User sequence modeling is crucial for modern large-scale recommendation systems, as it enables the extraction of informative representations of users and items from their historical interactions. These user representations are widely used for a variety of downstream tasks to enhance users' online experience. A key challenge for learning these representations is the lack of labeled training data. While self-supervised learning (SSL) methods have emerged as a promising solution for learning representations from unlabeled data, many existing approaches rely on extensive negative sampling, which can be computationally expensive and may not always be feasible in real-world scenario. In this work, we propose an adaptation of Barlow Twins, a state-of-the-art SSL methods, to user sequence modeling by incorporating suitable augmentation methods. Our approach aims to mitigate the need for large negative sample batches, enabling effective representation learning with smaller batch sizes and limited labeled data. We evaluate our method on the MovieLens-1M, MovieLens-20M, and Yelp datasets, demonstrating that our method consistently outperforms the widely-used dual encoder model across three downstream tasks, achieving an 8%-20% improvement in accuracy. Our findings underscore the effectiveness of our approach in extracting valuable sequence-level information for user modeling, particularly in scenarios where labeled data is scarce and negative examples are limited.