Many-body localization from a single-particle perspective

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• Fabian Heidrich-Meisner (LMU, Munich)
• Tuesday 09 May 2017, 13:45-15:00
• Theory Library.

If you have a question about this talk, please contact Mike Gunn.

NOTE TALK ON TUESDAY

We consider the paradigmatic model for many-body localization (MBL), spinless fermions in one dimension with a short-range repulsive interaction. This model, based on numerous previous studies, realizes a transition from an ergodic phase to the MBL phase at finite energy densities as a function of disorder strength.

We show that the one-particle density matrix can be used to characterize these two different phases by analyzing both its eigenstates and eigenvalues (the occupation spectrum). The eigenstates of the one-particle density matrix (OPDM) are localized in the many-body localized phase and spread out when one enters into the delocalized phase, in analogy to the behavior of single-particle energy eigenstates in the Anderson problem. In the MBL phase, the OPDM eigenstates have exponential tails and thus allow us to extract a measure of the localization length.

The OPDM eigenvalues reveal the distinctive Fock-space structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. This suggests a close analogy to weakly interacting Fermi gases: the MBL phase is very similar to a zero-temperature Fermi liquid and the discontinuity indicates the existence of quasiparticles in the MBL phase. These quasiparticles are identified as the emergent quasi-local conserved charges (l-bits) proposed to exist in the MBL phase in other studies. Computing the discontinuity in the occupation spectrum as a function of energy density, interaction strength or disorder strength can be used to detect the transition, resulting in a good agreement with other measures such as entanglement fluctuations or level spacing statistics.

This talk is part of the Theoretical Physics Seminars series.

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