Infinite-range correlations in 1D systems with continuous symmetry

TL;DR

This paper demonstrates that 1D O(N)-symmetric scalar field systems with chemical potential can exhibit infinite-range correlations and non-zero vacuum expectation values at specific chemical potential values, challenging traditional expectations.

Contribution

It reveals that such 1D systems can produce infinite-range correlations and spontaneous symmetry breaking under certain conditions, providing new insights into low-dimensional quantum field behaviors.

Findings

Infinite-range correlations occur at specific chemical potentials.

Non-zero vacuum expectation values are possible in 1D systems.

Discussion relates findings to the Mermin-Wagner theorem.

Abstract

O(N)-symmetric lattice scalar fields are considered, coupled to a chemical potential and source terms. At the example of N=2, it is shown that such systems can even in (0+1) dimensions produce infinite-range correlations and a non-zero vacuum expectation value whenever the chemical potential assumes certain discrete values. Different mechanisms for how the latter phenomena are produced are discussed, depending on whether source terms are set to zero or non-zero values. In the conclusion, the relation of these findings to the Mermin-Wagner theorem is addressed.