Tuesday **20.7.2021, 14:15h** in Kuščerjev seminar, Jadranska 19.

In low dimensional systems heat can propagate faster than diffusion. This leads to a thermal conductivity that diverges with system size pointing to a superdiffusive transport. This leads to the question, if there is an equivalent of the heat equation which can be used to study superdiffusive transport in low dimensional systems. In this talk, I will discuss two simplified models where we establish a Fractional equation description for anomalous heat transport.

***** Aritra Kundu*, SISSA, Trieste*

Tuesday **8.6.2021, 14:15h** in Kuščerjev seminar, Jadranska 19.

We compute the Floquet Hamiltonian H_F for weakly interacting fermions subjected to a continuous periodic drive using a Floquet perturbation theory (FPT) with the interaction amplitude being the perturbation parameter. This allows us to address the dynamics of the system at intermediate drive frequencies ~ω_D ≥ V_0 J_0 , where J_0 is the amplitude of the kinetic term, ω_D is the drive frequency, and V_0 is the typical interaction strength between the fermions. We compute, for random initial states, the fidelity F between wavefunctions after a drive cycle obtained using H_F and that obtained using exact diagonalization (ED). We find that FPT yields a substantially larger value of F compared to its Magnus counterpart for V_0 ≤ ~ω_D and V_0 J_0 . We use the H_F obtained to study the nature of the steady state of a weakly interacting fermion chain; we find a wide range of ω_D which leads to subthermal or superthermal steady states for finite chains. The driven fermionic chain displays perfect dynamical localization for V_0 = 0; we address the fate of this dynamical localization in the steady state of a finite interacting chain and show that there is a crossover between localized and delocalized steady states. We discuss the implication of our results for thermodynamically large chains.

Journal Ref:- Phys. Rev. B 102, 235114 – Published 4 December 2020

***** Roopayan Ghosh*, University of Ljubljana*

Tuesday **1.6.2021, 15:15h** in Kuščerjev seminar, Jadranska 19.

We apply the inverse scattering method to the sine-Gordon model in discrete space-time. Building on the results of integrability we formulate two complementary approaches to the thermodynamics of the model based on two distinct sets of canonical variables.

***** Žiga Krajnik*, University of Ljubljana*

Tuesday **18.5.2021, 15:15h** in Kuščerjev seminar, Jadranska 19.

We apply the inverse scattering method to the sine-Gordon model in discrete space-time. Building on the results of integrability we formulate two complementary approaches to the thermodynamics of the model based on two distinct sets of canonical variables.

***** Žiga Krajnik*, University of Ljubljana*

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