SciPost logo

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

Maurizio Fagotti

SciPost Phys. 6, 059 (2019) · published 15 May 2019

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.

Cited by 3

Crossref Cited-by

Ontology / Topics

See full Ontology or Topics database.

Quantum spin chains

Author / Affiliation: mappings to Contributors and Organizations

See all Organizations.
Funders for the research work leading to this publication