We theoretically study the dynamics of a transverse-field Ising chain with power-law decaying interactions characterized by an exponent α, which can be experimentally realized in ion traps. We focus on two classes of emergent dynamical critical phenomena following a quantum quench from a ferromagnetic initial state: The first one manifests in the time-averaged order parameter, which vanishes at a critical transverse field. We argue that such a transition occurs only for long-range interactions α≤2. The second class corresponds to the emergence of time-periodic singularities in the return probability to the ground-state manifold which is obtained for all values of α and agrees with the order parameter transition for α≤2. We characterize how the two classes of nonequilibrium criticality correspond to each other and give a physical interpretation based on the symmetry of the time-evolved quantum states.

Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging Different Concepts of Nonequilibrium Criticality / Žunkovič, Bojan; Heyl, Markus; Knap, Michael; Silva, Alessandro. - In: PHYSICAL REVIEW LETTERS. - ISSN 0031-9007. - 120:13(2018), pp. 1-6. [10.1103/PhysRevLett.120.130601]

Dynamical Quantum Phase Transitions in Spin Chains with Long-Range Interactions: Merging Different Concepts of Nonequilibrium Criticality

Žunkovič, Bojan;Silva, Alessandro
2018

Abstract

We theoretically study the dynamics of a transverse-field Ising chain with power-law decaying interactions characterized by an exponent α, which can be experimentally realized in ion traps. We focus on two classes of emergent dynamical critical phenomena following a quantum quench from a ferromagnetic initial state: The first one manifests in the time-averaged order parameter, which vanishes at a critical transverse field. We argue that such a transition occurs only for long-range interactions α≤2. The second class corresponds to the emergence of time-periodic singularities in the return probability to the ground-state manifold which is obtained for all values of α and agrees with the order parameter transition for α≤2. We characterize how the two classes of nonequilibrium criticality correspond to each other and give a physical interpretation based on the symmetry of the time-evolved quantum states.
120
13
1
6
130601
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.130601
https://arxiv.org/abs/1609.08482
Žunkovič, Bojan; Heyl, Markus; Knap, Michael; Silva, Alessandro
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/88226
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