Quantum dynamical phase transition in a system with many-body interactions

Abstract

We introduce a microscopic Hamiltonian model of a two level system with many-body interactions with an environment whose excitation dynamics is fully solved within the Keldysh formalism. If a particle starts in one of the states of the isolated system, the return probability oscillates with the Rabi frequency ${\omega }_0$. For weak interactions with the environment $1/{\tau }_{\mathrm{SE}}<2{\omega }_0,$ we find a slower oscillation whose amplitude decays with a decoherence rate $1/τ_ϕ=1/(2τ_{\mathrm{SE}% })$. However, beyond a finite critical interaction with the environment, $1/{\tau }_{\mathrm{SE}}>2{\omega }_0$, the decoherence rate becomes $1/{\tau }_{\varphi }\propto ({\omega }_0^2){\tau }_{\mathrm{SE}}$. The oscillation period diverges showing a \emph{quantum dynamical phase transition}to a Quantum Zeno phase.

5 pages, 3 figures, minor changes, fig.2 modified, added references

References in corpus (8)

• Decoherence, einselection, and the quantum origins of the classical
• Environment-independent decoherence rate in classically chaotic systems
• Environmentally induced Quantum Dynamical Phase Transition in the spin swapping operation
• Universality of the Lyapunov regime for the Loschmidt echo
• Signatures of a Noise-Induced Quantum Phase Transition in a Mesoscopic Metal Ring
• Non-Markovian decay beyond the Fermi Golden Rule: Survival Collapse of the polarization in spin chains
• Coherent-incoherent transition in the sub-Ohmic spin-boson model
• Dimensional Crossover in Spin Diffusion: A manifestation of the Quantum Zeno Effect

Cited by in corpus (20)

• Decoherence Induced Exceptional Points in a Dissipative Superconducting Qubit
• The Theory of Spin Noise Spectroscopy: A Review
• Revisiting the Fermi Golden Rule: Quantum Dynamical Phase Transition as a Paradigm Shift
• Crucial role of decoherence for electronic transport in molecular wires: Polyaniline as a case study
• Dynamical regimes of a quantum swap gate beyond the Fermi Golden Rule
• Localization effects induced by decoherence in superpositions of many-spin quantum states
• Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models
• Quantum Zeno effect as a topological phase transition in full counting statistics and spin noise spectroscopy
• Nuclear Spin Dynamics in Double Quantum Dots: Multi-Stability, Dynamical Polarization, Criticality and Entanglement
• Buffering plasmons in nanoparticle waveguides at the virtual-localized transition
• Dynamics of quantum information scrambling under decoherence effects measured via active spins clusters
• Decoherence as attenuation of mesoscopic echoes in a spin-chain channel
• Decoherent time-dependent transport beyond the Landauer-Büttiker formulation: a quantum-drift alternative to quantum jumps
• Decoherence under many-body system-environment interactions: a stroboscopic representation based on a fictitiously homogenized interaction rate
• Criticality of environmental information obtainable by dynamically controlled quantum probes
• Signatures of a quantum dynamical phase transition in a three-spin system in presence of a spin environment
• Non-Markovian decay and dynamics of decoherence in private and public environments
• Role of energy uncertainties in ergodicity breaking induced by competing interactions and disorder. A dynamical assessment through the Loschmidt echo
• Simulating a Catalyst induced Quantum Dynamical Phase Transition of a Heyrovsky reaction with different models for the environment
• Resonances and continued-fraction Green's functions in non-Hermitian Bose-Hubbard-like quantum models