Compact unary coding for bosonic states as efficient as conventional binary encoding for fermionic states
Compact unary coding for bosonic states as efficient as conventional binary encoding for fermionic states
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DOI：
10.1103/physrevb.105.l121116
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发表时间：
2021-09
影响因子：
3.7
通讯作者：
H. Barghathi;Caleb Usadi;Micah Beck;A. Del Maestro
中科院分区：
文献类型：
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作者：
H. Barghathi;Caleb Usadi;Micah Beck;A. Del Maestro
基于著名的“球和壁”理论，我们引入了一种玻色子占据态的一元编码方法，该方法计算了N个不可区分粒子在L个可区分位置上的构型数量。每个状态都由一个整数表示，该整数带有一个人类可读的位串，该位串具有一个组合结构，允许有效地应用局部修改玻色子数量的算子。通过利用平移和反转对称性，我们确定了在生成玻色子晶格模型的基态时，比现有方法有L阶的加速因子。一元编码应用于一维玻色-哈伯德哈密顿量，最高为$L=N=20$，生成基态块所需的时间减少到对角化时间的一小部分。对于基态对称分辨纠缠，我们证明了限制局域玻色子希尔伯特空间的变分方法可能导致随系统大小缩放的误差。
We introduce a unary coding of bosonic occupation states based on the famous"balls and walls"counting for the number of configurations of $N$ indistinguishable particles on $L$ distinguishable sites. Each state is represented by an integer with a human readable bit string that has a compositional structure allowing for the efficient application of operators that locally modify the number of bosons. By exploiting translational and inversion symmetries, we identify a speedup factor of order $L$ over current methods when generating the basis states of bosonic lattice models. The unary coding is applied to a one-dimensional Bose-Hubbard Hamiltonian with up to $L=N=20$, and the time needed to generate the ground state block is reduced to a fraction of the diagonalization time. For the ground state symmetry resolved entanglement, we demonstrate that variational approaches restricting the local bosonic Hilbert space could result in an error that scales with system size.