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arXiv:1506.05116 · Physical Review B

Probing many-body localization by spin noise spectroscopy

Dibyendu Roy, Rajeev Singh, Roderich Moessner

Published Nov 23, 2015• 24 citations
arXivHTMLPDF

Abstract

We propose to apply spin noise spectroscopy (SNS) to detect many-body localization (MBL) in disordered spin systems. The SNS methods are relatively noninvasive techniques to probe spontaneous spin fluctuations. Here, we show that the spin noise signals obtained by cross-correlation SNS with two probe beams can be used to separate the MBL phase from a noninteracting Anderson localized phase and a delocalized (diffusive) phase in the studied models for which we numerically calculate real-time spin noise signals and their power spectra. For an archetypical case of the disordered XXZ spin chain, we also develop a simple phenomenological model.

DOI
10.1103/physrevb.92.180205

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We propose to apply spin noise spectroscopy (SNS) to detect many-body localization (MBL) in disordered spin systems. The SNS methods are relatively noninvasive techniques to probe spontaneous spin fluctuations. Here, we show that the spin noise signals obtained by cross-correlation SNS with two probe beams can be used to separate the MBL phase from a noninteracting Anderson localized phase and a delocalized (diffusive) phase in the studied models for which we numerically calculate real-time spin noise signals and their power spectra. For an archetypical case of the disordered XXZ spin chain, we also develop a simple phenomenological model.
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.
Many-body localization (MBL) hinders the thermalization of quantum many-body systems in the presence of strong disorder. In this Letter, we study the MBL regime in bond-disordered spin-1/2 XXZ spin chain, finding the multimodal distribution of entanglement entropy in eigenstates, sub-Poissonian level statistics, and revealing a relation between operators and initial states required for examining the breakdown of thermalization in the time evolution of the system. We employ a real space renormalization group scheme to identify these phenomenological features of the MBL regime that extend beyond the standard picture of local integrals of motion relevant for systems with disorder coupled to on-site operators. Our results pave the way for experimental probing of MBL in bond-disordered spin chains.
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.
Characterizing out-of-equilibrium many-body dynamics is a complex but crucial task for quantum applications and understanding fundamental phenomena. A central question is the role of localization in quenching thermalization in many-body systems and whether such localization survives in the presence of interactions. Probing this question in real systems necessitates the development of an experimentally measurable metric that can distinguish between different types of localization. While it is known that the localized phase of interacting systems [many-body localization (MBL)] exhibits a long-time logarithmic growth in entanglement entropy that distinguishes it from the noninteracting case of Anderson localization (AL), entanglement entropy is difficult to measure experimentally. Here, we present a novel correlation metric, capable of distinguishing MBL from AL in high-temperature spin systems. We demonstrate the use of this metric to detect localization in a natural solid-state spin system using nuclear magnetic resonance (NMR). We engineer the natural Hamiltonian to controllably introduce disorder and interactions, and observe the emergence of localization. In particular, while our correlation metric saturates for AL, it slowly keeps increasing for MBL, demonstrating analogous features to entanglement entropy, as we show in simulations. Our results show that our NMR techniques, akin to measuring out-of-time correlations, are well suited for studying localization in spin systems.
The disordered XXZ model is a prototype model of the many-body localization (MBL) transition. Despite numerous studies of this model, the available numerical evidence of multifractality of its eigenstates is not very conclusive due to severe finite size effects. Moreover it is not clear if similarly to the case of single-particle physics, multifractal properties of the many-body eigenstates are related to anomalous transport, which is observed in this model. In this work, using a state-of-the-art, massively parallel, numerically exact method, we study systems of up to 24 spins and show that a large fraction of the delocalized phase flows towards ergodicity in the thermodynamic limit, while a region immediately preceding the MBL transition appears to be multifractal in this limit. We discuss the implication of our finding on the mechanism of subdiffusive transport.
We explore the applications of spin noise spectroscopy (SNS) for detection of the spin properties of atomic ensembles in and out of equilibrium. In SNS, a linearly polarized far-detuned probe beam on passing through an ensemble of atomic spins acquires the information of the spin correlations of the system which is extracted using its time-resolved Faraday-rotation noise. We measure various atomic, magnetic and sub-atomic properties as well as perform precision magnetometry using SNS in rubidium atomic vapor in thermal equilibrium. Thereafter, we manipulate the relative spin populations between different ground state hyperfine levels of rubidium by controlled optical pumping which drives the system out of equilibrium. We then apply SNS to probe such spin imbalance non-perturbatively. We further use this driven atomic vapor to demonstrate that SNS can have better resolution than typical absorption spectroscopy in detecting spectral lines in the presence of various spectral broadening mechanisms.