Dynamical Quantum Phase Transitions in Random Spin Chains

By Ronen Vosk, E. Altman. 2013

133 citations recorded by the source corpus.

Quantum systems can exhibit a great deal of universality at low temperature due to the structure of ground states and the critical points separating distinct states. On the other hand, quantum time evolution of the same systems involves all energies and it is therefore thought to be much harder, if at all possible, to have sharp transitions in the dynamics. In this paper we show that phase transitions characterized by universal singularities do occur in the time evolution of random spin chains. The sharpness of the transitions and integrity of the phases owes to many-body localization, which prevents thermalization in these systems. 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 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 $log(t)$ in the two "phases", while at the critical point it grows as $log^\a(t)$, with $\a$ a universal number. This universal entanglement growth requires generic ("integrability breaking") interactions to be added to the pure transverse field Ising model.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/03eed768520eb3a79e6a64f8317539568f7ba44d

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Citations in the corpus

Many-body localization: An introduction and selected topics (2017, unknown): “These two types of MBL phases have been observed in numerical simulations [105, 31, 106].”
Hilbert-Glass Transition: New Universality of Temperature-Tuned Many-Body Dynamical Quantum Criticality (2013, background): “Another paper posted in parallel to this one explores the HGT from the complementary viewpoint of the time evolution following a quench [38].”
Nonequilibrium quantum dynamics and transport: from integrability to many-body localization (2016, background): “The universal properties of such excited-state critical points (and critical phases) separating area-law entangled MBL phases can be efficiently captured by strong disorder real space renormalization group (RSRG) approaches [95, 3, 102, 100].”
Quantum quenches in 1 + 1 dimensional conformal field theories (2016, background): “The standard quasi-particle picture breaks down in models with disorder, for which it has been shown that the growth of entanglement is logarithmic in time (or slower) [63, 75, 76, 77, 78, 79], and in model with long-range interactions [80, 81, 82, 83, 85].”
Local integrals of motion in many‐body localized systems (2016, methodology): “2 This approach admits a natural dynamical interpretation [101, 102], as the renormalized Hamiltonian can be interpreted as the operator giving the effective dynamics at the largest time-scales, when the fastest degrees of freedom oscillating at the scale t ∼ Ω−1 have been integrated out.”
Out‐of‐time‐ordered correlators in many‐body localized systems (2016, background): “[20] Ronen Vosk and Ehud Altman, “Dynamical quantum phase transitions in random spin chains,” Phys.”
Gapless Symmetry-Protected Topological Order (2017, background): “[87] Ronen Vosk and Ehud Altman, “Dynamical Quantum Phase Transitions in Random Spin Chains,” Phys.”