Information storage capacity of discrete spin systems

TL;DR

This paper constructs gapped spin systems that asymptotically reach the theoretical maximum information storage capacity, using fractal properties inspired by the Sierpinski triangle, bridging physics and information science.

Contribution

It introduces a novel spin system design that saturates the information storage bound, advancing understanding of physical limits and error-correcting codes.

Findings

Constructed spin systems saturate the theoretical information capacity bound.

Provides a physically realizable classical error-correcting code in gapped Hamiltonians.

Opens new research directions in fractal spin phases and correlated spin configurations.

Abstract

Understanding the limits imposed on information storage capacity of physical systems is a problem of fundamental and practical importance which bridges physics and information science. There is a well-known upper bound on the amount of information that can be stored reliably in a given volume of discrete spin systems which are supported by gapped local Hamiltonians. However, all the previously known systems were far below this theoretical bound, and it remained open whether there exists a gapped spin system that saturates this bound. Here, we present a construction of spin systems which saturate this theoretical limit asymptotically by borrowing an idea from fractal properties arising in the Sierpinski triangle. Our construction provides not only the best classical error-correcting code which is physically realizable as the energy ground space of gapped frustration-free Hamiltonians, but also a new research avenue for correlated spin phases with fractal spin configurations.