Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets

TL;DR

This paper investigates how entropy influences correlations in one-dimensional SU(N) antiferromagnetic models, revealing that short-range correlations emerge at specific entropy levels, which vary with N and are experimentally accessible.

Contribution

It provides the first detailed analysis of entropy dependence of correlations in SU(N) Heisenberg chains using Monte Carlo simulations for N=2 to 5.

Findings

Short-range correlations develop at low temperature as precursors to algebraic ground state correlations.

The entropy at which short-range order appears increases with N, reaching 0.8k_B at N=4.

Results are relevant for experimental realization with multi-color fermionic atoms in optical lattices.

Abstract

Motivated by the possibility to load multi-color fermionic atoms in optical lattices, we study the entropy dependence of the properties of the one-dimensional antiferromagnetic SU(N) Heisenberg model, the effective model of the SU(N) Hubbard model with one particle per site (filling 1/N). Using continuous-time world line Monte Carlo simulations for N=2 to 5, we show that characteristic short-range correlations develop at low temperature as a precursor of the ground state algebraic correlations. We also calculate the entropy as a function of temperature, and we show that the first sign of short-range order appears at an entropy per particle that increases with N and already reaches 0.8k_B at N=4, in the range of experimentally accessible values.