arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2008.09736cond-mat.str-el
收藏

具有三体相互作用的可调谐量子自旋链

Tunable quantum spin chain with three-body interactions

Khagendra Adhikari, K. S. D. Beach

摘要:

我们介绍了一个推广的Fredkin自旋链与可调三体相互作用表示在传统的自旋半运营商。在模型的两个自由参数中,一个控制着对伊辛反铁磁性的偏好,另一个控制着量子涨落的强度。在这个公式中,所谓的$t$ -变形模型(一个精确可解的、无挫折的哈密顿量)存在于以相图原点为中心的单位圆上。这个圆圈划分了内部铁磁有序和外部各种反铁磁相之间的边界。在相图的大多数非铁磁部分中,基态具有戴克字形式:即,所有起作用的自旋构型都表现出上旋和下旋的完美匹配和嵌套。例外的是两个地区,其中戴克词不匹配是积极有利的。我们注意到,在这些地区的能级间距可以指数小的系统的大小。精确对角化也揭示了一个高度特异的能谱,这可能是因为链端的硬自旋扭曲在链长小时对本体系统产生了强烈的不可压缩性效应。作为收敛性检查,我们将DMRG结果与精确可解点的分析结果和整个参数空间中小系统尺寸的精确对角化结果进行基准测试,以接近双精度浮点精度。

英文摘要:

We introduce a generalization of the Fredkin spin chain with tunable three-body interactions expressed in terms of conventional spin-half operators. Of the model's two free parameters, one controls the preference for Ising antiferromagnetism and the other controls the strength of quantum fluctuations. In this formulation, the so-called $t$-deformed model (an exactly solvable, frustration-free Hamiltonian) lives on a unit circle centered on the origin of the phase diagram. The circle demarcates the boundary between ferromagnetic order inside and various antiferromagnetic phases outside. Throughout most of the non-ferromagnetic parts of the phase diagram, the ground state has Dyck word form: i.e., all contributing spin configurations exhibit perfect matching and nesting of spin up and spin down. The exceptions are two regions in which Dyck word mismatches are energetically favorable. We remark that in those regions the energy level spacing can be exponentially small in the system size. It is also the case that exact diagonalization reveals a highly idiosyncratic energy spectrum, presumably because the hard spin twist at the chain ends induces strong incommensurability effects on the bulk system when the chain length is small. As a convergence check, we benchmark our DMRG results to near-double-precision floating-point accuracy against analytical results at exactly solvable points and against exact diagonalization results for small system sizes across the entire parameter space.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