The emerging parallel chain protocols represent a breakthrough to address the scalability of blockchain. By composing multiple parallel chain instances, the whole systems' throughput can approach the network capacity. How to coordinate different chains' blocks and to construct them into a global ordering is critical to the performance of parallel chain protocol. However, the existed solutions use either the global synchronization clock with the single-chain bottleneck or pre-defined ordering sequences with distortion of blocks' causality to order blocks. In addition, the prior ordering methods rely on that honest participants faithfully follow the ordering protocol, but remain silent for any denial of ordering (DoR) attack. On the other hand, the conflicting transactions included into the global block sequence will make Simple Payment Verification (SPV) difficult. Clients usually need to store a full record of transactions to distinguish the conflictions and tell whether transactions are confirmed. However, the requirement for a full record will greatly hinder blockchains' application, especially for mobile scenarios. In this technical report, we propose Eunomia, which leverages logical clock and fine-grained UTXO sharding to realize a simple, efficient, secure and permissionless parallel chain protocol. By observing the characteristics of the parallel chain, we find the blocks ordering issue in parallel chain has many similarities with the event ordering in the distributed system. Eunomia thus adopts "virtual" logical clock, which is optimized to have the minimum protocol overhead and runs in a distributed way. In addition, Eunomia combines the mining incentive with block ordering, providing incentive compatibility against DoR attack. What's more, the fine-grained UTXO sharding does well solve the conflicting transactions in parallel chain and is shown to be SPV-friendly.