【摘要】：量子多體系統(tǒng)熱力學(xué)性質(zhì)的精確模擬在理論和實驗方面都具有重要的價值。局域相互作用量子多體系統(tǒng)的熱態(tài)滿足互信息(mutual information)面積律,對于這樣的系統(tǒng),熱態(tài)張量網(wǎng)絡(luò)可以提供滿足面積律的精確"波函數(shù)"擬設(shè),提供了模擬有限溫度系統(tǒng)的有力手段。文章介紹了關(guān)聯(lián)格點模型在有限溫度下的熱態(tài)張量網(wǎng)絡(luò)刻畫及相關(guān)模擬方法。作者按照世界線熱態(tài)張量網(wǎng)絡(luò)和級數(shù)展開熱態(tài)張量網(wǎng)絡(luò)來分別介紹,并討論了自由能極小變分原理與重正化群剪裁的優(yōu)化原則。世界線框架內(nèi),人們發(fā)展了轉(zhuǎn)移矩陣重正化群,基于純化策略的有限溫度密度矩陣重正化群,以及張量網(wǎng)絡(luò)的線性重正化群等方法。在此基礎(chǔ)上,介紹作者新近提出的級數(shù)展開熱態(tài)張量網(wǎng)絡(luò)方法,該方法受隨機級數(shù)展開量子蒙特卡羅方法的啟發(fā),突破了世界線方法的局限,提高了有限溫度計算重正化群模擬的精度標(biāo)準(zhǔn),并且在計算阻挫量子自旋鏈模型時不會有負(fù)符號問題。此外,文章討論了在兩維格點系統(tǒng)上推廣有限溫度張量網(wǎng)絡(luò)計算的進(jìn)展和未來展望。
[Abstract]:Accurate simulation of thermodynamic properties of quantum multibody systems is of great value in both theory and experiment. The thermal state of the local interacting quantum multi-body system satisfies the mutual information (mutual information) area law. For such a system, the hot Zhang Liang network can provide an accurate "wave function" to satisfy the area law and provide a powerful means to simulate the finite temperature system. This paper introduces the description of the hot Zhang Liang network and the related simulation method of the correlation lattice model at finite temperature. In this paper, the author introduces the hot state Zhang Liang network according to the world line hot Zhang Liang network and the series expansion, and discusses the principle of minimal variation of free energy and the optimization principle of renormalization group tailoring. Within the framework of the world line, transfer matrix renormalization group, finite temperature density matrix renormalization group based on purification strategy and linear renormalization group based on Zhang Liang network have been developed. On this basis, a series expansion hot Zhang Liang network method proposed by the author is introduced. The method is inspired by the random series expansion quantum Monte Carlo method and breaks through the limitation of the world line method. The precision standard of renormalization group simulation for finite temperature calculation is improved, and there is no negative sign problem in calculating the retarded quantum spin chain model. In addition, this paper discusses the progress and future prospects of extending the finite temperature Zhang Liang network on a two dimensional lattice system.
【作者單位】： 北京航空航天大學(xué)物理系;北京航空航天大學(xué)國際交叉科學(xué)研究院;
【基金】：國家自然科學(xué)基金(批準(zhǔn)號:11504014) 北京航空航天大學(xué)卓越百人計劃和拔尖人才支持計劃資助項目
【分類號】：O413.3

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