Bulletin of the American Physical Society
APS March Meeting 2016
Volume 61, Number 2
Monday–Friday, March 14–18, 2016; Baltimore, Maryland
Session X2: Recent Advances in Many Body LocalizationInvited
|
Hide Abstracts |
Sponsoring Units: DCMP DAMOP Chair: Christopher Laumann, University of Washington Room: Ballroom II |
Friday, March 18, 2016 8:00AM - 8:36AM |
X2.00001: A rigorous result on many-body localization Invited Speaker: John Imbrie The mathematical theory of many-body localization is in its infancy. Lack of thermalization is associated with the existence of a complete set of quasi-local integrals of motion. I will discuss a proof that a particular one-dimensional spin chain with random local interactions exhibits many-body localization. The proof depends on a physically reasonable assumption that limits the amount of level attraction in the system. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian and connect the exact many-body eigenfunctions to the original basis vectors. This provides an explicit construction of integrals of motion via convergent expansions. [Preview Abstract] |
Friday, March 18, 2016 8:36AM - 9:12AM |
X2.00002: Many-body localization: Entanglement and efficient numerical simulations Invited Speaker: Frank Pollmann Many-body localization (MBL) occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. To understand this phenomenon, the development of new efficient numerical methods to find highly excited many-body eigenstates is essential. In this talk, we will discuss two complimentary approaches to simulate MBL systems: First, we introduce a variant of the density-matrix renormalization group (DMRG) method that obtains individual highly excited eigenstates of MBL systems to machine precision accuracy at moderate to large disorder. This method explicitly takes advantage of the local spatial structure and the low entanglement which is characteristic for MBL eigenstates. Second, we propose an approach to directly find an approximate compact representation of the diagonalizing unitary by using a variational unitary matrix-product operator. [Preview Abstract] |
Friday, March 18, 2016 9:12AM - 9:48AM |
X2.00003: Dynamical Response of Many-Body Localized Systems Invited Speaker: Vedika Khemani Many-body localization (MBL) is the long sought-after generalization of Anderson localization to interacting systems. Many-body localized systems fail to thermalize, and display a variety of novel properties and phases that have no equilibrium analog. In this talk, I will review our rapidly evolving understanding of the MBL phase before describing the eigenstate properties and dynamical response of these phases in some detail. In particular, I will show how a slow local perturbation surprisingly induces a highly non-local charge response despite the localized nature of the phase. This effect lies beyond linear response theory and has implications for numerous fields, including topological quantum computation in quantum Hall systems and quantum control in disordered environments. I will also discuss the low-frequency Kubo conductivity of MBL systems, and discuss the crossover from the linear to the non-linear response regime with an emphasis on the time-scales and amplitudes of the drive. [Preview Abstract] |
Friday, March 18, 2016 9:48AM - 10:24AM |
X2.00004: Universal dynamics across many-body localization phase transition Invited Speaker: Maksym Serbyn Many body localization allows quantum systems to evade thermalization owing to the emergence of extensive number of local conserved quantities [1,2]. Many-body localized (MBL) systems exhibit universal dynamics, qualitatively distinct from dynamics in ergodic systems. In this talk I will survey recent progress in understanding the properties of the MBL phase, which follow from the picture of local conserved quantities. In particular, I will discuss the power-law relaxation of local observables [3], which gives an experimentally observable signatures of the MBL phase. In the second part of my talk, I will demonstrate how the delocalization transition can be probed by characterizing the breakdown of local conservation laws. Using statistics of matrix elements of local operators, I will introduce an analogue of many-body Thouless conductance which probes the response of the system to local perturbations [4]. Its scaling allows one to locate the MBL transition, and predicts the onset of logarithmically slow transport at the MBL transition, consistent with results from the renormalization group [5,6]. In addition, I will demonstrate how the properties of matrix elements govern the crossover of the level statistics across the MBL transition, and relate to the dynamics in the ergodic phase. I will conclude by discussing experimental implications and open challenges in understanding the MBL transition.\\[0pt] [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, Phys. Rev. B 90, 174202 (2014).\\[0pt] [3] M. Serbyn, Z. Papic, D. A. Abanin, Phys. Rev. B 90, 174302 (2014). \\[0pt] [4] M. Serbyn, Z. Papic, D. A. Abanin, arXiv: 1507.01635.\\[0pt] [5] R. Vosk, D. A. Huse, E. Altman, Phys. Rev. X 5, 031032 (2015).\\[0pt] [6] A. C. Potter, R. Vaseur, S. A. Parameswaran, Phys. Rev. X 5, 031033 (2015). [Preview Abstract] |
Friday, March 18, 2016 10:24AM - 11:00AM |
X2.00005: Many-body localisation of interacting fermions in a quasi-random optical lattice Invited Speaker: Immanuel Bloch We experimentally observe many-body localization (MBL) of interacting fermions in a one-dimensional quasi-random optical lattice. We identify the many-body localization transition through the relaxation dynamics of an initially-prepared charge density wave. For sufficiently weak disorder the time evolution appears ergodic and thermalizing, erasing all remnants of the initial order. In contrast, above a critical disorder strength a significant portion of the initial ordering persists, thereby serving as an effective order parameter for localization. The stationary density wave order and the critical disorder value show a distinctive dependence on the interaction strength, in agreement with numerical simulations. I will also present recent results on the fate of an MBL system upon coupling to the environment through photon scattering or by coupling identical 1d systems. Finally, progress to observe MBL in a 2d setting of interacting bosons will be presented that can provide a new route for identifying and characterizing the MBL phase transition [Preview Abstract] |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700