Variational counterdiabatic driving of the Hubbard model for ground-state preparation
Variational counterdiabatic driving of the Hubbard model for ground-state preparation
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DOI：
10.1103/physrevb.106.155153
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发表时间：
2022-06
影响因子：
3.7
通讯作者：
Q. Xie;K. Seki;S. Yunoki
中科院分区：
文献类型：
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作者：
Q. Xie;K. Seki;S. Yunoki
反绝热(CD)协议通过调用辅助绝热规范势(AGP)来实现量子态的快速驱动，该辅助绝热规范势在驱动过程中抑制到激发态的跃迁。通常情况下，原始非辅助哈密顿量的全谱是构造精确AGP的先决条件，这意味着CD协议对于多体系统来说是极端的diffi崇拜。在这里，我们应用了P.W.Claeys等人最近提出的变分CD协议。[物理。莱特牧师。123,090602(2019年)]到一个空间维度的两分量费米子哈伯德模型。该协议使用一个近似的AGP，表示为一系列嵌套的换向器。我们证明了近似AGP中的最优变分参数满足一组线性方程，其CoEffi系数由这些交换子的平方Frobenius范数给出。我们设计了一个精确的算法，它避开了强大的迭代矩阵-向量乘法，并计算了解析表示中的嵌套交换子和CD哈密顿量。然后，我们研究了一维Hubbard模型的CD驱动，直至L=14个位置，驱动顺序为L(CID：54)3。我们的结果证明了变分CD方案对Hubbard模型的有效性，并为多体系统的快速基态准备提供了一条可能的途径。
Counterdiabatic (CD) protocols enable fast driving of quantum states by invoking an auxiliary adiabatic gauge potential (AGP) that suppresses transitions to excited states throughout the driving process. Usually, the full spectrum of the original unassisted Hamiltonian is a prerequisite for constructing the exact AGP, which implies that CD protocols are extremely di ffi cult for many-body systems. Here, we apply a variational CD protocol recently proposed by P. W. Claeys et al. [Phys. Rev. Lett. 123 , 090602 (2019)] to a two-component fermionic Hubbard model in one spatial dimension. This protocol engages an approximated AGP expressed as a series of nested commutators. We show that the optimal variational parameters in the approximated AGP satisfy a set of linear equations whose coe ffi cients are given by the squared Frobenius norms of these commutators. We devise an exact algorithm that escapes the formidable iterative matrix-vector multiplications and evaluates the nested commutators and the CD Hamiltonian in analytic representations. We then examine the CD driving of the one-dimensional Hubbard model up to L = 14 sites with driving order l (cid:54) 3. Our results demonstrate the usefulness of the variational CD protocol to the Hubbard model and permit a possible route towards fast ground-state preparation for many-body systems.