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

Gapless quantum spin liquid and global phase diagram of the spin-1/2 J_(1)-J_(2) square antiferromagnetic Heisenberg model

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.

The nature of the zero-temperature phase diagram of the spin-1/2 J_(1)-J_(2)Heisenberg model on a square lattice has been debated in the past three decades,and it remains one of the fundamental problems unsettled in the study of quantum many-body theory.By using the state-of-the-art tensor network method,specifically,the finite projected entangled pair state(PEPS)algorithm,to simulate the global phase diagram of the J_(1)-J_(2)Heisenberg model up to 24×24 sites,we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid(QSL),whose spin-spin and dimer-dimer correlations both decay with a power law behavior.There also exists a valence-bond solid(VBS)phase in a very narrow region 0.56■J_(2)/J_(1)≤0.61 before the system enters the well known collinear antiferromagnetic phase.We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group(DMRG)method through one-to-one direct benchmark for small system sizes,and thus give rise to a very solid PEPS calculation beyond DMRG.Our numerical evidences explicitly demonstrate the huge power of PEPS for highly frustrated spin systems.Finally,an effective field theory is also proposed to understand the physical nature of the discovered gapless QSL and its relation to deconfined quantum critical point(DQCP).