Emergent symmetry in quantum phase transition:From deconfined quantum critical point to gapless quantum spin liquid

The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics,raising fundamental questions on the nature of quantum phase transitions.Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena,i.e.,the deconfined quantum critical point(DQCP)and the quantum spin liquid(QSL)state.Via large-scale tensor network simulations,we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic(AFM)model,namely the J1x-J1y-J2 model,which contains anisotropic nearestneighbor couplings J1x,J1y and the next nearest neighbor coupling J2.For small J1y/J1x,by tuning J2,a direct continuous transition between the AFM and valence bond solid phase is observed.With growing J1y/J1x,a gapless QSL phase gradually emerges between the AFM and VBS phases.We observe an emergent O(4)symmetry along the AFM–VBS transition line,which is consistent with the prediction of DQCP theory.Most surprisingly,we find that such an emergent O(4)symmetry holds for the whole QSL–VBS transition line as well.These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view,and strongly constrain the quantum field theory description of the QSL phase.The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems.

无能隙量子自旋液体和正方晶格自旋1/2阻挫反铁磁模型的相图

自高温超导发现以来,正方晶格上由自旋为1/2构成的包括近邻和次近邻海森堡相互作用的阻挫反铁磁模型,即J1±J2模型,因其基态被认为可以作为铜基超导的母态,在过去30多年中得到了广泛关注和深入研究.该模型包含的相互作用形式简单,如今也成为用来研究正方晶格上阻挫磁性的基本理论模型.但其基态性质仍然是一个悬而未决的问题.本文作者利用最近发展的二维张量网络态算法,对该模型进行了迄今为止精度最高的计算.详细的数值结果表明这个体系的基态包含了一个无能隙的量子自旋液体和价键固体态.他们进一步计算了相变的临界指数,提出了一个低能有效理论来描述这个量子自旋液体,并探讨了这个量子自旋液体与解禁闭量子临界性的关系.该工作通过仔细比较二维张量网络态和人们常用的密度矩阵重整化群两种算法的结果,提供了在正方晶格阻挫磁性体系的研究上第一个超越密度矩阵重整化方法的例子.他们也解释了以前研究结果矛盾之处的来源,为用二维张量网络态解决量子多体问题提供了一个范本.