Gunter Schuetz: Dynamical universality classes: Recent results and open questions

Universality asserts that, especially near phase transitions, the macroscopic properties of a physical system do not depend on its details such as the precise form of microscopic interactions. We show that the two best-known examples of dynamical universality classes, the diffusive and Kardar-Parisi-Zhang-classes, are only part of an infinite discrete family. The members of this family have dynamical exponents which surprisingly can be expressed by the Kepler ratio of consecutive Fibonacci numbers. This strongly indicates the existence of a simpler but still unknown underlying mechanism that determines the different classes.

* Gunter Schuetz: Institute of Complex Systems (ICS), Forschungszentrum Jülich · Germany

Felix Fritzsch: Universal Spectral Correlations in Bipartite Chaotic Quantum Systems

The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor in coupled bipartite chaotic quantum systems and obtain all moments of the spectral form factor exactly in the semiclassical limit of large Hilbert space dimension. Extrapolating those results to finite Hilbert space dimension we find a universal dependence of the spectral form factor on a single scaling parameter for times larger than the subsystem’s Heisenberg time. We complement our analysis by a perturbative approach covering the small coupling regime. Our results are derived in a random matrix model adapted to the bipartite nature of our setting in which we find excellent agreement between analytical results and extensive numerical studies. Moreover, we demonstrate that our results apply equally well to actual bipartite chaotic quantum systems by accurately describing the spectral form factor and its universal dependence on the scaling parameter in quantized coupled kicked rotors. Ultimately, we discuss an extension of our results to the many-body setting.

* Felix Fritzsch, FMF, University of Ljubljana

Bruno Bertini: Rényi Entropies and Charge Moments from Space-Time Duality

Rényi entropies are conceptually valuable and experimentally relevant generalisations of the celebrated von Neumann entanglement entropy. After a quantum quench in a clean quantum many-body system they generically display a universal linear growth in time followed by saturation. While a finite subsystem is essentially at local equilibrium when the entanglement saturates, it is genuinely out-of-equilibrium in the growth phase. In particular, the slope of the growth carries vital information on the nature of the system’s dynamics, and its characterisation is a key objective of current research. In the talk I will show that the slope of Rényi entropies can be determined by means of a spacetime duality transformation. I will argue that the slope coincides with the stationary density of entropy of the model obtained by exchanging the roles of space and time. Therefore, very surprisingly, the slope of the entanglement can be expressed as an equilibrium quantity. I will use this observation to find an explicit formula for the slope of Rényi entropies in all integrable models treatable by thermodynamic Bethe ansatz and evolving from integrable initial states. I will then show that the duality approach can be generalised to the computation of full-counting statistics and symmetry resolved entanglement.

* Bruno Bertini, University of Nottingham, United Kingdom

Yusuf Kasim: Dual unitary circuits in random geometries

Recently introduced dual unitary brickwork circuits have been recognised as paradigmatic exactly solvable quantum chaotic many-body systems with tunable degree of ergodicity and mixing. In this talk we show that regularity of the circuit lattice is not crucial for exact solvability. We consider a circuit where random 2-qubit dual unitary gates sit at intersections of random arrangements of straight lines in two dimensions (mikado) and analytically compute the variance of the spatio-temporal correlation function of local operators. Note that the average correlator vanishes due to local Haar randomness of the gates. The result can be physically motivated for two random mikado settings. The first corresponds to the thermal state of free particles carrying internal qubit degrees of freedom which experience interaction at kinematic crossings, while the second represents rotationally symmetric (random euclidean) space-time.

arXiv:2206.09665

* Yusuf Kasim, Faculty for Mathematics and Physics, University of Ljubljana

Timotej Lemut: Reconstruction of spectra and an algorithm based on the theorems of Darboux and Puiseux

Assuming only a known dispersion relation of a single mode in the spectrum of a two-point function in some quantum field theory, we investigate when and how the reconstruction of the complete spectrum of physical excitations is possible. In particular, we develop a constructive algorithm based on the theorems of Darboux and Puiseux that allows for such a reconstruction of all modes connected by level-crossings. For concreteness, we focus on theories in which the known mode is a gapless excitation described by the hydrodynamic gradient expansion, known at least to some (preferably high) order. We first apply the algorithm to a simple algebraic example and then to the transverse momentum excitations in the holographic theory that describes a stack of M2 branes and includes momentum diffusion as its gapless excitation.

