Unified theory of local integrals of motion

Abstract

Conservation laws are of paramount importance in our understanding of classical and quantum dynamics. Here, we present a general framework for constructing exact quantum integrals of motion with the desired locality and quantum numbers, which will be illustrated for the case of many-body-localization (MBL). The latter has been understood theoretically in terms of the existence of an extensive number of local integrals of motion (LIOMs). Using our approach, we show that one can express the task of finding LIOMs as an optimization problem. For some specifications, this problem surprisingly connects to the question of finding classical ground states of spin-glass models. Our work unifies previous results obtained in the MBL context and reveals intriguing connections between many-body localization, spin-glass physics, and constrained optimization problems.

v2: accepted for publication

References in corpus (12)

• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Spectral signatures of many-body localization with interacting photons
• QuSpin: a Python Package for Dynamics and Exact Diagonalisation of Quantum Many Body Systems part I: spin chains
• Constructing local integrals of motion in the many-body localized phase
• Many-Body Localization in the Age of Classical Computing
• Explicit construction of local conserved operators in disordered many-body systems
• Bounds on quantum evolution complexity via lattice cryptography
• Integrability and complexity in quantum spin chains
• Uncovering Local Integrability in Quantum Many-Body Dynamics
• Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction
• Finding local integrals of motion in quantum lattice models in the thermodynamic limit