The Han Dynasty had definitely excelled in most of the PERSIA subjects, however what they had most excelled in was their RELIGION
Confucius, one of the biggest religious/philosophic influences in history
What the Han dynasty definitely excelled in was religion as Confucius was a big part of their legacy. Confucius was a great influence mainly on east Asia who shared his wisdom and smart ethics that are still lived up to til this day. An example of Confucius's ethics is: "Confucius teaches his students how to live a contented, moral and happy life. He wants people to associate with others who can act as their teachers. He encourages people to live by their principles and continue to build upon them. He tells others to love their work, because they will realize that they are not really working at all. In this natural state of mind, all six of the essential ethical principles are automatically being assimilated into the person’s being." (www.robwaxman.com) An example of Confucius's religious beliefs (other known as Confucianism) is, "Confucianism concerns itself primarily with ethical principles and does not address many traditional religious beliefs. These are generally provided by Chinese religion, Taoism, Buddhism, or other religion which Confucians follow. However, Confucius regarded Heaven (T'ien) as a positive and personal force in the universe; he was not, as some have supposed, an agnostic or a skeptic. He also taught a highly optimistic view of human nature and potential." (www.religionfacts.com/confucianism/beliefs) As you can see from the examples provided of Confucianism and its ethics it gave an optimistic and happy perspective on life and was generally a good way to follow life back in ancient China and is still a good way to follow life.
The second greatest subject the Han dynasty contributed were INTELLECTUAL ACHIEVEMENTS
The first ever form of paper
In particular one of the best things the Han dynasty has done is make the first form of paper instead of Papyrus like the Egyptians. This paper was very easy to make and you could even write on it however, at the time the Chinese people didn't know they could write on it but instead used it to wrap fish which was still a pretty good way to use paper. The Han had made the paper by: "It was a eunuch named Cai Lun who, around 105 CE, came up with an innovation that would be invaluable for learning. A screen was dipped into a vat of watery oatmeal-like pulp made of rice straw and inner tree bark. When the screen was raised, it had a layer of dripping slush on top, which was later pressed and dried. The end result was a sheet of paper." (www.ancient.eu/Han_Dynasty) So indeed paper was a marvelous invention that impacted future generations even up to our modern society. Another intellectual achievement was having add on's/extensions to the Great wall. Although Shi Huang Di and the Qin dynasty had the great idea of making and building the great wall it wasn't nearly fortified/finished. The Han realizes this and takes the wall and strengthens it to be more durable and to protect them from enemies. An example of how the Han fortified the wall is, "In 127 BC, Shuofang City was constructed at Hetao Area, and the previous Qin Dynasty Great Wall was renovated.In 121 BC, the Han troops regained the Hexi Corridor. Thereafter, the wall was built between Lingju (today's Yongdeng County) and Jiuquan in Gansu Province. From 111 BC to 110BC, the wall was extended from Jiuquan to Yumenguan. From 104BC to 100BC, the defense stretched from Yumenguan to Lop Nur in Xinjiang.After two decades of construction, the Great Wall of the Han Dynasty was finally completed, running from Liaoning in the east and ending at Lop Nur, Xinjiang in the west. The Hexi Corridor section was the most important because it protected the ancient Silk Road. Hence, many beacon towers, fortresses, and passes were erected." (https://www.travelchinaguide.com/china_great_wall/history/han/) As you can see the wall was enhanced a lot more in the Han dynasty making it have an even better history. Lastly the Silk Road was also made which was basically Asia (and Europe's) Trade Center where there were trades that benefited every country involved. The reason why it was called the Silk Road was because of the mass trade and desire of Silk while it was running.
The Third Subject that contributed to a subtopic of Intellectual Achievements, the Silk Road. This of course is the Han's ECONOMY.
