Stark many-body localized (SMBL) systems have been shown both numerically and experimentally to have Bloch many-body oscillations, quantum many-body scars, and fragmentation in the large field tilt limit. Likewise, they are believed to show localization similar to disordered MBL. I will discuss how all of these observations can be analytically understood by rigorously showing the existence of novel algebraic structures that are exponentially stable in time in the large tilt limit. I call this novel operators dynamical l-bits. Moreover, I show that many-body Bloch oscillations persist even at infinite temperature for exponentially long-times. I provide numerical confirmation of these results by studying the prototypical Stark MBL model of a tilted XXZ spin chain. The work explains why thermalization was observed in a recent 2D tilted experiment. As dynamical l-bits are stable, localized and quantum coherent excitations, the work opens new possibilities for quantum information processing in Stark MBL systems.
Reference:
T. Gunawardana, B. Buča. Dynamical l-bits in Stark many-body localization. arXiv:2110.13135 (2021)
* Berislav Buča, University of Oxford
The seminar will be held online via Zoom (ID: 281 621 2459, Password: 667124)
https://uni-lj-si.zoom.us/j/2816212459
We present some solutions of the set-theoretic parametric Yang-Baxter equation. These solutions are birational maps with several invariants and a Lax representation[4]. We show that we can use these maps as building blocks in order to construct higher dimensional birational maps which have nice properties and we prove their integrability in the Liouville sense. These maps can be seen as higher dimensional generalisations of the famous integrable QRT maps [3], known as Adler’s Triad maps[1]. Finally, we discuss some new generalisations [2].
* Georgios Papamikos, University of Essex
The seminar will be held online via Zoom (ID: 281 621 2459, Password: 667124)
https://uni-lj-si.zoom.us/j/2816212459
References
[1]V. E. Adler, On a class of third order mappings with two rational invariants, preprint, arXiv:nlin/0606056v1
[2] S. Konstantinou-Rizos, G.Papamikos, Entwining Yang-Baxter maps related to NLS type equations, Journal of Physics A: Mathematical and Theoretical, 52, 2019
[3] G. R. W. Quispel, J. A. G. Roberts, C. J. Thompson, Integrable mappings and soliton equations II, Physica D: Nonlinear Phenomena34(1989), 183-192.
[4] A. P. Veselov, Yang-Baxter maps and integrable dynamics, Physics Letters A314 (2003), 214 – 221.
Studies of disordered spin chains have recently experienced a renewed interest, inspired by the question to which extent the exact numerical calculations comply with the existence of a many-body localization phase transition. For the paradigmatic random field Heisenberg spin chains, many intriguing features were observed when the disorder is considerable compared to the spin interaction strength. Here, we introduce a phenomenological theory that may explain some of those features [1]. The theory is based on the proximity to the noninteracting limit, in which the system is an Anderson insulator. Taking the spin imbalance as an exemplary observable, we demonstrate that the proximity to the local integrals of motion of the Anderson insulator determines the dynamics of the observable at infinite temperature. In finite interacting systems our theory quantitatively describes its integrated spectral function for a wide range of disorders.
[1] Vidmar, Krajewski, Bonča, Mierzejewski, arXiv:2105.09336 (PRL, in press)
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