Universal outofequilibrium dynamics of 1D critical quantum systems perturbed by noise coupled to energy
Abstract
We consider critical one dimensional quantum systems initially prepared in their groundstate and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the outofequilibrium dynamics. In particular, the full timedependent distribution of any $2$pt chiral correlation function can be obtained from solving two coupled ordinary stochastic differential equations. In contrast with the general expectation of heating, we demonstrate that the system reaches a nontrivial and universal stationary state characterized by broad distributions. As an example, we analyse the local energy density: while its first moment diverges exponentially fast in time, the stationary distribution, which we derive analytically, is symmetric around a negative median and exhibits a fat tail with $3/2$ decay exponent. We obtain a similar result for the entanglement entropy production associated to a given interval of size $\ell$. The corresponding stationary distribution has a $3/2$ right tail for all $\ell$, and converges to a onesided Levy stable for large $\ell$. Our results are benchmarked via analytical and numerical calculations for a chain of noninteracting spinless fermions with excellent agreement.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.15303
 Bibcode:
 2021arXiv211015303C
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Strongly Correlated Electrons;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 9 pages, 5 figures, Supplemental material (16 pages)