The Han were indeed the creators of the famous "Silk Road" which was basically a European and Asian highway for trades, where countries could exchange their common or rare goods for other countries goods that may not be common where the country is or where the specific person. Also people traded anything for Silk (the Chinese had mass production of it) which had significantly boosted China's economy and also they got lots of rare goods and uncommon goods just from trading Silk. An example to support how the Silk road boosted the Han's wealth is, "The Silk Roads were dynamic and porous; goods were traded with local populations throughout, and local products were added into merchants’ cargos. This process enriched not only the merchants’ material wealth and the variety of their cargos, but also allowed for exchanges of culture, language and ideas to take place along the Silk Roads." (http://en.unesco.org/silkroad/about-silk-road) Another example is, "Since it could only be made in that region, silk became high in demand along the silk because it was seen as luxurious and a symbol of wealth for only the wealthy could afford its high price due to high costs in transportation.This caused The Silk Road to be more inclined to trade luxury items rather than ordinary goods that were not rare like silk and spices." (http://apworldwiki2011-12.weebly.com/case-study--silk-road.html) As you can see since there was such a high demand for silk, it caused it to be manufactured more and to therefore be sold/traded more which gave China more profit
The 4th subject that contributed to the Han's success was POLITICS
First Han Emperor, Liu Bang
It is very surprising to see "politics" below the top three that contributed for a very civilized society but yet this turns to be the case for the Han dynasty. The politics of each dynasty mainly lied with the emperor and their decisions so we will observe one emperor in specific of the Han dynasty: Liu Bang. Brief history on Liu Bang: First emperor of Han dynasty, used to be a soldier reigned from 202-195 BC and origin was a peasant. Political abolishments Liu Bang had done is, "After he ascended the throne, his first step was to abolish the harsh law of the Qin Dynasty and establish a new one that was supported by the people. Liu also took a series of measures that were good for his people. He ordered the reduction of field taxes levied on the peasants and let the armies go back to farming. Because of his strong leadership and effective measures, the economy recovered quickly and stability returned to the society. In the annuals of Chinese history, Liu Bang was regarded as an emperor who contributed a tremendous amount to the prosperity of the Han Dynasty." (https://www.travelchinaguide.com/intro/history/han/liubang.htm) The way Liu Bang united forces is, "Credited with his ability to both adopt his subordinate’s good advice as well as the political acumen to unite other anti-Xiang Yu forces, he eventually won the war. Xiang Yu, well-known as the King of Western Chu, committed suicide by cutting his throat with a sword beside Wujiang River." (https://www.travelchinaguide.com/intro/history/han/liubang.htm) So all in all this evidence proves how the emperors had a mostly positive contribution to the dynasty.
The Second-to-last subject that contributed to the Han dynasty success is SOCIAL STRUCTURE
Social Structure of the Han dynasty
The social structure of the Han dynasty or of China overall didn't really change or contribute that much as its like any other social class, slaves/poor -> merchants -> government/rich -> EMPEROR. So poor/forced to rich basic structure. Even if it was basic it did keep order according to this example, "Social order. Beneath the emperor, there were four main social classes in ancient China. These four classes were nobles and officials, peasants, artisans and merchants." (http://www.skwirk.com/p-c_s-14_u-173_t-471_c-1707/social-hierarchy/nsw/social-hierarchy/ancient-societies-china/ancient-china-part-i) another example is, "Social structure was very important in ancient China. The Chinese believed in strict social groups and people were expected to behave according to their social position. This belief was further reinforced by the Chinese philosopher Confucius, who taught that strict social order and discipline was the key to a successful society. Men and women in ancient China were not equal and men were afforded far more privileges than women. The Chinese strongly believed in the wisdom of the elders and, as such, grandparents were greatly respected." (http://www.skwirk.com/p-c_s-14_u-173_t-471_c-1707/social-hierarchy/nsw/social-hierarchy/ancient-societies-china/ancient-china-part-i) So even though it is a basic social structure it contributed a little bit as it kept social order and praise through out each dynasty.
Finally, the subject of PERSIA that least contributed to the Han dynasty's success is..... Arts and Architecture
Architecture made in the Han dynasty
Everyone can agree that art sometimes doesn't contribute to a civilization and it turns out that it is the same case with the Han dynasty so we are just going to focus on the Han dynasty's architecture. As you can see from the above picture it looks very similar to the picture below and the thing is...
Architecture of the Qin dynasty
One on top is Han and the one below is Qin! So basically the Han dynasty basically just regurgitates the architecture from previous dynasties so it has no impact at all on the dynasty. Examples from sources are, "The dynamic Han Dynasty (206 BCE – 220 CE) witnessed a significant revival in Chinese art, compared to the preceding era of Qin Dynasty art (221-206 BCE). Chinese pottery (notably ceramic figurines), jade carving (notably jade suits), silk weaving and Chinese painting (on paper) were three areas of particular achievement." (http://www.visual-arts-cork.com/east-asian-art/han-dynasty.htm) Another example is, "Han tombs and graves also contained a wide variety of figurative terracotta sculpture, known as ming-chi or yong. This was because, in the afterlife, the Chinese wanted to surround themselves with representations of people who had given them particular pleasure during their life." (http://www.visual-arts-cork.com/east-asian-art/han-dynasty.htm) As you can see the Han dynasty literally just repeats what the Han dynasty has done.