9,917 research outputs found

### Lessons from $T^{\mu}_{~ \mu}$ on inflation models: two-scalar theory and Yukawa theory

We demonstrate two properties of the trace of the energy-momentum tensor
$T^{\mu}_{~ \mu}$ in the flat spacetime. One is the decoupling of heavy degrees
of freedom; i.e., heavy degrees of freedom leave no effect for low-energy
$T^{\mu}_{~ \mu}$-inserted amplitudes. This is intuitively apparent from the
effective field theory point of view, but one has to take into account the
so-called trace anomaly to explicitly demonstrate the decoupling. As a result,
for example, in the $R^{2}$ inflation model, scalaron decay is insensitive to
heavy degrees of freedom when a matter sector ${\it minimally}$ couples to
gravity (up to a non-minimal coupling of a matter scalar field other than the
scalaron). The other property is a quantum contribution to a non-minimal
coupling of a scalar field. The non-minimal coupling disappears from the action
in the flat spacetime, but leaves the so-called improvement term in $T^{\mu}_{~
\mu}$. We study the renormalization group equation of the non-minimal coupling
to discuss its quantum-induced value and implications for inflation dynamics.
We work it out in the two-scalar theory and Yukawa theory.Comment: 18+9 pages, 5 figures; minor changes to match the version accepted in
PR

### Connecting global and local energy distributions in quantum spin models on a lattice

Generally, the local interactions in a many-body quantum spin system on a
lattice do not commute with each other. Consequently, the Hamiltonian of a
local region will generally not commute with that of the entire system, and so
the two cannot be measured simultaneously. The connection between the
probability distributions of measurement outcomes of the local and global
Hamiltonians will depend on the angles between the diagonalizing bases of these
two Hamiltonians. In this paper we characterize the relation between these two
distributions. On one hand, we upperbound the probability of measuring an
energy $\tau$ in a local region, if the global system is in a superposition of
eigenstates with energies $\epsilon<\tau$. On the other hand, we bound the
probability of measuring a global energy $\epsilon$ in a bipartite system that
is in a tensor product of eigenstates of its two subsystems. Very roughly, we
show that due to the local nature of the governing interactions, these
distributions are identical to what one encounters in the commuting case, up to
some exponentially small corrections. Finally, we use these bounds to study the
spectrum of a locally truncated Hamiltonian, in which the energies of a
contiguous region have been truncated above some threshold energy $\tau$. We
show that the lower part of the spectrum of this Hamiltonian is exponentially
close to that of the original Hamiltonian. A restricted version of this result
in 1D was a central building block in a recent improvement of the 1D area-law.Comment: 23 pages, 2 figures. A new version with tigheter bounds and a
re-written introductio

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