Year: 2014
Type: article
Abstract: Using a renormalization group approach, we solve the time evolution of random Ising spin chains with generic interactions starting from initial states of arbitrary energy. As a function of the Hamiltonian parameters, the system is tuned through a dynamical transition, similar to the ground-state critical point, at which the local spin correlations establish true long-range temporal order. In the state with a dominant transverse field, a spin that starts in an up state loses its orientation with time, while in the ``ordered'' state it never does. As in ground-state quantum phase transitions, the dynamical transition has unique signatures in the entanglement properties of the system. When the system is initialized in a product state, the entanglement entropy grows as $\mathrm{log}(t)$ in the two ``phases,'' while at the critical point it grows as ${\mathrm{log}}^{\ensuremath{\alpha}}(t)$, with $\ensuremath{\alpha}$ a universal number. This universal entanglement growth requires generic (``integrability breaking'') interactions to be added to the pure transverse field Ising model.
Source: Physical Review Letters
Authors: Ronen Vosk, Ehud Altman
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, Adolph C. and Mary Sprague Miller Institute for Basic Research in Science, University of California Berkeley, Minerva Foundation, Israel Science Foundation, University of California, Santa Barbara, Kavli Institute for Theoretical Physics, University of California, Santa Barbara
Awards: G258938352, G4433229824, G4773563968
OpenAlex ID: W1916865636