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:
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11:45
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Access to Video Conference open
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12:00
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Welcome & Introduction
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12:15
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Frank Pollmann (TU Munich): Far-from-equilibrium dynamics of systems with conservation laws
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12:55
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Break
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13:20
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Robin Steinigeweg (University of Osnabrück): Tackling quantum many-body dynamics by typicality, numerical linked cluster expansions, and projection operator techniques
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14:00
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Lea Santos (Yeshiva University, N.Y.): Speck of Chaos in One-Dimensional Spin Models
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14:40
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Break
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15:00
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Ivana Dimitrova & Niklas Jespen (MIT): Spin transport in a tunable Heisenberg model realized with ultracold atoms
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16:00
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Break
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16:30
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Sarang Gopalakrishnan (CUNY N.Y.): Anomalous transport in integrable spin chains
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17:10
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Bruno Bertini (University of Ljubljana): Generalized hydrodynamics and universal aspects of one-dimensional transport at low temperatures
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17:50
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Break
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18:10
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Anatoli Polkovnikov (Boston University): Simulating transport in spin chains using cluster truncated Wigner approximation
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18:50
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Final comments
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Organizers:
Fabian Heidrich-Meisner (Georg-August-Universität 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., 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
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
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
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
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).
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).
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
Meeting ID: 483 251 248
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
Tuesday 3.3.2020, 13:15h in Kuščerjev seminar, Jadranska 19.
The Luttinger model with finite-range interactions is an exactly solvable model in 1+1 dimensions somewhere between conformal and Bethe-ansatz integrable ones. I will show how exact analytical results can be computed for the time evolution of this non-local Luttinger model following an inhomogeneous quench from initial states defined by smooth temperature and chemical-potential profiles. These results demonstrate that the finite-range interactions give rise to dispersive effects that are not present in the conformal case of point-like interactions. Combing the same methods with the recent proposal of generalized hydrodynamics, one finds that this model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. These results are shown to emerge from the exact analytical ones at the relevant time and length scales. As such, the non-local Luttinger model provides a simple tractable example to analytically study the emergence of hydrodynamics in a quantum many-body system.
* Per Moosavi, ETH, Zurich