Structure of Spin Correlations in High Temperature SU($N$) Quantum Magnets

TL;DR

This paper investigates the temperature-dependent spin correlations in SU(N) quantum magnets, revealing a common high-temperature correlation structure across lattices and N, with implications for experimental ultracold atom systems.

Contribution

It provides a detailed analysis of spin correlations in SU(N) models over a wide temperature range, highlighting a universal high-temperature regime and identifying disorder and Lifshitz temperatures.

Findings

Universal correlation structure at high temperatures for all N

Identification of disorder and Lifshitz temperatures in 1D and 2D lattices

Large-scale numerical results for SU(3) and SU(4) models

Abstract

Quantum magnets with a large SU($N$) symmetry are a promising playground for the discovery of new forms of exotic quantum matter. Motivated by recent experimental efforts to study SU($N$) quantum magnetism in samples of ultracold fermionic alkaline-earth-like atoms in optical lattices, we study here the temperature dependence of spin correlations in the SU($N$) Heisenberg spin model in a wide range of temperatures. We uncover a sizeable regime in temperature, starting at $T=\infty$ down to intermediate temperatures and for all $N\ge2$, in which the correlations have a common spatial structure on a broad range of lattices, with the sign of the correlations alternating from one Manhattan shell to the next, while the amplitude of the correlations is rapidly decreasing with distance. Focussing on the one-dimensional chain and the two-dimensional square and triangular lattice for certain $N$, we discuss the appearance of a disorder and a Lifshitz temperature, separating the commensurate Manhattan high-$T$ regime from a low-$T$ incommensurate regime. We observe that this temperature window is associated to an approximately $N$-independent entropy reduction from the $\ln(N)$ entropy at infinite temperature. Our results are based on high-temperature series arguments and as well as large-scale numerical full diagonalization results of thermodynamic quantities for SU($3$) and SU($4$) square lattice samples, corresponding to a total Hilbert space of up to $4\times 10^9$ states.