Out-of-horizon correlations following a quench in a relativistic quantum field theory
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Springer
Received: May 14, 2020 Accepted: June 15, 2020 Published: July 30, 2020
Out-of-horizon correlations following a quench in a relativistic quantum field theory
a
Max-Planck-Institute of Quantum Optics, Hans-Kopfermann-Str. 1, Garching DE-85748, Germany b Munich Center for Quantum Science and Technology, Schellingstr. 4, M¨ unchen DE-80799, Germany c University of Ljubljana, Faculty of Mathematics and Physics, Jadranska 19, Ljubljana SI-1000, Slovenia d BME “Momentum” Statistical Field Theory Research Group & BME Department of Theoretical Physics, Budapest H-1117, Budafoki u ´t 8, Hungary
E-mail: [email protected], [email protected], [email protected] Abstract: One of the manifestations of relativistic invariance in non-equilibrium quantum field theory is the “horizon effect” a.k.a. light-cone spreading of correlations: starting from an initially short-range correlated state, measurements of two observers at distant space-time points are expected to remain independent until their past light-cones overlap. Surprisingly, we find that in the presence of topological excitations correlations can develop outside of horizon and indeed even between infinitely distant points. We demonstrate this effect for a wide class of global quantum quenches to the sine-Gordon model. We point out that besides the maximum velocity bound implied by relativistic invariance, clustering of initial correlations is required to establish the “horizon effect”. We show that quenches in the sine-Gordon model have an interesting property: despite the fact that the initial states have exponentially decaying correlations and cluster in terms of the bosonic fields, they violate the clustering condition for the soliton fields, which is argued to be related to the non-trivial field topology. The nonlinear dynamics governed by the solitons makes the clustering violation manifest also in correlations of the local bosonic fields after the quench. Keywords: Boundary Quantum Field Theory, Field Theories in Lower Dimensions, Integrable Field Theories, Solitons Monopoles and Instantons ArXiv ePrint: 1906.02750
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)224
JHEP07(2020)224
I. Kukuljan,a,b S. Sotiriadisc and G. Tak´ acsd
Contents 2
2 A surprise: out-of-horizon spreading of correlations
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3 Analytical demonstration of the horizon violation
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4 Physical explanation of the effect
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5 Further properties of the horizon violation 5.1 Universal presence in quenches to the sine-Gordon model 5.2 Sensitivity to boundary conditions
10 10 10
6 Prospective realisation in ultra-cold atom experiments
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7 Conclusions
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A Horizon effect for free dynamics and local initial states
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B Details of the TCSA simulations
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C Analytical derivation of horizon violation in the SG model C.1 Fermionising the sine-Gordon model C.1.1 Equivalence of Hilbert spaces C.1.2 Bosonisation identities C.1.3 Sine-Gordon correlations at the free fermion point C.2 Computing the dynamics of correl
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