Max Planck Institute for the Physics of Complex Systems, Dresden
The study of quantum quenches had a vast contribution to our understanding of out-of-equilibrium dynamics and relaxation in closed many-body systems. The investigation of entanglement growth in a quench could shed light to various features of the underlying physics, in particular for integrable systems. However, most of the studies focus on setups where the system is driven far from equilibrium due to the inhomogeneity of the initial state. In my talk, I will present results for quenches where the time evolution operator is made inhomogeneous
by the presence of a localized defect. I will compare results on entanglement spreading across a conformal defect, obtained either by field theory or by a lattice realization of the defect.
In this talk, we investigate the behavior of purity and out-of-time-ordered correlations in random quantum circuits. We show that the time evolution of both quantities can be described by a Markov chain, and their relaxation towards their asymptotic values is not governed by the second largest eigenvalue of the transfer matrix, as one could expect. The exponential relaxation is instead given by an “eigenvalue”, which is not in the spectrum of the transfer matrix at all — a phantom eigenvalue. We shall explore this phenomenon and find that it is rooted in the non-Hermiticity of the transfer matrix and in the locality of the dynamics.
*Jaš Bensa: University of Ljubljana