We study random quantum circuits and their rate of producing bipartite entanglement, specifically with respect to the choice of 2-qubit gates and the order (protocol) in which these are applied. The problem is mapped to a Markovian process and proved that there are large spectral equivalence classes. The optimal gate and the protocol that generates entanglement the fastest is identified. Relaxation towards the asymptotic thermal entanglement proceeds via a series of phase transitions in the local relaxation rate, which are a consequence of non-Hermiticity. In particular, non-Hermiticity can cause the rate to be either faster, or, even more interestingly, slower than predicted by the matrix gap. This is caused by a many-body explosion of expansion coefficients due to non-orthogonality which can result in a ‘phantom’ eigenvalue and could be of interest in other non-Hermitian settings.

* Jaš Bensa, University of Ljubljana

The seminar will be online via Zoom (ID: 281 621 2459, Password: 667124)

https://uni-lj-si.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09

The recent decade has witnessed several breakthroughs in the description of relaxation of local observables in quantum many-body systems prepared far from equilibrium. In contrast, the time evolution on time scales that precede relaxation towards the stationary state  has remained much less explored. Strong coupling expansions offer a good starting point for investigation of such problems, since they provide  a natural time scale, on which prerelaxation can occur. I will discuss the microscopic and ballistic-scale mesoscopic dynamics, described by the effective Hamiltonian that arises in the large-coupling limit of the anisotropic Heisenberg spin-1/2 chain. In particular, I will revisit the ballistic scale
hydrodynamics emerging after a sudden junction of two thermal or chemical reservoirs. In its framework, the nonselective emergence of discontinuities  in the profiles of local observables suggests inherent nonballistic behaviour.

* Lenart Zadnik, Universite Paris-Saclay

The seminar will be online via Zoom (ID: 281 621 2459, Password: 667124)

https://uni-lj-si.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09

Open quantum systems are ubiquitous in the contexts of atomic and molecular physics, circuit QED and optomechanics. Couplings to an environment can also have very interesting effects on the dynamics of many-particle quantum systems. In order to arrive at a tractable description of such problems, it is customary to work within the Markovian approximation with the dynamics averaged over the environment, whereby the system is described by a Lindblad master equation. While much progress has been made in analysing Lindblad equations for many-particle systems by employing, for example, perturbative and matrix product states methods, it is clearly highly desirable to have exact solutions in specific, and hopefully representative, cases. This talk aims to show that for a number of interacting open quantum systems, it is possible to obtain exact analytic solutions through a connection with integrable models. I will describe how a correspondence between a Lindblad equation and an integrable Hamiltonian can be established and what information about the open systems it provides. In particular, I will discuss the equivalence in structure of generalised Hubbard models and vectorised Lindblad equations, which are already visible in the R-matrix of the integrable model. I will also mention how this construction can be extended by focusing purely on the integrability of the invariant subspaces of the Lindblad equations. The talk is based on the work presented in SciPost Phys. 8, 044 (2020) (doi: 10.21468/SciPostPhys.8.3.044).

* Aleksandra Ziołkowska, Rudolf Peierls Centre for Theoretical Physics | St. John’s College, University of Oxford

The seminar will be online via Zoom (ID: 281 621 2459, Password: 667124)

https://uni-lj-si.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09

Local quantum circuits have become an important paradigm of many-body physics as, in particular, they allow for the simulation of  complex quantum systems in emerging quantum computing facilities. While much is already known about unitary and projective-measurement circuits, it is also of interest to extend their study to open and nonequilibrium quantum setups. With this goal, we consider quantum circuits in the Kraus map representation of completely positive quantum dynamics and discuss the first exactly-solvable, yet strongly-interacting, non-unitary open quantum circuit. On the analytical side, we prove integrability by constructing an inhomogeneous transfer matrix generating conserved super-operator charges, show that the circuit is completely positive and trace-preserving, and identify regimes of integrability-breaking. From the numerical point of view, the study of dissipative chaos and integrability requires the generalization of the standard signatures of quantum chaos; we will introduce complex spacing ratios and show that they allow us to confirm all our analytical results.

