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Thermalization from quantum entanglement: jet simulations in the massive Schwinger model
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We investigate the emergence of thermalization in a quantum field-theoretic model mimicking the production of jets in QCD -- the massive Schwinger model coupled to external sources. Specifically, we compute the expectation values of local operators as functions of time and compare them to their thermal counterparts, quantify the overlap between the evolving density matrix and the thermal one, and compare the dynamics of the energy-momentum tensor to predictions from relativistic hydrodynamics. Through these studies, we find that the system approaches thermalization at late times and elucidate the mechanisms by which quantum entanglement drives thermalization in closed field-theoretic systems. Our results show how thermodynamic behavior emerges in real time from unitary quantum dynamics.
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Deep inelastic scattering as a probe of entanglement: the complete QCD dipole cascade
The Shannon entropy of dipole multiplicities from the full Levin–Lublinsky equation in DIS reproduces the H1 hadron entropy, growing linearly with ln(1/x) and described by S = ln(2/3⟨n⟩) + 0.85.
Reference graph
Works this paper leans on
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Exact diagonalization Thermal expectation values of local operators can be obtained in the lattice Schwinger model using different Hamiltonian approaches. For sufficiently small systems, the exact spectrum of the Hamiltonian can be obtained using exact diagonalization: H|E n⟩=E n|En⟩.(B1) Note that here we discuss thermal properties of the Schwinger model...
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We use the purification method to extract thermal expectation values of local observables [34–36]
Purification and MPS In order to address the finite volume issue we perform finite temperature tensor network simulations for larger system sizes. We use the purification method to extract thermal expectation values of local observables [34–36]. A thermal system is described in terms of a density ma- trix rather than a state vector. In the tensor network ...
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Construct the outer product Ψ A aαΨA∗ βb
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SGibbs / N T [Ms] m/ g 0.5 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.0 0.1 0.2 0.3 0.4 0.5 0.6 1 / N SGibbs / N T=0.2/a T=0.3/a T=0.4/a T=0.5/a T=0.7/a T=1/a FIG
0.2 0.4 0.6 0.8 1. SGibbs / N T [Ms] m/ g 0.5 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.140.0 0.1 0.2 0.3 0.4 0.5 0.6 1 / N SGibbs / N T=0.2/a T=0.3/a T=0.4/a T=0.5/a T=0.7/a T=1/a FIG. 12. Top panel: Gibbs entropy density for different values of the system sizeNas a function of temperature obtained with exact diagonalization as explained in the main text. Bo...
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freeze-out time
described in terms of a reduced density matrixρ A. We measure the distance of this reduced density matrix to thermal states, characterized by density matricesρ β, and determine a temperature by selecting the thermal state closest toρ A. To measure the proximity ofρ A and ρβ, different metrics can be used [46]. Two prominent measures of the distance betwee...
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1.2 -6 -5 -4 -3 T [Ms] log10 error FIG
0.2 0.4 0.6 0.8 1. 1.2 -6 -5 -4 -3 T [Ms] log10 error FIG. 14. Local observables (chiral condensate ¯ψψ, kinetic en- ergy densityKand condensate-condensate correlation func- tion ¯ψψ ¯ψψ) obtained with exact diagonalization (ED) and the purification algorithm realized with tensor network methods (TN) shown as a function of temperature. Inset: logarithm of...
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0.5 1. 1.50. 0.2 0.4 0.6 0.8 1. 1.2 1/N2 Ms(N)- Ms(∞) [1/a] m= 10-3 10-2 FIG. 16. Masses of the first excited states shown for a variety of fermion mass valuesmas functions of the inverse square of the system sizeN. Linear fits for infinite volume extrapola- tion are shown in dashed lines. Infinite volume extrapolated values are subtracted. Fermion coup...
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This achieves that all the tensors to the left/right ofAare in left/right canonical form; this is illus- trated by drawing diamonds for the tensors outside ofA
Select a subregionAand choose the center of or- thogonality of the MPS to lie within this subregion. This achieves that all the tensors to the left/right ofAare in left/right canonical form; this is illus- trated by drawing diamonds for the tensors outside ofA
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