Motivated by the search for a quantum analogue of the macroscopic fluctuation
theory, we study quantum spin chains dissipatively coupled to quantum noise.
The dynamical processes are encoded in quantum stochastic differential
equations. They induce dissipative friction on the spin chain currents. We show
that, as the friction becomes stronger, the noise induced dissipative effects
localize the spin chain states on a slow mode manifold, and we determine the
effective stochastic quantum dynamics of these slow modes. We illustrate this
approach by studying the quantum stochastic Heisenberg spin chain.
We discuss and compute entanglement entropy (EE) in (1+1)-dimensional free
Lifshitz scalar field theories with arbitrary dynamical exponents. We consider
both the subinterval and periodic sublattices in the discretized theory as
subsystems. In both cases, we are able to analytically demonstrate that the EE
grows linearly as a function of the dynamical exponent. Furthermore, for the
subinterval case, we determine that as the dynamical exponent increases, there
is a crossover from an area law to a volume law. Lastly, we deform Lifshitz
field theories with certain relevant operators and show that the EE decreases
from the ultraviolet to the infrared fixed point, giving evidence for a
possible $c$-theorem for deformed Lifshitz theories.
We present an algorithmic construction scheme for matrix-product-operator
(MPO) representations of arbitrary $U(1)$-invariant operators whenever there is
an expression of the local structure in terms of a finite-states machine (FSM).
Given a set of local operators as building blocks, the method automatizes two
major steps when constructing a $U(1)$-invariant MPO representation: (i) the
bookkeeping of auxiliary bond-index shifts arising from the application of
operators changing the local quantum numbers and (ii) the appearance of phase
factors due to particular commutation rules. The automatization is achieved by
post-processing the operator strings generated by the FSM. Consequently, MPO
representations of various types of $U(1)$-invariant operators can be
constructed generically in MPS algorithms reducing the necessity of expensive
MPO arithmetics. This is demonstrated by generating arbitrary products of
operators in terms of FSM, from which we obtain exact MPO representations for
the variance of the Hamiltonian of a $S=1$ Heisenberg chain.
We analyze how maximal entanglement is generated at the fundamental level in
QED by studying correlations between helicity states in tree-level scattering
processes at high energy. We demonstrate that two mechanisms for the generation
of maximal entanglement are at work: i) $s$-channel processes where the virtual
photon carries equal overlaps of the helicities of the final state particles,
and ii) the indistinguishable superposition between $t$- and $u$-channels. We
then study whether requiring maximal entanglement constrains the coupling
structure of QED and the weak interactions. In the case of photon-electron
interactions unconstrained by gauge symmetry, we show how this requirement
allows reproducing QED. For $Z$-mediated weak scattering, the maximal
entanglement principle leads to non-trivial predictions for the value of the
weak mixing angle $\theta_W$. Our results are a first step towards
understanding the connections between maximal entanglement and the fundamental
symmetries of high-energy physics.