论文标题
边界磁场任意方向的量子自旋链中的纠缠和边界熵
Entanglement and boundary entropy in quantum spin chains with arbitrary direction of the boundary magnetic fields
论文作者
论文摘要
我们在临界量子旋转链中计算纠缠和通用边界熵（BE），例如横向场ISING链和XXZ链，具有边界磁场（ADBMF）的任意方向。我们确定ADBMF引起的边界通用类别。特别是，我们表明诱导的边界形式磁场理论（BCFT）取决于边界磁场指向的Bloch球上的点。我们表明，方向的分类归结为一个简单的事实，即边界场打破了散装对称性或没有。我们提出了一个适用于ADBMF的纠缠熵的有限尺寸校正，以估算通用BE。为了计算XXZ链中的通用BE，我们使用密度矩阵重新归一化组（DMRG）。 Jordan-Wigner（JW）转换后，带有ADBMF的横向场XY链并不是二次自由费米昂Hamiltonian。我们通过引入两个额外的辅助旋转与边界的主链相结合的两个额外的辅助旋转，从而将此模型映射到一个二次自由费。横向场XY链的本征态可以通过放大链中的适当投影获得。使用此映射，我们能够使用通常的相关矩阵技术来计算横向场XY链的纠缠熵，直到相对较大的尺寸。
We calculate the entanglement and the universal boundary entropy (BE) in the critical quantum spin chains, such as the transverse field Ising chain and the XXZ chain, with arbitrary direction of the boundary magnetic field (ADBMF). We determine the boundary universality class that an ADBMF induces. In particular, we show that the induced boundary conformal field theory (BCFT) depends on the point on the Bloch sphere where the boundary magnetic field directs. We show that the classification of the directions boils down to the simple fact that the boundary field breaks the bulk symmetry or does not. We present a procedure to estimate the universal BE, based on the finite-size corrections of the entanglement entropy, that apply to the ADBMF. To calculate the universal BE in the XXZ chain, we use the density matrix renormalization group (DMRG). The transverse field XY chain with ADBMF after Jordan-Wigner (JW) transformation is not a quadratic free fermion Hamiltonian. We map this model to a quadratic free fermion chain by introducing two extra ancillary spins coupled to the main chain at the boundaries, which makes the problem {\it{integrable}}. The eigenstates of the transverse field XY chain can be obtained by proper projection in the enlarged chain. Using this mapping, we are able to calculate the entanglement entropy of the transverse field XY chain using the usual correlation matrix technique up to relatively large sizes.
