The entanglement spectrum of the reduced density matrix contains information beyond the von Neumann entropy and provides unique insights into exotic orders or critical behavior of quantum systems. Here, we show that strongly disordered systems in the many-body localized phase have power-law entanglement spectra, arising from the presence of extensively many local integrals of motion. The power-law entanglement spectrum distinguishes many-body localized systems from ergodic systems, as well as from ground states of gapped integrable models or free systems in the vicinity of scale-invariant critical points. We confirm our results using large-scale exact diagonalization. In addition, we develop a matrix-product state algorithm which allows us to access the eigenstates of large systems close to the localization transition, and discuss general implications of our results for variational studies of highly excited eigenstates in many-body localized systems.
Physical Review Letters
We thank M. Stoudenmire and C. Turner for useful discussions. M. S. was supported by Gordon and Betty Moore Foundation's EPiQS Initiative through Grant No. GBMF4307. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915, and by the Swiss National Science Foundation and Alfred Sloan Foundation (D. A.). This work made use of the facilities of N8 HPC Centre of Excellence, provided and funded by the N8 consortium and EPSRC (Grant No. EP/K000225/1). The Centre is coordinated by the Universities of Leeds and Manchester.
Serbyn M, Michailidis A, Abanin D, Papić Z. Power-law entanglement spectrum in many-body localized phases. Physical Review Letters. 2016;117(16). doi:10.1103/PhysRevLett.117.160601
Serbyn, M., Michailidis, A., Abanin, D., & Papić, Z. (2016). Power-law entanglement spectrum in many-body localized phases. Physical Review Letters. American Physical Society. https://doi.org/10.1103/PhysRevLett.117.160601
Serbyn, Maksym, Alexios Michailidis, Dmitry Abanin, and Zlatko Papić. “Power-Law Entanglement Spectrum in Many-Body Localized Phases.” Physical Review Letters. American Physical Society, 2016. https://doi.org/10.1103/PhysRevLett.117.160601.
M. Serbyn, A. Michailidis, D. Abanin, and Z. Papić, “Power-law entanglement spectrum in many-body localized phases,” Physical Review Letters, vol. 117, no. 16. American Physical Society, 2016.
Serbyn M, Michailidis A, Abanin D, Papić Z. 2016. Power-law entanglement spectrum in many-body localized phases. Physical Review Letters. 117(16).
Serbyn, Maksym, et al. “Power-Law Entanglement Spectrum in Many-Body Localized Phases.” Physical Review Letters, vol. 117, no. 16, American Physical Society, 2016, doi:10.1103/PhysRevLett.117.160601.