On the size of the space spanned by a nonequilibrium state in a quantum spin lattice system

Abstract

We consider the time evolution of a state in an isolated quantum spin lattice system with energy cumulants proportional to the number of the sites $L^d$. We compute the distribution of the eigenvalues of the time averaged state over a time window $[t_0,t_0+t]$ in the limit of large $L$. This allows us to infer the size of a subspace that captures time evolution in $[t_0,t_0+t]$ with an accuracy $1-\epsilon$. We estimate the size to be $\frac{\sqrt{2{\mathfrak{e}}_2}}{\pi }{\mathrm{erf}}^{-1}(1-\epsilon )L^{\frac{d}{2}}t$, where ${\mathfrak{e}}_2$ is the energy variance per site, and ${\mathrm{erf}}^{-1}$ is the inverse error function.

arXiv comment25 pages, 7 figures; new appendix with a proof that the energy cumulants are extensive whenever the Hamiltonian is quasilocal and the state has finite correlation lengths

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Cited by in corpus (3)

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• Macroscopic Length Correlations in Non-Equilibrium Systems and Their Possible Realizatons
• Energy-filtered quantum states and the emergence of non-local correlations