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arXiv:1607.08617 · Physical review. B./Physical review. B

Single spin probe of many-body localization

Evert van Nieuwenburg, Sebastian D. Huber, R. Chitra

Published Nov 23, 2016• 5 citations
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Abstract

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.

DOI
10.1103/physrevb.94.180202

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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.
We analyze a disordered central spin model, where a central spin interacts equally with each spin in a periodic one-dimensional (1D) random-field Heisenberg chain. If the Heisenberg chain is initially in the many-body localized (MBL) phase, we find that the coupling to the central spin suffices to delocalize the chain for a substantial range of coupling strengths. We calculate the phase diagram of the model and identify the phase boundary between the MBL and ergodic phase. Within the localized phase, the central spin significantly enhances the rate of the logarithmic entanglement growth and its saturation value. We attribute the increase in entanglement entropy to a nonextensive enhancement of magnetization fluctuations induced by the central spin. Finally, we demonstrate that correlation functions of the central spin can be utilized to distinguish between MBL and ergodic phases of the 1D chain. Hence, we propose the use of a central spin as a possible experimental probe to identify the MBL phase.
We study the effects of dephasing noise on a prototypical many-body localized system---the XXZXXZXXZ spin 1/21/21/2 chain with a disordered magnetic field. At times longer than the inverse dephasing strength the dynamics of the system is described by a probabilistic Markov process on the space of diagonal density matrices, while all off-diagonal elements of the density matrix decay to zero. The generator of the Markovian process is a bond-disordered spin chain. The scaling variable is identified, and independence of relaxation on the interaction strength is demonstrated. We show that purity and von Neumann entropy are extensive, showing no signatures of localization, while the operator space entanglement entropy exhibits a logarithmic growth with time until the final saturation corresponding to localization breakdown, suggesting a many-body localized dynamics of the effective Markov process.
Many-body localization is characterized by a slow logarithmic growth of the entanglement entropy after a global quantum quench while the local memory of an initial density imbalance remains at infinite time. We investigate how much the proximity of a many-body localized phase can influence the dynamics in the delocalized ergodic regime where thermalization is expected. Using an exact Krylov space technique, the out-of-equilibrium dynamics of the random-field Heisenberg chain is studied up to L=28L=28L=28 sites, starting from an initially unentangled high-energy product state. Within most of the delocalized phase, we find a sub-ballistic entanglement growth $S(t)\ensuremath{\propto}{t}^{1/z}$ with a disorder-dependent exponent $z\ensuremath{\ge}1$, in contrast with the pure ballistic growth z=1z=1z=1 of clean systems. At the same time, anomalous relaxation is also observed for the spin imbalance $\mathcal{I}(t)\ensuremath{\propto}{t}^{\ensuremath{-}\ensuremath{\zeta}}$ with a continuously varying disorder-dependent exponent $\ensuremath{\zeta}$, vanishing at the transition. This provides a clear experimental signature for detecting this nonconventional regime.
We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a noninteracting localized phase and a delocalized phase. In particular, we show that for a properly chosen pulse sequence the MBL phase exhibits a characteristic power-law decay reflecting its slow growth of entanglement. We find that this power-law decay is robust with respect to thermal and disorder averaging, provide numerical simulations supporting our results, and discuss possible experimental realizations in solid-state and cold-atom systems.
The law of statistical physics dictates that generic closed quantum many-body systems initialized in nonequilibrium will thermalize under their own dynamics. However, the emergence of many-body localization (MBL) owing to the interplay between interaction and disorder, which is in stark contrast to Anderson localization, which only addresses noninteracting particles in the presence of disorder, greatly challenges this concept, because it prevents the systems from evolving to the ergodic thermalized state. One critical evidence of MBL is the long-time logarithmic growth of entanglement entropy, and a direct observation of it is still elusive due to the experimental challenges in multiqubit single-shot measurement and quantum state tomography. Here we present an experiment fully emulating the MBL dynamics with a 10-qubit superconducting quantum processor, which represents a spin-1/2 XY model featuring programmable disorder and long-range spin-spin interactions. We provide essential signatures of MBL, such as the imbalance due to the initial nonequilibrium, the violation of eigenstate thermalization hypothesis, and, more importantly, the direct evidence of the long-time logarithmic growth of entanglement entropy. Our results lay solid foundations for precisely simulating the intriguing physics of quantum many-body systems on the platform of large-scale multiqubit superconducting quantum processors.
Dephasing of spins is a major roadblock to scaling up the size of quantum computing systems. We explore the possibility of utilizing highly disordered environments which are in the Many-Body Localized phase to arrest this dephasing. We embedded 2 `special' spins in such a highly disordered environment of Heisenberg spins to act as the target qubits and use the long-time value of the spin-spin correlator ⟨σ⃗i⋅σ⃗j⟩\langle \vecσ_i \cdot \vecσ_j\rangle⟨σi​⋅σj​⟩ as an order parameter to quantify the transition between the thermal and MBL phases of this system. It is seen that the dephasing between spins, as encoded in this correlator, is impeded in a disordered environment when the system is fully localized. The order parameter yields a critical exponent, to characterize the transition between the thermal and MBL phases, that appears to be robust to changes in microscopic parameters of the system or the choice of pair of spins.