基于双曲变形的间隙估计
Gap Estimation by means of Hyperbolic Deformation
摘要：
提出了一种适用于一维无限均匀量子系统的数值能隙估计方法。利用密度矩阵重整化群方法，对非均匀哈密顿量进行了分析，得到了非均匀哈密顿量作为$j$的一个极限，该非均匀哈密顿量具有与$\cosh λj$成正比的变形相互作用强度.作为变形的结果，激发的准粒子围绕系统的中心是弱有界的，并且远离系统边界。因此，变形系统的估计激发间隙对边界的不敏感性允许我们具有体激发间隙$Δ(λ)$，并且当$λ\ll 1$时，$Δ(λ)$从$Δ(0)$的偏移在$λ$中几乎是线性的。这种估计的效率证明通过应用到S=1反铁磁海森堡链。结合上述估计和由数值对角化估计的有限尺寸间隙的收敛加速技术获得的另一个估计，我们得出结论，Haldom间隙在$[0.41047905,~0.41047931]$中。
英文摘要：
We present a way of numerical gap estimation applicable for one-dimensional infinite uniform quantum systems. Using the density matrix renormalization group method for a non-uniform Hamiltonian, which has deformed interaction strength of $j$-th bond proportional to $\cosh λj$, the uniform Hamiltonian is analyzed as a limit of $λ\to 0$. As a consequence of the deformation, an excited quasi-particle is weakly bounded around the center of the system, and kept away from the system boundary. Therefore, insensitivity of an estimated excitation gap of the deformed system to the boundary allows us to have the bulk excitation gap $Δ(λ)$, and shift in $Δ(λ)$ from $Δ(0)$ is nearly linear in $λ$ when $λ\ll 1$. Efficiency of this estimation is demonstrated through application to the S=1 antiferromagnetic Heisenberg chain. Combining the above estimation and another one obtained from the technique of convergence acceleration for finite-size gaps estimated by numerical diagonalizations, we conclude that the Haldane gap is in $[0.41047905,~0.41047931]$.
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