量子自旋梯子磁体有限温度结题thesis defence.pptxVIP

量子自旋梯子磁体的有限温度张量网络算法研究——本科学位论文答辩答辩人：董勇良指导老师：李伟

PART01PART02PART03PART05研究背景双层线性张量网络重整化群梯子结构热张量网络发表论文PART04结论PART06参考文献PART07致谢

01研究背景01准一维量子自旋材料的奇特性质021DQuasi1D低维强关联量子多体系统Field-InducedSuperconductivityinaSpin-LadderCuprate,Science293(5539):2430-2Ch.Rüeggetal.,ThermodynamicsoftheSpinLuttingerLiquidinaModelLadderMaterial,Phys.Rev.Lett.101,247202

01研究背景01研究现状超格点矩阵乘积算符（matrixproductoperator，MPO）含长程相互作用的蛇形MPO梯子结构张量网络算法，LadderTensorNetworkAlgorithm02简单的优化策略，Simpleupdate全局的优化策略，Fullupdate

01研究背景毕业论文主要工作双层线性张量网络重整化群算法准一维梯子结构热张量网络Y.Dong,LeiChen,Yun-JingLiu,andWeiLi.Bilayerlinearizedtensorrenormalizationgroupapproachforthermaltensornetworks.Phys.Rev.B95,144428(2017)Finite-TemperatureTensorNetworkAlgorithmsinSpinLadderQuantumMagnets

02双层线性张量网络重整化群TrotterpositionTrotterpositionPartitionfunction01转移矩阵重整化群，Transfermatrixrenormalizationgroup(TMRG)02X.WangandT.Xiang,Transfer-matrixdensity-matrixrenormalization-grouptheoryforthermodynamicsofone-dimensionalquantumsystems,Phys.Rev.B56,5061(1997)

02双层线性张量网络重整化群线性张量网络重整化群，LinearizedTensorRenormalizationGroup(LTRG)ThermaltensornetworkrepresentationConsiderhorizontaltransfermatrices1.W.Li,S.J.Ran,S.S.Gong,Y.Zhao,B.Xi,F.Ye,andG.Su,LinearizedTensorRenormalizationGroupAlgorithmfortheCalculationofThermodynamicPropertiesofQuantumLatticeModels,Phys.Rev.Lett.106,127202(2011).

02双层线性张量网络重整化群?????Y.Dong,LeiChen,Yun-JingLiu,andWeiLi.Bilayerlinearizedtensorrenormalizationgroupapproachforthermaltensornetworks.Phys.Rev.B95,144428(2017)

02双层线性张量网络重整化群（a）双层LTRG算法在全温区的计算结果都更精确。（b）双层LTRG算法在不同链长情况下计算结果都更精确。Single-layerDouble-layer

03梯子结构热张量网络梯子结构张量网络算法，LadderTensorNetworkAlgorithmQuasione-dimensionalTMRGLTRG0102简单的优化策略，Simpleupdate全局的优化策略，Fullupdate

03梯子结构热张量网络SimpleUpdate约化矩阵，ReducedmatrixComputationcost:???Computationcost:runglegW.Li,J.vonDelft,andT.Xiang.