Probing many-body localization by spin noise spectroscopy

Abstract

We propose to apply spin noise spectroscopy (SNS) to detect many-body localization (MBL) in disordered spin systems. The SNS methods are relatively non-invasive technique to probe spontaneous spin fluctuations. We here 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 the archetypical case of the disordered XXZ spin chain we also develop a simple phenomenological model.The fate of Anderson localization in the presence of inter-particle interactions in a disordered quantum medium is an exciting frontier in condensed matter physics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. It is well known that all states of a onedimensional (1D) disordered chain of noninteracting particles are Anderson localized (AL) for any amount of disorder [20,21]. Thus, the AL state is a perfect insulator as long as the particles are not coupled to other degrees of freedom. In the presence of inter-particle interactions, a dynamical transition from a delocalized (diffusive) phase to a many-body localized (MBL) phase has been predicted in disordered quantum media when the strength of (quenched) randomness is increased [4][5][6][7][8][9].The MBL state is also a perfect insulator, but it has different dynamical properties compared to the AL state of noninteracting particles [10][11][12]16]. For example, entanglement entropy in the MBL phase shows a slow logarithmic growth following a global quench in an isolated system [10][11][12]. However, the entanglement entropy is very difficult to measure experimentally, and electrons or spins in conventional solid-state systems are coupled to an environment such as a phonon bath. Recent studies show that signatures of the MBL phase can survive in the presence of weak coupling to a thermalizing environment [22,23]. In particular, the spectral functions of local operators can be used to identify the MBL phase in the presence of weak dissipation [22,23].A new experimental approach based on a modified nonlocal spin-echo protocol along with a double electronelectron resonance technique in electron spin resonance has been proposed to distinguish the MBL phase from a noninteracting AL phase and a delocalized phase at infinite temperature [24]. The proposed approach can probe interaction effects, thus is able to separate the MBL phase from the AL phase. The method does involve optical pumping or polarization of local spins by external pulse fields, which can in principle lead to unwanted local heating and excitations. Here we propose a relatively non-invasive method based on spin noise spectroscopy (SNS) to distinguish the MBL phase from the AL phase and the delocalized phase in disordered spin systems.The optical SNS method has been developed recently as an alternative to conventional perturbation-based (pump-probe)...

Nonequilibrium quantum dynamics and transport: from integrability to many-body localization

“…5). Similar probes have been proposed in the literature, relying on spin echo techniques [88] or relaxation after a quantum quench [90] (see also [91,92] for more recent proposals).…”

Single spin probe of many-body localization

“…The experiments show that order in the initial state can be preserved for much longer timescales in the presence of disorder and interactions than in the case without, although the long term behaviour is governed by the coupling to the environment 11,17 . All in all, there is a need for experimentally relevant probes of many-body localization 20,21 .…”

The theory of spin noise spectroscopy: a review

“…The two-beam SNS was also proposed to detect a dynamic localization of quasiparticles in spin chains [263]. As SNS sensitivity has reached the single spin limit [104], one can realistically expect the spin noise detection in thin nanowires or from single magnetic impurities.…”