$N$-Scaling of Timescales in Long-Range $N$-Body Quantum Systems

Abstract

Long-range interacting many-body systems exhibit a number of peculiar and intriguing properties. One of those is the scaling of relaxation times with the number $N$ of particles in a system. In this paper I give a survey of results on long-range quantum spin models that illustrate this scaling behaviour, and provide indications for its common occurrence by making use of Lieb-Robinson bounds. I argue that these findings may help in understanding the extraordinarily short equilibration timescales predicted by typicality techniques.

11 pages, 4 figures. Invited contribution to the STATPHYS26 Special Issue in JSTAT

References in corpus (9)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
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• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Propagation of Correlations in Quantum Lattice Systems
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Cited by in corpus (4)

• Symmetries and conserved quantities of boundary time crystals in generalized spin models
• Suppression of heating by long-range interactions in periodically driven spin chains
• Impact of dephasing on non-equilibrium steady-state transport in fermionic chains with long-range hopping
• Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators