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Register a new userParticle level screening of scalar forces in 1+1 dimensions
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We investigate how non-linear scalar field theories respond to point sources. Taking the symmetron as a specific example of such a theory, we solve the non-linear equation of motion in one spatial dimension for (i) an isolated point source and (ii) two identical point sources with arbitrary separation. We find that the mass of a single point source can be screened by the symmetron field, provided that its mass is above a critical value. We find that two point sources behave as independent, isolated sources when the separation between them is large, but, when their separation is smaller than the symmetrons Compton wavelength, they behave much like a single point source with the same total mass. Finally, we explore closely related behavior in a toy Higgs-Yukawa model, and find indications that the maximum fermion mass that can be generated consistently via a Yukawa coupling to the Higgs in 1+1 dimensions is roughly the mass of the Higgs itself, with potentially intriguing implications for the hierarchy problem.
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We study three different measures of quantum correlations -- entanglement spectrum, entanglement entropy, and logarithmic negativity -- for (1+1)-dimensional massive scalar field in flat spacetime. The entanglement spectrum for the discretized scalar field in the ground state indicates a cross-over in the zero-mode regime, which is further substantiated by an analytical treatment of both entanglement entropy and logarithmic negativity. The exact nature of this cross-over depends on the boundary conditions used -- the leading order term switches from a $log$ to $log-log$ behavior for the Periodic and Neumann boundary conditions. In contrast, for Dirichlet, it is the parameters within the leading $log-log$ term that are switched. We show that this cross-over manifests as a change in the behavior of the leading order divergent term for entanglement entropy and logarithmic negativity close to the zero-mode limit. We thus show that the two regimes have fundamentally different information content. Furthermore, an analysis of the ground state fidelity shows us that the region between critical point $Lambda=0$ and the crossover point is dominated by zero-mode effects, featuring an explicit dependence on the IR cutoff of the system. For the reduced state of a single oscillator, we show that this cross-over occurs in the region $Nam_fsim mathscr{O}(1)$.
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