Dynamical quantum phase transitions in the transverse-field Ising model.

By Markus Heyl, A. Polkovnikov, S. Kehrein. Physical Review Letters, 2012

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A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to nonanalytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this Letter we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely nonanalytic behavior at a critical time. We denote such behavior a dynamical phase transition and explore its properties in the transverse-field Ising model. Specifically, we show that the equilibrium quantum phase transition and the dynamical phase transition in this model are intimately related.

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

View Paper: https://www.semanticscholar.org/paper/1984c9f061a4dcc49f8db69001fc2430eaa035f2

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, background): “It was noted in [42] that the period of the oscillations in (141) coincides with cusps in the time evolution of the logarithm of the return probability per unit length ( ) ⟨ ( ) ( )⟩ → = − | Ψ | |Ψ | ∞ − f t lim log 0 e 0 L L Ht 1 i 2”
Many-body energy localization transition in periodically driven systems (2012, background): “istical physics. In this sense this transition is reminiscent of the divergence of the short time expansion in the Loschmidt echo recently obtained for a quench in the transverse eld Ising spin chain [32]. The precise characterization of the two phases and of the nature of the transition and its con”
Programmable quantum simulations of spin systems with trapped ions (2019, background): “The first type of DQPT (type I) is based on the formal analogy between the non-analytic behaviour of the return probability to the initial state |ψ0〉 after a quantum quench under the Hamiltonian H , defined as G(t) = 〈ψ0| e−iHt |ψ0〉, and the partition function of the corresponding equilibrium system”
Quantum quenches in 1 + 1 dimensional conformal field theories (2016, background): “We note in passing that in recent papers [139] a similar quantity has been studied for various lattice models, and its singularities interpreted as dynamical phase transitions at finite t.”
Geometry of quantum phase transitions (2019, background): “Fidelity susceptibility [231, 166, 232], Fisher information [159, 127], geometric phases [186, 187, 188] and geometric curvature [233, 118, 119] can be probed through experimentally viable procedures.”
Ultrafast optical spectroscopy of strongly correlated materials and high-temperature superconductors: a non-equilibrium approach (2016, background): “The limited simulation time does not however rule out the possibility that on a longer timescale the system actually relaxes to a conventional Fermi liquid, which would signal a similarity between the behavior of the photo excited Mott insulator and systems with broken symmetry[599, 600].”
Real-time dynamics of lattice gauge theories with a few-qubit quantum computer (2016, neutral): “3(a,c) is also known as the Loschmidt echo, which is important in other contexts such as the theory of quantum chaos [28] and dynamical critical phenomena far from equilibrium [29].”