Constructing local integrals of motion in the many-body localized phase

By Anushya Chandran, Isaac H. Kim, Guifré Vidal, D. Abanin. 2014

224 citations recorded by the source corpus.

Many-body localization provides a generic mechanism of ergodicity breaking in quantum systems. In contrast to conventional ergodic systems, many-body localized (MBL) systems are characterized by extensively many local integrals of motion (LIOM), which underlie the absence of transport and thermalization in these systems. Here we report a physically motivated construction of local integrals of motion in the MBL phase. We show that any local operator (e.g., a local particle number or a spin flip operator), evolved with the system's Hamiltonian and averaged over time, becomes a LIOM in the MBL phase. Such operators have a clear physical meaning, describing the response of the MBL system to a local perturbation. In particular, when a local operator represents a density of some globally conserved quantity, the corresponding LIOM describes how this conserved quantity propagates through the MBL phase. Being uniquely defined and experimentally measurable, these LIOMs provide a natural tool for characterizing the properties of the MBL phase, both in experiments and numerical simulations. We demonstrate the latter by numerically constructing an extensive set of LIOMs in the MBL phase of a disordered spin chain model. We show that the resulting LIOMs are quasi-local, and use their decay to extract the localization length and establish the location of the transition between the MBL and ergodic phases.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/068b015a6dda38b9cc009d03786d96df5b082564

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In Atomic and Molecular Physics, and Optics

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

In Condensed Matter Physics

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

Citations in the corpus

• Local integrals of motion in many‐body localized systems (2016, background): “It was pointed out in [26] that the infinite-time average of any local operator O is a conserved quantity.”
• Colloquium : Many-body localization, thermalization, and entanglement (2018, result): “The critical exponent ν ≈ 3.3 found by both RG schemes is consistent with the Harris bound ν > 2/d (Chayes et al., 1986; Harris, 1974).”
• Complex Spacing Ratios: A Signature of Dissipative Quantum Chaos (2019, background): “In fact, some proposals to model MBL rely on approximate locally conserved quantities [103].”
• Criterion for Many-Body Localization-Delocalization Phase Transition (2015, unknown): “[13] and was also found to decay exponentially in the MBL phase.”