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Dynamical Quantum Phase Transitions in the Transverse Field Ising Model · Around

2012

Dynamical Quantum Phase Transitions in the Transverse Field Ising Model

Heyl, Markus, Polkovnikov, Anatoli, Kehrein, Stefan

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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 non-analytic 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 paper we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely non-analytic behavior at a critical time.
We denote such behavior a dynamical phase transition and explore its properties in the transverse field Ising model.

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See Supplementary material for details about Loschmidt echos for symmetry broken initial states and post-selection

Cited in the paper.

For a general ramping protocol g ⁡ ( t ) g(t) with g ⁡ ( t = 0 ) = g 0 , g ⁡ ( t = τ ) = g 1 g(t=0)=g_{0},g(t=\tau)=g_{1} we define | Ψ i ⟩ = | ψ ⁡ ( τ ) ⟩ |\Psi_{i}\rangle=|\psi(\tau)\rangle and | ψ ⁡ ( t ) ⟩ |\psi(t)\rangle is the solution of the Schroedinger equation: i ∂ t | ψ ⁡ ( t ) ⟩ = H ⁡ ( g ⁡ ( t ) ) | ψ ⁡ ( t ) ⟩ , | ψ ⁡ ( t = 0 ) ⟩ = | Ψ G S ( g 0 ) ⟩ i\,\partial_{t}\,|\psi(t)\rangle=H(g(t))\,|\psi(t)\rangle\ ,\,|\psi(t=0)\rangle=|\Psi_{GS}(g_{0})\rangle

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