We investigate the trends of information backflow associated with the dynamics of a sub-part of a disordered spin-1/2 transverse field Heisenberg chain for different regimes of the Hamiltonian. Towards this aim, the decay profile of bipartite entanglement shared between a probe-qubit and a system-qubit (sub-part) of the chain is monitored in time. A clear shift in the trends of the decay profiles of the bipartite entanglement from monotonic in the low-disorder limit to non-monotonic in the moderately large disorder limit occurs due to strong information backflow from the environment (complementary part) to the system-qubit. A connection between environmental interruption caused by the information backflow and the disorder strength is established by examining the entanglement revival frequencies. The growth patterns of the revival frequencies in the localized phase plays an instrumental role to effectively distinguish an interacting system (many-body localized) from its non-interacting (Anderson localized) counterpart.
We investigate the trends of information backflow associated with the dynamics of a sub-part of a disordered spin-1/2 transverse field Heisenberg chain for different regimes of the Hamiltonian. Towards this aim, the decay profile of bipartite entanglement shared between a probe-qubit and a system-qubit (sub-part) of the chain is monitored in time. A clear shift in the trends of the decay profiles of the bipartite entanglement from monotonic in the low-disorder limit to non-monotonic in the moderately large disorder limit occurs due to strong information backflow from the environment (complementary part) to the system-qubit. A connection between environmental interruption caused by the information backflow and the disorder strength is established by examining the entanglement revival frequencies. The growth patterns of the revival frequencies in the localized phase plays an instrumental role to effectively distinguish an interacting system (many-body localized) from its non-interacting (Anderson localized) counterpart.
Within a framework based on the tools of the theory of open quantum systems, we study non-Markovianity trends in a disordered spin chain. Towards this aim, we investigate the decay profile of bipartite entanglement shared between an ancilla-qubit and a system-qubit, which is locally connected with a disordered transverse field Heisenberg chain, acting as an effective environment for it. Subsequently, the evolution of the system part can be described using a dynamical map acting on it. The non-Markovian nature of the dynamical map is imprinted in the form of a non-monotonic decay of the initial entanglement. We show that a connection between environmental interruption and disorder strength can be established by monitoring the frequency of the entanglement revival, which effectively accounts for the backflow of information from the environment to the system.
We use an external spin as a dynamical probe of many-body localization. The probe spin is coupled to an interacting and disordered environment described by a Heisenberg spin chain in a random field. The spin-chain environment can be tuned between a thermalizing delocalized phase and nonthermalizing localized phase, both in its ground and high-energy states. We study the decoherence of the probe spin when it couples to the environment prepared in three states: the ground state, the infinite temperature state, and a high-energy N\'eel state. In the nonthermalizing many-body localized regime, the coherence shows scaling behavior in the disorder strength. The long-time dynamics of the probe spin shows a logarithmic dephasing in analogy with the logarithmic growth of entanglement entropy for a bipartition of a many-body localized system. In summary, we show that decoherence of the probe spin provides clear signatures of many-body localization.
The non-equilibrium dynamics of disordered many-body quantum systems after a global quantum quench unveils important insights about the competition between interactions and disorder, yielding in particular an insightful perspective on many body localization (MBL). Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on the quantum quench dynamics have so far not been investigated. In this letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power α. Using a dynamical version of the strong disorder renormalization group (SDRG) we find for α>αc that the entanglement entropy grows logarithmically with time and becomes smaller with larger α as S(t)=Spln(t)/(2α). Here, Sp=2ln2−1. We use numerical exact diagonalization (ED) simulations to verify our results for system sizes up to $ N\sim 16$ spins, yielding good agreement for sufficiently large α>αc≈1.8. For α<αc, we find that the entanglement entropy grows as a power-law with time, S(t)∼tγ(α) with 0<γ(α)<1 a decaying function of the interaction exponent α.
The Einstein-Podolsky-Rosen (EPR) pair of qubits plays a critical role in many quantum protocol applications such as quantum communication and quantum teleportation. Due to interactions with the environment, an EPR pair can lose its entanglement and no longer serve as a useful quantum resource. On the other hand, it has been suggested that introducing disorder into environment might help prevent thermalization and improve the preservation of entanglement. Here, we theoretically investigate the time evolution of quantum entanglement of an EPR pair in a random-field XXZ spin chain model in the Anderson localized (AL) and many-body localized (MBL) phase. We find that the entanglement between qubits decreases and approaches a plateau in the AL phase, but shows a power-law decrease after some critical time determined by the interaction strength in the MBL phase. Our findings shed light on applying AL/MBL to improve quantum information storage, and can be used as a practical indicator to distinguish the AL and MBL phase.
The nonequilibrium dynamics of disordered many-body quantum systems after a quantum quench unveils important insights about the competition between interactions and disorder, yielding, in particular, an interesting perspective toward the understanding of many-body localization. Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on their dynamical properties have so far not been investigated. In this Letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power $\ensuremath{\alpha}$. Using a dynamical version of the strong disorder renormalization group we find for $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}$ that the entanglement entropy grows logarithmically with time and becomes smaller with larger $\ensuremath{\alpha}$ as $S(t)={S}_{p}ln(t)/(2\ensuremath{\alpha})$. Here, ${S}_{p}=2ln2\ensuremath{-}1$. We present results of numerical exact diagonalization calculations for system sizes up to $N\ensuremath{\sim}16$ spins, in good agreement with the analytical results for sufficiently large $\ensuremath{\alpha}>{\ensuremath{\alpha}}_{c}\ensuremath{\approx}1.8$. For $\ensuremath{\alpha}<{\ensuremath{\alpha}}_{c}$, we find that the entanglement entropy grows as a power law with time, $S(t)\ensuremath{\sim}{t}^{\ensuremath{\gamma}(\ensuremath{\alpha})}$ with $0<\ensuremath{\gamma}(\ensuremath{\alpha})<1$ a decaying function of the interaction exponent $\ensuremath{\alpha}$.
The Einstein–Podolsky–Rosen (EPR) pair of qubits plays a critical role in many quantum protocol applications such as quantum communication and quantum teleportation. Due to interactions with the environment, an EPR pair can lose its entanglement and no longer serve as a useful quantum resource. On the other hand, it has been suggested that introducing disorder into environment might help prevent thermalization and improve the preservation of entanglement. Here, we theoretically investigate the time evolution of quantum entanglement of an EPR pair in a random-field XXZ spin chain model in the Anderson localized (AL) and many-body localized (MBL) phase. We find that the entanglement between qubits decreases and approaches a plateau in the AL phase, but shows a power-law decrease after some critical time determined by the interaction strength in the MBL phase. Our findings shed light on applying AL/MBL to improve quantum information storage, and can be used as a practical indicator to distinguish the AL and MBL phase.