Abstract
One of the most interesting directions in theoretical high-energy and condensed-matter physics is understanding dynamical properties of collective states of quantum field theories. The most elementary tool in this quest is retarded equilibrium correlators governing the linear response theory. In this article we examine tensor networks as a way of determining them in a fully ab initio way in a class of (1+1)-dimensional quantum field theories arising as infrared descriptions of quantum Ising chains.We show that, complemented with signal analysis using the Prony method, tensor network calculations for intermediate times provide a powerful way to explore the structure of singularities of the correlator in the complex frequency plane and to make predictions about the thermal response to perturbations in a class of nonintegrable interacting quantum field theories.
Highlights
AND MOTIVATIONMuch of the progress in quantum field theory (QFT) to date has been driven by challenges posed by quantum chromodynamics (QCD)
In this article we explore the use of tensor networks (TNs) [19,20,21,22,23,24,25,26], in particular matrix product operator (MPO) methods, to study thermal retarded correlators in complexified frequency space
TN 1.6147(7) 1.962(1) 2.413(2) 2.936(3) 3.165(6) 3.52(3) E8 1.6180 1.9890 2.4049 2.9563 3.2183 3.891 contains stable and unstable bound states [27,28,29,31]. We study this regime at nonzero temperature numerically using MPO methods in combination with Prony analysis, which we review later
Summary
Much of the progress in quantum field theory (QFT) to date has been driven by challenges posed by quantum chromodynamics (QCD). One motivation behind this work comes from ultrarelativistic heavy-ion collisions, which probe collective states of QCD in a nonequilibrium setting [1] Important insights in this context have been gained by studying small perturbations of equilibrium in soluble models, such as holography or kinetic theory [2]. Linear response theory provides a natural point of departure to study real-time dynamics of QFTs and is the subject of the present article In this framework, the response of an equilibrium state to a (small) perturbation triggered by a source J coupled to an operator O is captured by the retarded thermal two-point correlator.
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