DMRG study of FQHE systems in the open cylinder geometry
G. Misguich, Th. Jolicoeur
备注：
11 pages, 5 figures, proceedings of the International Conference on Computer Simulation in Physics and beyond (CSP2020), October 12-16, 2020, Moscow, Russia
The study of the fractional quantum Hall liquid state of two-dimensional electrons requires a non-perturbative treatment of interactions. It is possible to perform exact diagonalizations of the Hamiltonian provided one considers only a small number of electrons in an appropriate geometry. Many insights have been obtained in the past from considering electrons moving on a sphere or on a torus. In the Landau gauge it is also natural to impose periodic boundary conditions in only one direction, the cylinder geometry. The interacting problem now looks formally like a one-dimensional problem that can be attacked by the standard DMRG algorithm. We have studied the efficiency of this algorithm to study the ground state properties of the electron liquid at lowest Landau level filling factor $ν=1/3$ when the interactions are truncated to the two most important repulsive hard-core components. Use of finite-size DMRG allows us to conclude that the ground state is a compressible two-electron bubble phase in agreement with previous Hartree-Fock calculations. We discuss the treatment of Coulomb interactions in the cylinder geometry. To regularize the long-distance behavior of the Coulomb potential, we compare two methods: using a Yukawa potential or forbidding arbitrary long distances by defining the interelectron distance as the chord distance through the cylinder. This allows us to observe the Wigner crystal state for small filling factor.
Nature of quantum spin liquids of the S=1/2 Heisenberg antiferromagnet on the triangular lattice: A parallel DMRG study
School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University（斯坦福材料能源科学研究所、SLAC国家加速器实验室和斯坦福大学）
Phase diagram of the anisotropic triangular lattice Hubbard model
在最近的一项研究[Phys. Rev. X 10，021042（2020）]中，我们使用无限圆柱体上的大规模密度矩阵重整化群（DMRG）模拟表明，三角晶格哈伯德模型具有手性自旋液相。在这项工作中，我们在模型中引入跳跃各向异性，使晶格上的三个不同的键之一比其他两个更强或更弱。我们实现的各向异性在两个不等价的方式，一个尊重镜像对称的圆柱和一个打破这种对称性。在各向异性的全范围内，从正方形晶格到弱耦合一维链，我们发现了各种各样的相。在各向同性极限附近，我们发现在我们以前的工作中确定的三个阶段：金属，手性自旋液体，和120 $^\circ$螺旋顺序，我们注意到，最近的一篇论文表明，显然金属相实际上可能是路德-金刚砂液体，这也将与我们的结果一致。当一个键被削弱一个相对较小的量时，基态很快变成正方晶格Néel序。当一个键被加强时，情况就不那么清楚了，我们发现的相位取决于各向异性的方向和圆柱体的周长。虽然我们的工作是我们所知的各向异性三角晶格哈伯德模型的第一个DMRG研究，我们发现的整体相图与以前发现的其他方法，如变分蒙特卡罗和动态平均场论是大致一致的。
Superconductivity and competing orders in honeycomb $t$-$J$ model: interplay of lattice geometry and next-nearest-neighbor hopping
School of Physical Science and Technology, ShanghaiTech University（上海科技大学物理科学与技术学院）；Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory and Stanford University（斯坦福材料能源科学研究所，SLAC国家加速器实验室和斯坦福大学）
Characterizing Random-singlet State in Two-dimensional Frustrated Quantum Magnets and Implications for the Double Perovskite Sr$_2$CuTe$_{1-x}$W$_{x}$O$_6$
受实验观察到的具有阻挫和无序的化合物中非磁性相的启发，我们研究了具有随机分布的最近邻$J_1$和次最近邻$J_2$耦合的自旋- $1/2$正方晶格海森堡模型的基态.利用密度矩阵重整化群（DMRG）方法，对周长达到$10$格点的圆柱体系进行了计算，发现在强键随机性存在的情况下，随着$J_2 / J_1$的增长，在Néel和条形磁性相之间存在一个无序相.自旋冻结参数的消失表明自旋玻璃有序的缺乏。大尺度DMRG结果揭示了自旋冻结参数的尺寸标度行为、平均自旋关联的幂律衰减和典型自旋关联的指数衰减，这与一维随机单重态的相应行为一致，并表征了这种无序相的随机单重态性质. DMRG模拟还为表征二维受抑磁体中的一类无序非磁性状态提供了见解和机会。我们还与现有的实验进行了比较，并提出了更多的测量方法来理解双钙钛矿Sr $_2$ CuTe $_{1-x}$ W $_{x}$ O $_6$中的类自旋液体行为。
