Liquids in multi-orbital SU(N) Magnets with Ultracold Alkaline Earth Atoms

TL;DR

This paper explores algebraic liquid states in multi-orbital SU(N) spin systems realized with ultracold alkaline earth atoms, analyzing their stability, phase transitions, and underlying gauge symmetries for large N.

Contribution

It introduces five algebraic liquid states in k=2 orbital SU(N) systems, detailing their stabilization, properties, and phase transitions, expanding understanding of quantum liquids in cold atom systems.

Findings

Algebraic liquid states are stabilized at large N.

Scaling dimensions of order parameters are calculated systematically.

Phase transitions between liquid states are characterized.

Abstract

In this work we study one family of liquid states of k-orbital SU(N) spin systems, focusing on the case of k = 2 which can be realized by ultracold alkaline earth atoms trapped in optical lattices, with N as large as 10. Five different algebraic liquid states with selectively coupled charge, spin and orbital quantum fluctuations are considered. The algebraic liquid states can be stabilized with large enough N, and the scaling dimension of physical order parameters is calculated using a systematic 1/N expansion. The phase transitions between these liquid states are also studied, and all the algebraic liquid states discussed in this work can be obtained from one "mother" state with SU(2) x U(1) gauge symmetry.