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

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

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

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

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

One of the most general results of non-equilibrium statistical physics is the fluctuation symmetry, which relates the probabilities of forwards and backward fluctuations even far away from equilibrium. We present a novel mechanism that generates dynamical phase transitions, which spontaneously break the fluctuation symmetry. Moreover, the same mechanism leads to universal non-Gaussian typical fluctuations in equilibrium.

An attempt at a pedagogical presentation will be made.

Ongoing development of quantum simulators allows for a progressively finer degree of control of quantum many-body systems. This motivates the development of efficient approaches to facilitate the control of such systems and enable the preparation of non-trivial quantum states using a limited set of available controls. In this talk I will present a new approach which can be used to find the locally optimal driving protocol for trajectories within an MPS manifold. I will then focus on a specific example, namely the PXP model, where I will compare our approach to

counter-diabatic driving using numerical simulations. Lastly, I will present two use cases. Firstly, I will present how this approach can be used to stabilise quantum scars by constructing a Floquet model with nearly ideal scars and secondly, I will present a step towards full trajectory optimization and demonstrate the entanglement steering capabilites that allow us to construct entangled states with high fidelity.

* Marko Ljubotina, IST Vienna

Spatiotemporal correlation functions provide the key diagnostic tool for studying spatially extended complex quantum many-body systems. In ergodic systems scrambling causes initially local observables to spread uniformly over the whole available Hilbert space and causes exponential suppression of correlation functions with the spatial size of the system. In this talk, we present a perturbed free quantum circuit model, in which ergodicity is induced by a unitary impurity placed on the system’s boundary. We refer to this setting as boundary chaos. It allows for computing the asymptotic scaling of correlations with system size.

This is achieved by mapping dynamical correlation functions of local operators in a system of linear size L at time t to a partition function with complex weights defined on a two-dimensional lattice of smaller size t/L × L with a helix topology. We evaluate this partition function in terms of suitable transfer matrices. As this drastically reduces the complexity of the computation of correlation functions, we are able to treat system sizes far beyond what is accessible by exact diagonalization. By studying the spectra of transfer matrices numerically and combining our findings with analytical arguments we determine the asymptotic scaling of correlation functions with system size.

For impurities that remain unitary under partial transpose, we demonstrate that correlation functions between local operators at the system’s boundary at times proportional to system size L are generically exponentially suppressed with L. In contrast, for generic unitary impurities or generic locations of the operators correlations show persistent revivals with a period given by the system size.

Moreover we justify the notion of boundary chaos by demonstrating that spectral fluctuations follow predictions from random matrix theory: We compute the spectral form factor exactly in the limit of large local Hilbert space dimension, which agrees with random matrix results after possible non-universal initial behavior. For small local Hilbert space dimension we support our claim by extensive numerical investigations.

The nonequilibrium steady states of open quantum many-body systems can undergo phase transitions due to the competition of unitary and dissipative dynamics. We consider translation-invariant systems governed by Lindblad master equations, where the Hamiltonian is quadratic in the ladder operators, and the Lindblad operators are either linear or quadratic and Hermitian. These systems are called quasi-free and quadratic, respectively.

Quadratic one-dimensional systems with finite-range interactions necessarily have exponentially decaying Green’s functions. For the quasi-free case without quadratic Lindblad operators, we find that fermionic systems with finite-range interactions are non-critical for any number of spatial dimensions and provide bounds on the correlation lengths. Quasi-free bosonic systems can be critical in D>1 dimensions. Lastly, we address the question of phase transitions in quadratic systems and find that, without symmetry constraints beyond invariance under single-particle basis and particle-hole transformations, all gapped Liouvillians belong to the same phase.

Technically, we use that the Green’s function equations of motion for quadratic systems form closed hierarchies, that the Liouvillians can be brought into a useful block-triangular form, and that quasi-free models can be solved exactly using the formalism of third quantization as previously discussed by Prosen and Seligman.

***** Thomas Barthel*, Duke University*

**The seminar will be held online via Zoom (****ID: 281 621 2459****)**

https://uni-lj-si.zoom.us/j/2816212459

**References**

[1] Y. Zhang and T. Barthel, “Criticality and phase classification for quadratic open quantum many-body systems”, arXiv:2204.05346

[2] T. Barthel and Y. Zhang, “Solving quasi-free and quadratic Lindblad master equations for open fermionic and bosonic systems”, arXiv:2112.08344

[3] T. Barthel and Y. Zhang, “Super-operator structures and no-go theorems for dissipative quantum phase transitions”, arXiv:2012.05505

Supersolids are phases of matter that spontaneously and simultaneously break both a global U(1) and translational symmetry. In this talk I will show how to derive a phenomenological description — in the spirit of Ginzburg-Landau theory — valid near the supersolid transition, and use it to find a few model-independent relationships between quantities of interest around it. Such relationships are then confirmed by performing calculations in the framework of the holographic correspondence, which provides some predictions even away from the transition itself. I will later discuss future possible developments of this model.