We study correlations, transport and chaos in a Heisenberg magnet as a classical model many-body system. By varying temperature and dimensionality, we can tune between settings with and without symmetry breaking and accompanying collective modes or quasiparticles. We analyse both conventional and out-of-time-ordered spin correlators (`decorrelators') to track the spreading of a spatiotemporally localised perturbation -- the wingbeat of the butterfly -- as well as transport coefficients and Lyapunov exponents. We identify a number of qualitatively different regimes. Trivially, at T=0 there is no dynamics at all. In the limit of low temperature, T=0^+ integrability emerges, with infinitely long-lived magnons; here the wavepacket created by the perturbation propagates ballistically, yielding a lightcone at the spin wave velocity which thus subsumes the butterfly velocity; inside the lightcone, a pattern characteristic of the free spin wave spectrum is visible at short times. On top of this, residual interactionslead to spin wave lifetimes which, while divergent in this limit, remain finite at any nonzero T At the longest times, this leads to a `standard' chaotic regime; for this regime, we show that the Lyapunov exponent is simply proportional to the inverse spin-wave lifetime. Visibly strikingly, between this and the `short-time' integrable regimes, a scarred regime emerges: here, the decorrelator is spatiotemporally highly non-uniform, being dominated by rare and random scattering events seeding secondary lightcones. As the spin correlation length decreases with increasing T the distinction between these regimes disappears and at high temperature the previously studied chaotic paramagnetic regime emerges. For this, we elucidate how, somewhat counterintuitively, the ballistic butterfly velocity arises from a diffusive spin dynamics.
#2Sumilan Banerjee(IISc: Indian Institute of Science)H-Index: 19
Chaos, the sensitivity to initial conditions, is an important tool to classify intermediate-time behaviour of classical dynamical systems. On the other hand, the long-time dynamical properties of interacting many-body systems, in symmetry broken and unbroken phases, and across phase transitions, are often characterized by the properties of the collective low-energy excitations, hydrodynamic and critical modes. How are the short-time chaotic properties of classical many-body systems related to th...
#1Das A(TIFR: Tata Institute of Fundamental Research)H-Index: 1
#2Kedar Damle(TIFR: Tata Institute of Fundamental Research)H-Index: 21
Last. Herbert Spohn(TUM: Technische Universität München)H-Index: 87
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Using the framework of nonlinear fluctuating hydrodynamics (NFH), we examine equilibrium spatio-temporal correlations in classical ferromagnetic spin chains with nearest neighbor interactions. In particular, we consider the classical XXZ-Heisenberg spin chain (also known as Lattice Landau–Lifshitz or LLL model) evolving deterministically and chaotically via Hamiltonian dynamics, for which energy and z-magnetization are the only locally conserved fields. For the easy-plane case, this system has a...
We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids to fast scramblers. The analytic calculation, controlled by a small coupling constant and large N allows us to clarify the relations between the quasi-particle relaxation rate 1/\tauand the Lyapunov exponent \lambda_Lcharacterizing scrambling. In the Fermi liquid s...
Over the last decade, systems of individually-controlled neutral atoms, interacting with each other when excited to Rydberg states, have emerged as a promising platform for quantum simulation of many-body problems, in particular spin systems. Here, we review the techniques underlying quantum gas microscopes and arrays of optical tweezers used in these experiments, explain how the different types of interactions between Rydberg atoms allow a natural mapping onto various quantum spin models, and d...
We study chaos in a classical limit of the Sachdev-Ye-Kitaev (SYK) model obtained in a suitably defined large-S limit. The low-temperature Lyapunov exponent is found to depend linearly on temperature, with a slope that is parametrically different than in the quantum case: it is proportional to N/S. The classical dynamics can be understood as the rotation of an N-dimensional body with a random inertia tensor, corresponding to the random couplings of the SYK Hamiltonian. This allows us to find an ...
#2Michael Knap(TUM: Technische Universität München)H-Index: 34
We study many-body chaos in a (2+1)D relativistic scalar field theory at high temperatures in the classical statistical approximation, which captures the quantum critical regime and the thermal phase transition from an ordered to a disordered phase. We evaluate out-of-time ordered correlation functions (OTOCs) and find that the associated Lyapunov exponent increases linearly with temperature in the quantum critical regime, and approaches the non-interacting limit algebraically in terms of a fluc...
We use a new measure of many-body chaos for classical systems---cross-correlators---to show that in a thermalised fluid (obtained from a non-linear, prototypical equation of hydrodynamics sharing formal similarities with models of turbulence) characterised by a temperature Tand N_Gdegrees of freedom, the Lyapunov exponent \lambdascales as N_G\sqrt{T} This bound, obtained from detailed numerical simulations and theoretical estimates, provides compelling evidence not only for recent co...
We study the scrambling of local quantum information in chaotic many-body systems in the presence of a locally conserved quantity like charge or energy that moves diffusively. The interplay between conservation laws and scrambling sheds light on the mechanism by which unitary quantum dynamics, which is reversible, gives rise to diffusive hydrodynamics, which is a dissipative process. We obtain our results in a random quantum circuit model that is constrained to have a conservation law. We find t...
Last. Johannes Knolle(TUM: Technische Universität München)H-Index: 29
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We provide a comprehensive account of prethermal discrete time crystals within classical Hamiltonian dynamics, complementing and extending our recent work [Phys. Rev. Lett. 127, 140602 (2021)]. Considering power-law interacting spins on one-, two-, and three-dimensional hypercubic lattices, we investigate the interplay between dimensionality and interaction range in the stabilization of these non-equilibrium phases of matter that break the discrete time-translational symmetry of a periodic drive...
Last. Johannes Knolle(TUM: Technische Universität München)H-Index: 29
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Systems subject to a high-frequency drive can spend an exponentially long time in a prethermal regime, in which novel phases of matter with no equilibrium counterpart can be realized. Due to the notorious computational challenges of quantum many-body systems, numerical investigations in this direction have remained limited to one spatial dimension, in which long-range interactions have been proven a necessity. Here, we show that prethermal non-equilibrium phases of matter are not restricted to t...
The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimension. Here we study one of the simplest classical interacting lattice models, the nearest-neighbour Heisenberg chain, with temperature as tuning parameter. Our numerics expose strikingly different spin dynamics between the antiferromagnet, where it is largely diffusive, and the ferromagnet, where we observe strong evidence either of spin super-diffusion or an...
#2Sumilan Banerjee(IISc: Indian Institute of Science)H-Index: 19
Chaos, the sensitivity to initial conditions, is an important tool to classify intermediate-time behaviour of classical dynamical systems. On the other hand, the long-time dynamical properties of interacting many-body systems, in symmetry broken and unbroken phases, and across phase transitions, are often characterized by the properties of the collective low-energy excitations, hydrodynamic and critical modes. How are the short-time chaotic properties of classical many-body systems related to th...
We use a new measure of many-body chaos for classical systems---cross-correlators---to show that in a thermalised fluid (obtained from a non-linear, prototypical equation of hydrodynamics sharing formal similarities with models of turbulence) characterised by a temperature Tand N_Gdegrees of freedom, the Lyapunov exponent \lambdascales as N_G\sqrt{T} This bound, obtained from detailed numerical simulations and theoretical estimates, provides compelling evidence not only for recent co...
