Local quantum circuits have become an important paradigm of manybody 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 projectivemeasurement 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 exactlysolvable, yet stronglyinteracting, nonunitary open quantum circuit. On the analytical side, we prove integrability by constructing an inhomogeneous transfer matrix generating conserved superoperator charges, show that the circuit is completely positive and tracepreserving, and identify regimes of integrabilitybreaking. 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://uniljsi.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 firstprinciples derivation of which remains elusive. Further, the role of spacetime 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 nonabelian symmetry, starting with a minimal example. A nonzero density of the Noether charge generated by the nonabelian 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://uniljsi.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09
Emergence of anomalous transport laws in deterministic interacting manybody 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 KardarParisiZhang 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://uniljsi.zoom.us/j/2816212459?pwd=UUs5MDdTNmVzRkorRmc3ZFNZTzVKQT09
We will discuss the effective Hamiltonian that generates time evolution of states on intermediate time scales in the strongcoupling limit of the spin1/2 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 quasiparticle 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 ParisSaclay
Online Workshop
Transport and emergence of hydrodynamics in 1d quantumlattice models
10. July 2020
Access details (Zoom) will be sent a couple of days before the meeting. The videoconference will start at 11:45am. During the breaks, we will have several breakout rooms for smallgroup discussions.
The event is open to all members of the invited speaker’s groups and other scientists interested in the topic. For all attendees other than the invited speakers: Please register via email, sent to Kati Oldenburg at kati.oldenburg@theorie.physik.unigoettingen.de, to make sure that we know who will be joining the Zoom video conference. Thank you!
Program:
11:45

Access to Video Conference open

12:00

Welcome & Introduction


12:15

Frank Pollmann (TU Munich): Farfromequilibrium dynamics of systems with conservation laws


12:55

Break


13:20

Robin Steinigeweg (University of Osnabrück): Tackling quantum manybody dynamics by typicality, numerical linked cluster expansions, and projection operator techniques

14:00

Lea Santos (Yeshiva University, N.Y.): Speck of Chaos in OneDimensional Spin Models

14:40

Break


15:00

Ivana Dimitrova & Niklas Jespen (MIT): Spin transport in a tunable Heisenberg model realized with ultracold atoms


16:00

Break


16:30

Sarang Gopalakrishnan (CUNY N.Y.): Anomalous transport in integrable spin chains


17:10

Bruno Bertini (University of Ljubljana): Generalized hydrodynamics and universal aspects of onedimensional transport at low temperatures


17:50

Break


18:10

Anatoli Polkovnikov (Boston University): Simulating transport in spin chains using cluster truncated Wigner approximation


18:50

Final comments


Organizers:
Fabian HeidrichMeisner (GeorgAugustUniversität 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., lowrank, diagonal local operators. I will provide numerical evidence that the bound is saturated in the rule 54 chain, and, remarkably, in the spin1/2 Heisenberg XXZ chain. Finally, I will focus on the effect of integrability breaking, showing that strong finitetime 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://fmfuniljsi.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 nonequilibrium 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 YangBaxter 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://fmfuniljsi.zoom.us/j/99208844366?pwd=Mm9Xa3F1Nzl6emExNEZ6UGpqTEFiUT09
The assumption that quantum systems relax to a stationary (timeindependent) state in the longtime limit underpins statistical physics and much of our intuitive understanding of scientific phenomena. For isolated systems this follows from the eigenstate thermalization hypothesis. When an environment is present the expectation is that all of phase space is explored, eventually leading to stationarity. However, realworld phenomena, from life to weather patterns are persistently nonstationary. We will discuss simple algebraic conditions that lead to a quantum manybody system never reaching a stationary state, not even a nonequilibrium one. This unusual state of matter characterized by persistent oscillations has been recently called a time crystal. We show that it’s existence can be, counterintuitively, induced through the dissipation itself. We further present necessary and sufficient conditions for the occurrence of persistent oscillations in an open quantum system. Finally, we also discuss how our framework allows for open quantum manybody system displaying complex dynamical behaviour, usually found in macroscopic classical systems, such as synchronization.
References:
B Buca, J Tindall, D Jaksch. Nat. Comms. 10 (1), 1730 (2019)
M Medenjak, B Buca, D Jaksch. arXiv:1905.08266 (2019)
B Buca, D Jaksch. Phys. Rev. Lett. 123, 260401 (2019)
J Tindall, B Buca, J R Coulthard, D Jaksch. Phys. Rev. Lett. 123, 030603 (2019)
J Tindall, C Sanchez Munoz, B Buca, D Jaksch. New J. Phys. 22 013026 (2020)
C Booker, B Buca, D Jaksch. arXiv:2005.05062 (2020)
* Berislav Buča, Department of Physics, University of Oxford
The seminar will be online via Zoom (ID: 930 5528 5938, Password: 373842)
https://fmfuniljsi.zoom.us/j/93055285938?pwd=WHI5RW5aUlVRU3JYd2RLVHpFbjBhUT09
I will discuss how to use Bethe Ansatz techniques for studying the properties of certain systems experiencing loss. First of all, I will describe the general approach to obtain the Liouvillian spectrum of a wide range of experimentally relevant models. This includes any integrable model with particle number conservation experiencing the single particle bulk loss throughout the system. Following the general discussion, I will address different aspects of the XXZ spin chain driven at the single boundary. In particular, I will consider the scaling of Liouvillian gap, the dynamical dissipative phase transition, and the physics of the boundary bound states. The existence of infinitely many boundary bound states translates into the formation of a stable domain wall in the easyaxis regime despite the presence of loss.
[1] B. Buca, C. Booker, M. Medenjak, D. Jaksch, arXiv:2004.05955
* Marko Medenjak, Institut de Physique Theorique Philippe Meyer, Ecole Normale Superieure, Paris
The seminar will be online via Zoom (ID: 925 5819 1511, Password: 669133)
https://zoom.us/j/92558191511?pwd=Q3hyL1N6S21SSHRpS0lURHkzMGVTdz09
We examine novel links between the theory of braces and set theoretical solutions of the YangBaxter equation, and fundamental concepts from the theory of quantum integrable systems. More precisely, we make connections with Hecke algebras, we identify quantum groups associated to settheoretic solutions coming from braces and we also derive new classes of symmetries for the corresponding periodic transfer matrices.
* Anastasia Doikou, HeriotWatt University, Edinburgh
The seminar will be online via Zoom (ID: 917 7027 2241, Password: 820642).