# Chiral Spin Condensation in a One-Dimensional Optical Lattice

## TL;DR

This paper predicts a novel chiral spin condensate in a one-dimensional optical lattice, characterized by staggered spin currents and described by a two-component Luttinger liquid, with potential experimental detection methods.

## Contribution

It introduces the concept of a chiral spin quasicondensate in a double-valley optical lattice and confirms its robustness through numerical simulations.

## Key findings

- Identification of a chiral spin order with staggered spin currents
- Confirmation of the phase's stability against interactions and fluctuations
- Establishment of a low-energy effective field theory as a two-component Luttinger liquid

## Abstract

We study a spinor (two-component) Bose gas confined in a one-dimensional double-valley optical lattice which has a double-well structure in momentum space. Based on field theory analysis, it is found that spinor bosons in the double-valley band may form a spin-charge mixed chiral spin quasicondensate under certain conditions. Our numerical calculations in a concrete $\pi$-flux triangular ladder system confirm the robustness of the chiral spin order against interactions and quantum fluctuations. This exotic atomic Bose-Einstein condensate exhibits spatially staggered spin loop currents without any charge dynamics despite the complete absence of spin-orbit coupling in the system, creating an interesting approach to atom spintronics. The entanglement entropy scaling allows us to extract conformal-field-theory central charge and establish the low-energy effective field theory for the chiral spin condensate as a two-component Luttinger liquid. Our predictions should be detectable in atomic experiments through spin-resolved time-of-flight techniques.