Integrals of motion in the many-body localized phase

By V. Ros, Markus P. Müller, Antonello Scardicchio. 2014

405 citations recorded by the source corpus.

Abstract We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum { 0 , 1 } , thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization–delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d4d1e65729109b6191e3ea27adb6e58ec90aa9f3

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In Atomic and Molecular Physics, and Optics

1. V. Khemani
2. D. Abanin
3. Tomaz Prosen
4. Maksym Serbyn
5. I. Bloch
6. D. Huse
7. J. Imbrie
8. E. Altman

Citations in the corpus

• Ergodicity breaking transition in finite disordered spin chains (2020, methodology): “[76] V.”
• On Many-Body Localization for Quantum Spin Chains (2014, background): “The idea is to compare the energy differences of H ( j−1) ′ 0 + J ( j)sint that are associated with the block b̄( j) with those of another Hamiltonian ¯̄H in the volume ¯̄b( j) ∩ .”
• Low-frequency conductivity in many-body localized systems (2015, background): “[16] V.”
• Local integrals of motion in many‐body localized systems (2016, background): “It is shown in [90] that there exists a unique choice of ∆Kn α ∈ K that ensures that the spectrum of (28) is binary, i.”
• Constructing local integrals of motion in the many-body localized phase (2014, methodology): “[20] follows the approximate perturbative arguments of Basko, et al.”
• Colloquium : Many-body localization, thermalization, and entanglement (2018, methodology): “Ros et al. (2015) constructed the LIOMs using a perturbative technique similar to the self-consistent Born approximation of (Basko et al., 2006).”
• Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “(56) has zero bipartite entanglement; in the thermal phase, h < hc, the half-chain entanglement entropy grows rapidly (red curve) towards a value which is extensive in system size; the growth on the MBL side, h > hc, in contrast is much slower, first achieving a sub-extensive level similar to that o”