Lucas Sa: Chaos and integrability in non-unitary open quantum circuits

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

Žiga Krajnik: Undular diffusion

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

Enej Ilievski: Superuniversality of superdiffusion

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

Lenart Zadnik: Revisiting the large-anisotropy limit of the antiferromagnetic Heisenberg model

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

Workshop: Transport and emergence of hydrodynamics in 1d quantum-lattice models

Online Workshop

Transport and emergence of hydrodynamics in 1d quantum-lattice 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 break-out rooms for small-group 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): Far-from-equilibrium dynamics of systems with conservation laws

12:55

Break

13:20

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

14:00

Lea Santos (Yeshiva University, N.Y.): Speck of Chaos in One-Dimensional 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 one-dimensional 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 Heidrich-Meisner (Georg-August-Universität Göttingen)

Tomaz Prosen (University of Ljubljana)

Vincenzo Alba: Diffusion and operator entanglement spreading

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

Balazs Pozsgay: Algebraic construction of current operators in integrable spin chains

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

Berislav Buča: Non-stationary quantum many-body dynamics and synchronization

The assumption that quantum systems relax to a stationary (time-independent) state in the long-time 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, real-world phenomena, from life to weather patterns are persistently non-stationary. We will discuss simple algebraic conditions that lead to a quantum many-body system never reaching a stationary state, not even a non-equilibrium 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, counter-intuitively, 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 many-body 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://fmf-uni-lj-si.zoom.us/j/93055285938?pwd=WHI5RW5aUlVRU3JYd2RLVHpFbjBhUT09

Marko Medenjak: Dissipative Bethe Ansatz: Exact Solutions of Quantum Many-Body Dynamics Under Loss

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 easy-axis 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

Anastasia Doikou: Set theoretic Yang-Baxter equation and quantum integrability

We examine novel links between the theory of braces and set theoretical solutions of the Yang-Baxter 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 set-theoretic solutions coming from braces and we also derive new classes of symmetries for the corresponding periodic transfer matrices.

* Anastasia Doikou, Heriot-Watt University, Edinburgh

The seminar will be online via Zoom (ID: 917 7027 2241, Password: 820642).