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).

Žiga Krajnik: (Integrable) G-invariant Matrix Models in Discrete Space-Time

We define and study an integrable G-invariant dynamics of a field subject to a nonlinear constraint on a 1+1 dimensional discrete space-time lattice. The model allows for efficient numerical simulations, which suggest superdiffusion and Kardar-Parisi-Zhang physics in the entire family of models (arXiv:2003.05957). Further, I will present some recent results on extending the model onto other symmetric spaces and more general symmetry groups. Lastly I will discuss a recent surprising observation of conic sections in the correlation tensor of (non)-integrable G-invariant models of Landau-Lifshitz type.

* Žiga Krajnik, FMF, Ljubljana

The seminar will be online via Zoom (ID: 969 2016 1126, Password: 432541).

Katja Klobas: Rule 54 reversible cellular automaton: recent progress

Rule 54 reversible cellular automaton (RCA54) is a 1-dim lattice model of solitons that move with fixed velocities and undergo nontrivial scattering. In the past years, numerous exact results have been found, ranging from the exact non-equilibrium steady state and exact large deviation treatment of the boundary driven setup to the matrix product form of time evolution of local observables. In the talk I will discuss recent progress. In particular I will present the matrix product form of multi-time correlation functions (arXiv:1912.09742) and the formulation of space-like evolution of such time-states (arXiv:2004.01671).

* Katja Klobas, FMF, Ljubljana

The seminar will be online at https://zoom.us/j/483251248
Meeting ID: 483 251 248

Sašo Grozdanov: From hydrodynamics to quantum chaos

Thursday 5.3.2020, 11:15h in Kuščerjev seminar, Jadranska 19.

Hydrodynamics is a theory of the collective properties of fluids and gases that can also be successfully applied to the description of the dynamics of quark-gluon plasma. It is an effective field theory formulated in terms of an infinite-order gradient expansion. For any collective physical mode, hydrodynamics will predict a dispersion relation that expresses this mode’s frequency in terms of an infinite series in powers of momentum. By using the theory of complex spectral curves from the mathematical field of algebraic geometry, I will describe how these dispersion relations can be understood as Puiseux series in (fractional powers of) complex momentum. The series have finite radii of convergence determined by the critical points of the associated spectral curves. For theories that admit a dual gravitational description through holography (AdS/CFT), the critical points correspond to level-crossings in the quasinormal spectrum of a dual black hole. Interestingly, holography implies that the convergence radii can be orders of magnitude larger than what may be naively expected. This fact could help explain the “unreasonable effectiveness of hydrodynamics” in describing the evolution of quark-gluon plasma. In the second part of my talk, I will discuss a recently discovered phenomenon called “pole-skipping” that relates hydrodynamics to the underlying microscopic quantum many-body chaos. This new and special property of quantum correlation functions allows for a precise analytic connection between resummed, all-order hydrodynamics and the properties of quantum chaos (the Lyapunov exponent and the butterfly velocity).

* Sašo Grozdanov, FMF, Ljubljana