本論文研究由存在交互作用的無自旋費米子所組成的多量子線接點的傳輸性質。結合密度矩陣重整化群以及無限邊界條件，我們開發一系列張量網絡方法，有效地模擬無限長量子線系統中鄰近接點的一段有限長範圍。在線性反應區間，系統的電導可藉由計算基態的電流—電流關聯函數，或在時間演化的模擬中直接測量求得。我們運用這些方法研究兩條與三條量子線的接點。關於由兩條相同量子線組成的接點，我們的數值結果不僅得到與理論預測相符的傳輸性質，更完整地求得關聯函數由短距離到長距離極限的跨度。此外我們發現在兩條異質量子線的接點，由基態關聯函數求得的電導與從動態模擬中測量到的不符。與理論比較後，我們認為電導與關聯函數的關係式需要進一步修正。針對三條量子線的Y接點，我們成功地模擬此前相關數值研究未曾達到的重整化群相態。本論文的數值結果可以為理論模型提供有效的驗證。

We investigate the transport in quantum multi-wire junctions of interacting spinless fermions. Combining the density matrix renormalization group with infinite boundary conditions, we develop tensor network methods to effectively simulate in the vicinity of the junction a finite region of an infinite quantum wire system. The linear-response conductance is then obtained either from the static current-current correlation function of the ground state, or from the direct measurement of the real-time transport. We apply the methods to two- and three-wire junctions. Our results for two-identical-wire junctions not only show good agreement with the theoretical predictions, but also reveal the full crossover of correlation functions between the short- and long-distance regimes. We further discuss the inconsistency in the conductance of two-different-wire junctions calculated from the static and the dynamic methods. We conclude that the static method needs more scrutiny when the two wires are different. For three-wire Y-junctions, we simulate a wide range of fermion interactions, including the regions with no numerical study reported before. Our results serve as a test for candidate theories of this system.

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