* Timotej Lemut, Faculty for Mathematics and Physics, University of Ljubljana

Tony Jin: Measurement-induced phase transition and KPZ physics in a classical random walker

Measurement-induced phase transitions (MIPT) were discovered for chaotic random quantum model undergoing projective or continuous measurements. In these models, depending on the rate of measurement, the system is either in an entangling phase or disentangling phase. The existence of MIPT was first demonstrated for quantum systems using quantities such as entanglement or Rényi entropy for the characterization of the phase transition. In this talk, I will present a classical model showing the same phenomenology which consists of a single random walker undergoing continuous weak measurement. Importantly, our approach relies on an analytical map in the weak/short time regime between the probability distribution of our model and the interface height of the Kardar-Parisi-Zhang equation which unveils an unexpected connection between the physics of interface growth and information theory.

* Tony Jin: University of Chicago

Francisco Gonzalez Montoya: From classical chaotic scattering to the calculation of long term dynamics of an spin chain using coupled coherent states

The first part of the talk is about the multidimensional generalization of the hyperbolic periodic orbits and their invariant manifolds in Hamiltonian systems. Those manifolds play an essential roll to understand the transport and the dynamics in multidimentional phase space.

The second part of the talk is about quantum dynamics and its connection with classical dynamics. The time dependent variational principle and coherent states has been successfully used to calculate the evolution of quantum systems with classical analog. Some remarkable examples are chemical systems with large dimension. Based on this approach, we explore the possibility to calculate the long term dynamics of a experimental time dependent spin chain.

* Francisco Gonzalez Montoya, Centro International de Ciencias AC, Mexico and University of Leeds, UK

Thomas H. Seligman: Molecular Materials and Quantum transport in Molecular Nano-Systems

Quasi 2-D and even quasi 1-D materials are at the forefront of many ideas for molecular devices. I plan to present a panorama driven by the possibility of simulating small and medium sized flakes and ribbons of such materials by DFT calculations with a fairly high confidence that they predict the behaviour of such materials at least qualitatively very well. In the domain of transport through Benzene and small polyacenes we shall even present experiments where transmissions have been measured and compared with tight binding calculations and emulation experiments with microwaves. This brings us directly to ring currents which seem to occur at certain voltages and in turn connect the subject with the one of (non-superconducting) persistent currents.

* Thomas H. Seligman, Instituto de Ciencias Fïscas,  University of Mexico (UNAM)
and Centro Internacional de Ciencias Cuernavaca, Mexico

Guillermo Preisser: The rise and fall, and slow rise again, of operator entanglement under dephasing

The operator space entanglement entropy, or simply ‘operator entanglement’ (OE), is an indicator of the complexity of quantum operators and of their approximability by Matrix Product Operators (MPO). In this talk I will present the study of OE of the density matrix of a 1D spin chain undergoing dissipative evolution. While it is expected that, after an initial linear growth the OE should be supressed by dissipative processes as the system evolves to a simple stationary state, we find that this scenario breaks down for one of the most fundamental dissipative mechanisms: dephasing. Under dephasing, after the initial ‘rise and fall’ the OE can rise again, increasing logarithmically at long times. Through a combination of MPO simulations for chains of infinite length and analytical arguments valid for strong dephasing, I show that the growth is inherent to a U(1) conservation law. I argue that in an XXZ model the OE grows universally as 1/4log_2 t at long times, and trace this behavior back to an anomalous classical diffusion process. 

* Guillermo Preisser, University of Strasbourg, France

Alberto Catalano: Topological frustration in 1D spin chains

Especially in one dimension, models with discrete and continuous symmetries display different physical properties, starting from the existence of long-range order. Introducing topological frustration in spin chains characterized by a discrete local symmetry, they develop a region in parameter space which mimics the features of models with continuous symmetries. After discussing the emergence and the characterization of this novel region, I will show how these effects of frustration can be exploited for the development of efficient quantum technologies such as quantum batteries.

* Alberto Catalano, Institut Ruđer Bošković, Zagreb