Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userLog to log-log crossover of entanglement in $(1+1)-$ dimensional massive scalar field
100
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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 $Nam_fsim mathscr{O}(1)$.
rate research
Read More
We determine both analytically and numerically the entanglement between chiral degrees of freedom in the ground state of massive perturbations of 1+1 dimensional conformal field theories quantised on a cylinder. Analytic predictions are obtained from a variational Ansatz for the ground state in terms of smeared conformal boundary states recently proposed by J. Cardy, which is validated by numerical results from the Truncated Conformal Space Approach. We also extend the scope of the Ansatz by resolving ground state degeneracies exploiting the operator product expansion. The chiral entanglement entropy is computed both analytically and numerically as a function of the volume. The excellent agreement between the analytic and numerical results provides further validation for Cardys Ansatz. The chiral entanglement entropy contains a universal $O(1)$ term $gamma$ for which an exact analytic result is obtained, and which can distinguish energetically degenerate ground states of gapped systems in 1+1 dimensions.
Finding pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace is necessarily a challenging task. Nevertheless, such purifications play the key role in characterizing quantum information-theoretic properties of mixed states via entanglement and complexity of purifications. In this article, we analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories using, for the first time, the~most general Gaussian purifications. We provide a comprehensive comparison with existing results and identify universal properties. We further discuss important subtleties in our setup: the massless limit of the free bosonic theory and the corresponding behaviour of the mutual information, as well as the Hilbert space structure under the Jordan-Wigner mapping in the spin chain model of the Ising conformal field theory.
We show how to efficiently compute the derivative (when it exists) of the solution map of log-log convex programs (LLCPs). These are nonconvex, nonsmooth optimization problems with positive variables that become convex when the variables, objective functions, and constraint functions are replaced with their logs. We focus specifically on LLCPs generated by disciplined geometric programming, a grammar consisting of a set of atomic functions with known log-log curvature and a composition rule for combining them. We represent a parametrized LLCP as the composition of a smooth transformation of parameters, a convex optimization problem, and an exponential transformation of the convex optimization problems solution. The derivative of this composition can be computed efficiently, using recently developed methods for differentiating through convex optimization problems. We implement our method in CVXPY, a Python-embedded modeling language and rewriting system for convex optimization. In just a few lines of code, a user can specify a parametrized LLCP, solve it, and evaluate the derivative or its adjoint at a vector. This makes it possible to conduct sensitivity analyses of solutions, given perturbations to the parameters, and to compute the gradient of a function of the solution with respect to the parameters. We use the adjoint of the derivative to implement differentiable log-log convex optimization layers in PyTorch and TensorFlow. Finally, we present applications to designing queuing systems and fitting structured prediction models.
We calculate log corrections to the entropy of three-dimensional black holes with soft hairy boundary conditions. Their thermodynamics possesses some special features that preclude a naive direct evaluation of these corrections, so we follow two different approaches. The first one exploits that the BTZ black hole belongs to the spectrum of Brown-Henneaux as well as soft hairy boundary conditions, so that the respective log corrections are related through a suitable change of the thermodynamic ensemble. In the second approach the analogue of modular invariance is considered for dual theories with anisotropic scaling of Lifshitz type with dynamical exponent z at the boundary. On the gravity side such scalings arise for KdV-type boundary conditions, which provide a specific 1-parameter family of multi-trace deformations of the usual AdS3/CFT2 setup, with Brown-Henneaux corresponding to z=1 and soft hairy boundary conditions to the limiting case z=0. Both approaches agree in the case of BTZ black holes for any non-negative z. Finally, for soft hairy boundary conditions we show that not only the leading term, but also the log corrections to the entropy of black flowers endowed with affine u(1) soft hair charges exclusively depend on the zero modes and hence coincide with the ones for BTZ black holes.
We study in this article the hydrodynamic limit in the macroscopic regime of the coupled system of stochastic differential equations, begin{equation} dlambda_t^i=frac{1}{sqrt{N}} dW_t^i - V(lambda_t^i) dt+ frac{beta}{2N} sum_{j ot=i} frac{dt}{lambda^i_t-lambda^j_t}, qquad i=1,ldots,N, end{equation} with $beta>1$, sometimes called generalized Dysons Brownian motion, describing the dissipative dynamics of a log-gas of $N$ equal charges with equilibrium measure corresponding to a $beta$-ensemble, with sufficiently regular convex potential $V$. The limit $Ntoinfty$ is known to satisfy a mean-field Mac-Kean-Vlasov equation. We prove that, for suitable initial conditions, fluctuations around the limit are Gaussian and satisfy an explicit PDE. The proof is very much indebted to the harmonic potential case treated in Israelsson cite{Isr}. Our key argument consists in showing that the time-evolution generator may be written in the form of a transport operator on the upper half-plane, plus a bounded non-local operator interpreted in terms of a signed jump process. As an essential technical argument ensuring the convergence of the above scheme, we give an $N$-independent large-deviation type estimate for the probability that $sup_{tin[0,T]}max_{i=1,ldots,N} |lambda_t^i|$ is large, based on a multi-scale argument and entropic bounds.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
