Many-body chaos near a thermal phase transition

Published on Aug 19, 2019
· DOI :10.21468/SCIPOSTPHYS.7.2.022
Alexander Schuckert5
Estimated H-index: 5
(TUM: Technische Universität München),
Michael Knap36
Estimated H-index: 36
(TUM: Technische Universität München)
Sources
Abstract
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 fluctuation parameter. OTOCs spread ballistically in all regimes, also at the thermal phase transition, where the butterfly velocity is maximal. Our work contributes to the understanding of the relation between quantum and classical many-body chaos and our method can be applied to other field theories dominated by classical modes at long wavelengths.
References73
Newest
#1Asier Piñeiro Orioli (CU: University of Colorado Boulder)H-Index: 6
#2Jürgen Berges (Heidelberg University)H-Index: 30
Universal phenomena far from equilibrium exhibit additional independent scaling exponents and functions as compared to thermal universal behavior. For the example of an ultracold Bose gas we simulate nonequilibrium transport processes in a universal scaling regime and show how they lead to the breaking of the fluctuation-dissipation relation. As a consequence, the scaling of spectral functions (commutators) and statistical correlations (anti-commutators) between different points in time and spac...
Source
Last. Ana Maria ReyH-Index: 62
view all 4 authors...
Scrambling of quantum information is the process by which information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom, becoming inaccessible to local probes and thus apparently lost. Scrambling and entanglement are key concepts reconciling seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes, and have revolutionized our understanding of non-equilibrium ph...
Source
We propose a method of estimating ergodization time of a chaotic many-particle system by monitoring equilibrium noise before and after time reversal of dynamics (Loschmidt echo). The ergodization time is defined as the characteristic time required to extract the largest Lyapunov exponent from a system's dynamics. We validate the method by numerical simulation of an array of coupled Bose-Einstein condensates in the regime describable by the discrete Gross-Pitaevskii equation. The quantity of inte...
Source
#1Michael Knap (TUM: Technische Universität München)H-Index: 36
We study theoretically entanglement and operator growth in a spin system coupled to an environment, which is modeled with classical dephasing noise. Using exact numerical simulations we show that the entanglement growth and its fluctuations are described by the Kardar-Parisi-Zhang equation. Moreover, we find that the wavefront in the out-of-time ordered correlator (OTOC), which is a measure for the operator growth, propagates linearly with the butterfly velocity and broadens diffusively with a d...
Source
#1Amos Chan (University of Oxford)H-Index: 7
#2Andrea De Luca (University of Oxford)H-Index: 27
Last. J. T. Chalker (University of Oxford)H-Index: 48
view all 3 authors...
We solve a minimal model for an ergodic phase in a spatially extended quantum many-body system. The model consists of a chain of sites with nearest-neighbor coupling under Floquet time evolution. Quantum states at each site span a q-dimensional Hilbert space, and time evolution for a pair of sites is generated by a q2 × q2 random unitary matrix. The Floquet operator is specified by a quantum circuit of depth two, in which each site is coupled to its neighbor on one side during the first half of ...
Source
#1Josef RammenseeH-Index: 1
#2Juan Diego UrbinaH-Index: 15
Last. Klaus RichterH-Index: 60
view all 3 authors...
Out-of-time-order correlators (OTOCs) have been proposed as sensitive probes for chaos in interacting quantum systems. They exhibit a characteristic classical exponential growth, but saturate beyond the so-called scrambling or Ehrenfest time τE in the quantum correlated regime. Here we present a path-integral approach for the entire time evolution of OTOCs for bosonic N-particle systems. We first show how the growth of OTOCs up to τE=(1/λ)logN is related to the Lyapunov exponent λ of the corresp...
Source
Last. Ana Maria ReyH-Index: 62
view all 4 authors...
Scrambling of quantum information is the process by which information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom, becoming inaccessible to local probes and thus apparently lost. Scrambling and entanglement are key concepts reconciling seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes, and have revolutionized our understanding of non-equilibrium ph...
Source
#1Thomas Bilitewski (MPG: Max Planck Society)H-Index: 8
#2Subhro Bhattacharjee (TIFR: Tata Institute of Fundamental Research)H-Index: 17
Last. Roderich Moessner (MPG: Max Planck Society)H-Index: 73
view all 3 authors...
We study the chaotic dynamics in a classical many-body system of interacting spins on the kagome lattice. We characterise many-body chaos via the butterfly effect as captured by an appropriate out-of-time-ordered correlator. Due to the emergence of a spin liquid phase, the chaotic dynamics extends all the way to zero temperature. We thus determine the full temperature dependence of two complementary aspects of the butterfly effect: the Lyapunov exponent, \mu and the butterfly speed, v_b an...
Source
#1Das A (TIFR: Tata Institute of Fundamental Research)H-Index: 17
#2Saurish Chakrabarty (TIFR: Tata Institute of Fundamental Research)H-Index: 10
Last. Subhro Bhattacharjee (TIFR: Tata Institute of Fundamental Research)H-Index: 17
view all 8 authors...
We find that localised perturbations in a chaotic classical many-body system-- the classical Heisenberg spin chain -- spread ballistically with a finite speed and little change in form as a function of distance from the origin of the perturbation even when the local spin dynamics is diffusive. We study this phenomenon by shedding light on the two complementary aspects of this butterfly effect-- the rapid growth of perturbations and its simultaneous ballistic (light-cone) spread, as characterised...
Source
#1C. W. von Keyserlingk (University of Birmingham)H-Index: 12
#2Tibor Rakovszky (University of Birmingham)H-Index: 10
Last. Shivaji Lal Sondhi (Princeton University)H-Index: 60
view all 4 authors...
Thermalization and information scrambling can provide insight into fields as diverse as many-body quantum physics, quantum field theory, and holography. A new theoretical analysis of one-dimensional spin chains reveals details about how information moves and entanglement grows in such systems.
Source
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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 Lyapu...
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#1Sibaram RuidasH-Index: 1
#2Sumilan Banerjee (IISc: Indian Institute of Science)H-Index: 25
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...
#1Ben CrapsH-Index: 34
#2Marine De ClerckH-Index: 6
Last. Charles Rabideau (Vrije Universiteit Brussel)H-Index: 2
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The Ising spin chain with longitudinal and transverse magnetic fields is often used in studies of quantum chaos, displaying both chaotic and integrable regions in its parameter space. However, even at a strongly chaotic point this model does not exhibit Lyapunov growth of the commutator squared of spin operators, as this observable saturates before exponential growth can manifest itself (even in situations where a spatial suppression factor makes the initial commutator small). We extend this mod...
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We study the dynamics of a three-mode bosonic system with mode-changing interactions. For large mode occupations the short-time dynamics is well described by classical mean-field equations allowing us to study chaotic dynamics in the classical system and its signatures in the corresponding quantum dynamics. By introducing a symmetry-breaking term we tune the classical dynamics from integrable to strongly chaotic which we demonstrate by calculating Poincare sections and Lyapunov exponents. The co...
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