Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions
Exploiting translational invariance in matrix product state simulations of spin chains with periodic boundary conditions
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DOI：
10.1103/physrevb.83.125104
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发表时间：
2010-05
影响因子：
3.7
通讯作者：
Bogdan Pirvu;F. Verstraete;G. Vidal
中科院分区：
文献类型：
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作者：
Bogdan Pirvu;F. Verstraete;G. Vidal
提出了一种近似具有周期边界条件的平移不变系统基态的矩阵积态算法。对于固定值的MPS键维D，我们讨论了如何使计算成本最小化以获得看似最优的MPS近似基态。在具有N个站点和相关长度ξ的链中，计算成本的形式缩放为g(D,ξ/N)D3，其中g（D,ξ/N）是一个非平凡函数。对于ξ <e:1> N，这种缩放减少到D3，与系统大小N无关，使我们的方法比以前的建议快N倍。我们应用该算法获得临界量子Ising和Heisenberg自旋-1/2模型以及非临界Heisenberg自旋-1模型基态的MPS近似。在临界情况下，对于任何链长N，我们发现一个依赖于模型的键维D(N)，在此之上，相关性的多项式衰减在整个系统中忠实地再现。
We present a matrix product state (MPS) algorithm to approximate ground states of translationally invariant systems with periodic boundary conditions. For a fixed value of the bond dimension D of the MPS, we discuss how to minimize the computational cost to obtain a seemingly optimal MPS approximation to the ground state. In a chain with N sites and correlation length ξ, the computational cost formally scales as g(D,ξ/N)D3, where g(D,ξ/N) is a nontrivial function. For ξâN, this scaling reduces to D3, independent of the system size N, making our method N times faster than previous proposals. We apply the algorithm to obtain MPS approximations for the ground states of the critical quantum Ising and Heisenberg spin-1/2 models as well as for the noncritical Heisenberg spin-1 model. In the critical case, for any chain length N, we find a model-dependent bond dimension D(N) above which the polynomial decay of correlations is faithfully reproduced throughout the entire system.