Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userEntanglement Entropy: Non-Gaussian States and Strong Coupling
114
0
0.0
(
0
)
Added by
Jose Juan Fernandez-Melgarejo
Publication date
2020
fields
Physics
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
In this work we provide a method to study the entanglement entropy for non-Gaussian states that minimize the energy functional of interacting quantum field theories at arbitrary coupling. To this end, we build a class of non-Gaussian variational trial wavefunctionals with the help of exact nonlinear canonical transformations. The calculability emph{bonanza} shown by these variational emph{ansatze} allows us to compute the entanglement entropy using the prescription for the ground state of free theories. In free theories, the entanglement entropy is determined by the two-point correlation functions. For the interacting case, we show that these two-point correlators can be replaced by their nonperturbatively corrected counterparts. Upon giving some general formulae for general interacting models we calculate the entanglement entropy of half space and compact regions for the $phi^4$ scalar field theory in 2D. Finally, we analyze the r^ole played by higher order correlators in our results and show that strong subadditivity is satisfied.
rate research
Read More
We argue that the entanglement entropy for a very small subsystem obeys a property which is analogous to the first law of thermodynamics when we excite the system. In relativistic setups, its effective temperature is proportional to the inverse of the subsystem size. This provides a universal relationship between the energy and the amount of quantum information. We derive the results using holography and confirm them in two dimensional field theories. We will also comment on an example with negative specific heat and suggest a connection between the second law of thermodynamics and the strong subadditivity of entanglement entropy.
We would like to put the area law -- believed to by obeyed by entanglement entropies in the ground state of a local field theory -- to scrutiny in the presence of non-perturbative effects. We study instanton corrections to entanglement entropy in various models whose instanton effects are well understood, including $U(1)$ gauge theory in 2+1 dimensions and false vacuum decay in $phi^4$ theory, and we demonstrate that the area law is indeed obeyed in these models. We also perform numerical computations for toy wavefunctions mimicking the theta vacuum of the (1+1)-dimensional Schwinger model. Our results indicate that such superpositions exhibit no more violation of the area law than the logarithmic behavior of a single Fermi surface.
The partial entanglement entropy (PEE) $s_{mathcal{A}}(mathcal{A}_i)$ characterizes how much the subset $mathcal{A}_i$ of $mathcal{A}$ contribute to the entanglement entropy $S_{mathcal{A}}$. We find one additional physical requirement for $s_{mathcal{A}}(mathcal{A}_i)$, which is the invariance under a permutation. The partial entanglement entropy proposal satisfies all the physical requirements. We show that for Poincare invariant theories the physical requirements are enough to uniquely determine the PEE (or the entanglement contour) to satisfy a general formula. This is the first time we find the PEE can be uniquely determined. Since the solution of the requirements is unique and the textit{PEE proposal} is a solution, the textit{PEE proposal} is justified for Poincare invariant theories.
The continuous Multi Scale Entanglement Renormalization Anstaz (cMERA) consists of a variational method which carries out a real space renormalization scheme on the wavefunctionals of quantum field theories. In this work we calculate the entanglement entropy of the half space for a free scalar theory through a Gaussian cMERA circuit. We obtain the correct entropy written in terms of the optimized cMERA variational parameter, the local density of disentanglers. Accordingly, using the entanglement entropy production per unit scale, we study local areas in the bulk of the tensor network in terms of the differential entanglement generated along the cMERA flow. This result spurs us to establish an explicit relation between the cMERA variational parameter and the radial component of a dual AdS geometry through the Ryu-Takayanagi formula. Finally, based on recent formulations of non-Gaussian cMERA circuits, we argue that the entanglement entropy for the half space can be written as an integral along the renormalization scale whose measure is given by the Fisher information metric of the cMERA circuit. Consequently, a straightforward relation between AdS geometry and the Fisher information metric is also established.
We investigate a weak version of subsystem eigenstate thermalization hypothesis (ETH) for a two-dimensional large central charge conformal field theory by comparing the local equivalence of high energy state and thermal state of canonical ensemble. We evaluate the single-interval Renyi entropy and entanglement entropy for a heavy primary state in short interval expansion. We verify the results of Renyi entropy by two different replica methods. We find nontrivial results at the eighth order of short interval expansion, which include an infinite number of higher order terms in the large central charge expansion. We then evaluate the relative entropy of the reduced density matrices to measure the difference between the heavy primary state and thermal state of canonical ensemble, and find that the aforementioned nontrivial eighth order results make the relative entropy unsuppressed in the large central charge limit. By using Pinskers and Fannes-Audenaert inequalities, we can exploit the results of relative entropy to yield the lower and upper bounds on trace distance of the excited-state and thermal-state reduced density matrices. Our results are consistent with subsystem weak ETH, which requires the above trace distance is of power-law suppression by the large central charge. However, we are unable to pin down the exponent of power-law suppression. As a byproduct we also calculate the relative entropy to measure the difference between the reduced density matrices of two different heavy primary states.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
