PIRSA:14020127

Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics

Abanin, D. (2014). Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics. Perimeter Institute. https://pirsa.org/14020127

Abanin, Dmitry. Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics. Perimeter Institute, Feb. 12, 2014, https://pirsa.org/14020127 

          @misc{ pirsa_PIRSA:14020127,
            doi = {10.48660/14020127},
            url = {https://pirsa.org/14020127},
            author = {Abanin, Dmitry},
            keywords = {},
            language = {en},
            title = {Many-body localization: Local integrals of motion, area-law entanglement, and quantum dynamics},
            publisher = {Perimeter Institute},
            year = {2014},
            month = {feb},
            note = {PIRSA:14020127 see, \url{https://pirsa.org}}
          }

Dmitry Abanin

Talk number
PIRSA:14020127
Collection
Talk Type
Abstract
We demonstrate that the many-body localized phase is characterized by the existence of infinitely many local conservation laws. We argue that many-body eigenstates can be obtained from product states by a sequence of nearly local unitary transformation, and therefore have an area-law entanglement entropy, typical of ground states. Using this property, we construct the local integrals of motion in terms of projectors onto certain linear combinations of eigenstates [1]. The local integrals of motion can be viewed as effective quantum bits which have a conserved z-component that cannot decay. Thus, the dynamics is reduced to slow dephasing between distant effective bits. For initial product states, this leads to a characteristic slow power-law decay of local observables, which is measurable experimentally, as well as to logarithmic in time growth of entanglement entropy [2,3]. We support our findings by numerical simulations of random-field XXZ spin chains. Our work shows that the many-body localized phase is locally integrable, reveals a simple entanglement structure of eigenstates, and establishes the laws of dynamics in this phase.

[1] M. Serbyn, Z. Papic, D. A. Abanin, Phys. Rev. Lett. 111, 127201 (2013).
[2] Jens H. Bardarson, Frank Pollmann, and Joel E. Moore, Phys. Rev. Lett. 109, 017202 (2012).
[3] M. Serbyn, Z. Papic, D. A. Abanin, Phys. Rev. Lett. 110, 260601 (2013)