The eigenstate thermalization hypothesis provides to date the most successful description of thermalization in isolated quantum systems by conjecturing statistical properties of matrix elements of typical operators in the (quasi-)energy eigenbasis. Here we study the distribution of matrix elements for a class of operators in dual-unitary quantum circuits in dependence of the frequency associated with the corresponding eigenstates. We provide an exact asymptotic expression for the spectral function, i.e., the second moment of this frequency resolved distribution. The latter is obtained from the decay of dynamical correlations between local operators which can be computed exactly from the elementary building blocks of the dual-unitary circuits. Comparing the asymptotic expression with results obtained by exact diagonalization we find excellent agreement. Small fluctuations at finite system size are explicitly related to dynamical correlations at intermediate times and the deviations from their asymptotical dynamics. Moreover, we confirm the expected Gaussian distribution of the matrix elements by computing higher moments numerically.
* Felix Fritzsch, 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
Using continued fractions and recurrence relations for the corresponding convergents we derive an expression for the reservoir self-energy which enables numerical simulation of the semi-infinite generalized Aubry-André-Harper (AAH) model with finite periodicity within the Green’s functions formalism. To demonstrate the effectiveness of the derived expression we compute the local and total density of states, density per lattice site, and examine the existence of a phase transition using Inverse Participation Ratio (IPR) in the thermodynamic limit. Furthermore, we discuss the possibility of the identification of topological regimes within the periodic hopping lattice models using the exact reservoir self-energy expression.’
* Jovan Odavić, Institut Ruđer Bošković, Zagreb
The seminar will be online via Zoom (ID: 281 621 2459, Password: 667124)
https://uni-lj-si.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09
Bounds on transport represent a way of understanding allowable regimes of quantum and classical dynamics. Numerous such bounds have been proposed, either for classes of theories or (by using general arguments) universally for all theories. Few are exact and inviolable. I will present a new set of methods and sufficient conditions for deriving exact, rigorous, and sharp bounds on all coefficients of hydrodynamic dispersion relations, including diffusivity and the speed of sound. These general techniques combine analytic properties of hydrodynamics and the theory of univalent (complex holomorphic and injective) functions. Particular attention will be devoted to bounds relating transport to quantum chaos, which can be established through pole-skipping in theories with holographic duals. I will also discuss potential applications of univalence methods to bounds without relation to chaos, such as for example the conformal bound on the speed of sound.
* Sašo Grozdanov, 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 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