Surveying structural complexity in quantum many-body systems. (English) Zbl 1487.81119

Suen, Whei Yeap; Elliott, Thomas J.; Thompson, Jayne; Garner, Andrew J. P.; Mahoney, John R.; Vedral, Vlatko; Gu, Mile

J. Stat. Phys. 187, No. 1, Paper No. 4, 18 p. (2022).

Summary: Quantum many-body systems exhibit a rich and diverse range of exotic behaviours, owing to their underlying non-classical structure. These systems present a deep structure beyond those that can be captured by measures of correlation and entanglement alone. Using tools from complexity science, we characterise such structure. We investigate the structural complexities that can be found within the patterns that manifest from the observational data of these systems. In particular, using two prototypical quantum many-body systems as test cases – the one-dimensional quantum Ising and Bose-Hubbard models – we explore how different information-theoretic measures of complexity are able to identify different features of such patterns. This work furthers the understanding of fully-quantum notions of structure and complexity in quantum systems and dynamics.

MSC:

81S25	Quantum stochastic calculus
82B20	Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
68Q12	Quantum algorithms and complexity in the theory of computing
81V73	Bosonic systems in quantum theory
81P40	Quantum coherence, entanglement, quantum correlations
90C60	Abstract computational complexity for mathematical programming problems

Keywords:

quantum Ising; Bose Hubbard; complexity; quantum complexity; quantum model; stochastic process

Software:

Tensor Network Theory

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