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.

The full counting statistics encodes the probability distribution of a dynamical observable and is a dynamical analogue of the thermodynamic partition function. It is naturally discussed within the frameworks of the large deviation theory and the Lee-Yang theory of phase transitions, which we briefly review. By combining the two approaches we point out that, in the presence of dynamical critical point, a rich phenomenology of fluctuations is permissible. As an explicit demonstration we introduce an interacting cellular automaton, where an analytical computation of the full counting statistics is feasible. Asymptotic analysis of the exact solution gives access to the current distribution on all scales and explicit cumulant asymptotics, revealing, among other anomalous features, non-Gaussian typical fluctuations in equilibrium. The scaled cumulant generating function does not generate scaled cumulants. If time permits we will also discuss some recent results on anomalous fluctuations in the (anisotropic) Landau-Lifshitz model, a paradigmatic integrable model of interacting classical spins.

References:
Ž. Krajnik, J. Schmidt, V. Pasquier, E. Ilievski, T. Prosen. Exact anomalous current fluctuations in a deterministic interacting model. arXiv: 2201.05126
Ž. Krajnik, E. Ilievski, T. Prosen. Absence of Normal Fluctuations in an Integrable Magnet, arXiv:2109.13088

The understanding of the relaxation of large quantum systems has received an important boost from the point of view of pure state quantum statistical mechanics, and in particular from the eigenstate thermalization hypothesis. At the same time, the dynamics of quantum systems has been investigated by out of time ordered correlators. Interestingly it was shown, using hydrodynamic theory, that such correlators relax algebraically in the presence of conserved quantities. Here we show how such slow relaxation can be expected from the eigenstate thermalization hypothesis.

At the same time, conserved quantities can lead to the phenomenon of pre-thermalization. Here we show that considering two large non-integrable systems weakly coupled to each other, one can show that in the thermodynamic limit a steady current between the two will emerge, and that this current is typical.

* Dario Poletti, Singapore University for Technology and Design

We study the growth of the number entropy S_N in one-dimensional number-conserving interacting systems with strong disorder, which are believed to display many-body localization. Recently a slow and small growth of S_N has been numerically reported, which, if holding at asymptotically long times in the thermodynamic limit, would imply ergodicity and therefore the absence of true localization. By numerically studying S_N in the disordered isotropic Heisenberg model we first reconfirm that, indeed, there is a small growth of S_N. However, we show that such growth is fully compatible with localization. To be specific, using a simple model that accounts for expected rare resonances we can analytically predict several main features of numerically obtained S_N: trivial initial growth at short times, a slow power-law growth at intermediate times, and the scaling of the saturation value of S_N with the disorder strength. Because resonances crucially depend on individual disorder realizations, the growth of S_N also heavily varies depending on the initial state, and therefore S_N and von Neumann entropy can behave rather differently.