Universal Out-of-Equilibrium Dynamics of 1D Critical Quantum Systems Perturbed by Noise Coupled to Energy

We consider critical one-dimensional quantum systems initially prepared in their ground state and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the out-of-equilibrium dynamics. In particular, the full time-dependent d...

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Bibliographic Details
Published in:Physical review. X 2023-01, Vol.13 (1), p.011043, Article 011043
Main Authors: Christopoulos, Alexios, Le Doussal, Pierre, Bernard, Denis, De Luca, Andrea
Format: Article
Language:English
Subjects:
Condensed Matter
Couplings
Differential equations
Disordered Systems and Neural Networks
Energy distribution
Equilibrium
Fermions
Field theory
Heating
Phase transitions
Physics
Random noise
Statistical Mechanics
Strongly Correlated Electrons
Time dependence
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Summary:We consider critical one-dimensional quantum systems initially prepared in their ground state and perturbed by a smooth noise coupled to the energy density. By using conformal field theory, we deduce a universal description of the out-of-equilibrium dynamics. In particular, the full time-dependent distribution of any two-point chiral correlation function can be obtained from solving two coupled ordinary stochastic differential equations. In contrast to the general expectation of heating, we demonstrate that, over the noise realizations, the system reaches a nontrivial and universal stationary distribution of states characterized by broad tails of physical quantities. As an example, we analyze the entanglement entropy production associated to a given interval of sizeℓ. The corresponding stationary distribution has a3/2right tail for allℓand converges to a one-sided Levy stable for largeℓ. We obtain a similar result for 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 with3/2decay exponent. We show that this stationary distribution for the energy density emerges even if the initial state is prepared at finite temperature. Our results are benchmarked via analytical and numerical calculations for a chain of noninteracting spinless fermions with excellent agreement.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.13.011043