Session L52: Invited Session: Many Body Localization and Entanglement

Renormalization group studies of many-body localization

Quantum correlations do not usually persist for long in systems at finite energy density and disappear once the system thermalizes. But many-body localization offers an alternative paradigm, whereby quantum matter can evade the usual fate of thermal equilibrium and retain retrievable quantum correlations even at high energies. I will survey a dynamical renormalization group (RG) approach used to characterize the novel dynamics and entanglement structures, which develop in the localized phase in lieu of classical thermalization. Then I will present a theory of the transition between the ergodic and the many-body localized phase based on a novel RG framework. Here eigenstate entanglement entropy emerges as a natural scaling variable; the RG describes a change from area-law to volume law entanglement through an intriguing critical point, where the distribution of entanglement entropy becomes maximally broad. The ergodic phase established near the critical point is a Griffiths phase, which exhibits sub-diffusive energy transport and sub-ballistic entanglement propagation. The anomalous diffusion exponent vanishes continuously at the critical point. Before closing I will discuss recent progress in confronting the emerging theoretical understanding of many-body localization with experimental tests.   

Evidence for Many-Body Localization in an Ultracold Fermi-Hubbard Gas

Many-body localization (MBL) is a promising new paradigm for understanding disorder-induced localization in interacting quantum systems at non-zero temperature. We observe the emergence of an insulating state consistent with MBL in a strongly correlated atomic Fermi gas trapped in a disordered optical lattice, a closed system that realizes the disordered Fermi-Hubbard model. In measurements of disorder-induced localization obtained via mass transport, we detect three phenomena characteristic of MBL. We measure localization of this strongly interacting system at non-zero temperature, and we observe interaction-driven delocalization. We also observe localization that persists as the temperature and energy density of the gas are increased.   

Entanglement and universal dynamics in many-body localized systems

We are used to describing systems of many particles by statistical mechanics. However, the basic postulate of statistical mechanics -- ergodicity -- breaks down in so-called many-body localized systems, where disorder prevents particle transport and thermalization. In this talk, I will describe a phenomenological theory of the many-body localized (MBL) phase, based on new insights from quantum entanglement [1]. I will argue that, in contrast to ergodic systems, MBL eigenstates are not highly entangled, but rather obey so-called area law, typical of ground states in gapped systems. I will use this fact to show that MBL phase is characterized by an infinite number of emergent local conservation laws, in terms of which the Hamiltonian acquires a universal form. Turning to the experimental implications, I will describe the behavior of MBL systems following quantum quenches: surprisingly, entanglement shows logarithmic in time growth [1,2], reminiscent of glasses, while local observables exhibit power-law approach to ``equilibrium'' values [3]. I will support the presented theory with the results of numerical experiments. I will close by discussing experimental implications and other directions in exploring ergodicty and its breaking in quantum many-body systems, including many-body localization in periodically driven systems. \\[4pt] [1] M. Serbyn, Z. Papic, D. A. Abanin, Phys. Rev. Lett. 110, 260601 (2013); Phys. Rev. Lett. 111, 127201 (2013)\\[0pt] [2] D. A. Huse, V. Oganesyan, arXiv:1305.4915 (2013).\\[0pt] [3] M. Serbyn, Z. Papic, D. A. Abanin, Phys. Rev. B 90, 174302 (2014).   

Localization protected quantum order

Many body localization occurs in isolated quantum systems, usually with strong disorder, and is marked by absence of dissipation, absence of thermal equilibration, and a memory of the initial conditions that survives in local observables for arbitrarily long times. The many body localized regime is a non-equilibrium, strongly disordered, non-self averaging regime that presents a new frontier for quantum statistical mechanics. In this talk, I point out that there exists a vast zoo of correlated many body localized states of matter, which may be classified using familiar notions of spontaneous symmetry breaking and topological order. I will point out that in the many body localized regime, spontaneous symmetry breaking can occur even at high energy densities in one dimensional systems, and topological order can occur even without a bulk gap. I will also discuss the phenomenology of imperfectly isolated many body localized systems, which are weakly coupled to a heat bath. I will conclude with a brief discussion of how these phenomena may best be detected in experiments. References: Phys. Rev. B 88, 014206 (2013), Phys. Rev. B 90, 195115 (2014), Phys. Rev. B 90, 064203 (2014)   

Entanglement in the many-body localized phase and transition

The study of entanglement, both in eigenstates and its evolution after quenches, has been instrumental in advancing our understanding of many-body localized phases---the interacting analogs of the Anderson insulator. In this talk I will discuss in detail three observations related to the entanglement properties of many-body localized systems: (i) A global quench within the many-body localized phase gives rise to a slowly (logarithmically) increasing entanglement entropy. This is due to interaction induced dephasing that is absent in the Anderson insulator and therefore serves as a unique signature of the many-body localized phase. (ii) A local quench from an eigenstate leads to an extensive increase in the entanglement entropy only at the many-body localization transition itself. And (iii) at the many-body localization transition the distribution of entanglement entropies becomes extensively broad, while it vanishes both in the extended metallic phase and in the localized phases. The width of the entanglement distribution, like the long time limit of the local quench, is therefore a useful diagnostic for a many-body localization transition. I explicitly demonstrate how all these features are observed in microscopic spin chain models of many-body localization, and, in particular, discuss how they can be used to detect a many-body mobility edge.\\[4pt] [1] Jens H. Bardarson, Frank Pollmann, and Joel E. Moore, Phys. Rev. Lett. 109, 017202 (2012).\\[0pt] [2] Jonas A. Kjall, Jens H. Bardarson, and Frank Pollmann, Phys. Rev. Lett. 113, 107204 (2014).