張量網絡演算法研究一維無限長耗散量子鏈的穩定態

在多體物理的領域,利用張量演算法來模擬量子系統是一個快速發展的領域,而其中已經過透測研究的時間演化區塊消除法可以讓我們精準的找到各種量子系統的基態,並也已經應用再各種不同的模型上。在這篇論文中,我們主要是建立在虛數一維無線時間演化區塊消除法的理論上,模擬利用電腦運算找到一維無線長耗散系統的穩定態。建立在傳統的虛數時間演化區塊消除法之上,我們也針對耗散量子系統做了一些演算法上的改進,包含:四個局部的時間演化區塊、多次根時間演化區塊。藉由這些改進方法,我們讓虛數時間演化區塊消除法更適合處理耗散量子系統。這個方法主要的優點在於:它能夠避開在實數時間演化區塊消除法演化到穩定態時的高度的量子糾纏區域。我們在易辛模型與橫向外加磁場的量子鏈上展現我們的成果,並且利用實數時間演化區塊消除法與其他數值方法來驗證我們結果。

關鍵字

時間演化區塊消除法；耗散系統；易辛模型

並列摘要

Using tensor netwrok to simulate quantum system has been rapidly developed recently. A well-developed tensor network algorithm called infinite time-evolving block decimation (iTEBD) allows us to find the ground state and detect the phase transitions of various quantum systems with great accuracy. In this work, we show that using iTEBD we can also determine the nonequilibrium steady states of one-dimensional dissipative quantum lattices in the thermodynamic limit. Besides conventional iTEBD algorithm, we propose some improvements on this algorithm, including four-local gate evolving block operator and k-th root on evolving block operator. By this means, we make the iTEBD algorithm more suitable for simulating dissipative quantum system. The primary benefit of using iTEBD algorithm on dssipative quantum systems is allowing one to bypass the potentially high entanglement during the transient dynamis of real time evolution to the steady states. We provide a demonstration with the transversed dissipative quantum Ising chain. We validate our results using real time evolution and some numerical methods.

並列關鍵字

Matrix product state ； imaginary time-evolving block decimation ； dissipative system

參考文獻

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國際替代計量

張量網絡演算法研究一維無限長耗散量子鏈的穩定態

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