BASED ON: L. Sá, P. Ribeiro, and T. Prosen, PRX 10,021019 (2020)
[arXiv:1910.12784] L. Sá, P. Ribeiro, and T. Prosen, arXiv:2011.06565

* Lucas Sa, University of Lisbon

The seminar will be online via Zoom (ID: 281 621 2459, Password: 667124)

https://uni-lj-si.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09

The investigation of nonequilibrium properties of models with many degrees of freedom is a formidable analytical challenge that has recently aroused renewed interest. While many free theories display ballistic behaviour, generic interacting theories give rise to diffusive behaviour, a first-principles derivation of which remains elusive. Further, the role of space-time and internal symmetries in determining transport properties remains unsettled. With these questions in mind I will discuss some recent work on the classification of dynamical correlators in generic (chaotic) theories with non-abelian symmetry, starting with a minimal example. A non-zero density of the Noether charge generated by the non-abelian symmetry breaks the full symmetry of the state and gives rise to several distinct sectors. One of the sectors displays a novel undulating transport law that combines the diffusive and Goldstone modes generated by the broken symmetry. I will also touch upon the interaction of distinct Goldstone modes in higher rank models.

* Žiga Krajnik, University of Ljubljana

The seminar will be online via Zoom (ID: 281 621 2459, Password: 667124)

https://uni-lj-si.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09

Emergence of anomalous transport laws in deterministic interacting many-body systems has become a subject of intense study in the past few years, a prominent example of which is the unexpected discovery of superdiffusive spin dynamics in the isotropic Heisenberg quantum spin chain, conjectured to belong to the Kardar-Parisi-Zhang universality class. In this seminar, we will argue and theoretically justify why the observed anomalous transport of the Noether charges with fractional dynamical exponent z=3/2 is superuniversal, namely a feature of all integrable interacting lattice models (and even quantum field theories) which exhibit global symmetry of simple Lie group G (in ensembles that fully preserve group invariance). The phenomenon can be attributed to thermally dressed giant quasiparticles, whose properties can be traced back to fusion relations among characters of certain quantum groups called Yangians.

* Enej Ilievski, University of Ljubljana

The seminar will be online via Zoom (ID: 281 621 2459, Password: 667124)

https://uni-lj-si.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09

We will discuss the effective Hamiltonian that generates time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, such an effective Hamiltonian describes an integrable model with local interactions. I will present a full coordinate Bethe Ansatz solution that manifestly breaks the translational symmetry of the model, and describe its quasi-particle content. The corresponding Bethe equations are completely solvable, allowing for exact characterisation of degeneracies, as well as specification of a generic (thermodynamically relevant) state. I will also discuss jammed states and their stability under the leading correction to the effective Hamiltonian. Finally, if time permits, I will also visit the subjects of Thermodynamic Bethe Ansatz and Generalised Hydrodynamics.

* Lenart Zadnik, Universite Paris-Saclay

Program:

Organizers:

Fabian Heidrich-Meisner (Georg-August-Universität Göttingen)

Tomaz Prosen (University of Ljubljana)

I will discuss the dynamics of operator space entanglement entropy (OSEE) in integrable models. In particular, I will focus on the rule 54 chain and the XXZ chain, discussing the relationship between OSEE and diffusion. I will discuss the bound 1/2ln(t) for the OSEE of some
simple, i.e., low-rank, diagonal local operators. I will  provide numerical evidence that the bound is saturated in the rule 54 chain, and, remarkably, in the spin-1/2 Heisenberg XXZ chain.  Finally, I will focus on the effect of integrability breaking, showing that strong finite-time effects are present in generic systems, which prevent from probing the asymptotic behavior of the OSEE.

* Vincenzo Alba, University of Amsterdam

The seminar will be online via Zoom (ID: 973 3107 0547, Password: 808995)

https://fmf-uni-lj-si.zoom.us/j/99208844366?pwd=Mm9Xa3F1Nzl6emExNEZ6UGpqTEFiUT09

Integrable models possess infinite families of conserved charges. The current operators that describe the flow of these charges play a special role in the non-equilibrium dynamics of these systems. It was known since beginning of the 80’s that in spin chains the charge operators can be constructed using the Quantum Inverse Scattering Method (QISM), pioneered by the Leningrad group. In this talk we show that the current operators can also be constructed within the QISM, using standard tools of Yang-Baxter integrability. This leads to a simple derivation of their mean values, important for Generalized Hydrodynamics. The construction is rather general, it applies to ,,all” local spin chains. We also discuss connections to the theory of factorized correlation functions, and to AdS/CFT through the long range deformed models.

* Balazs Pozsgay, Budapest University of Technology and Economics (BME)

The seminar will be online via Zoom (ID: 992 0884 4366, Password: 968128)

https://fmf-uni-lj-si.zoom.us/j/99208844366?pwd=Mm9Xa3F1Nzl6emExNEZ6UGpqTEFiUT09