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理论物理通讯：英文版

Entanglement Entropy Signature of Quantum Phase Transitions in a Multiple Spin Interactions Model

黄海林

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

通过 JordanWigner 转变，确切可解决的纺纱的纠纷熵和地面状态阶段图与轮流出现和多重旋转交换相互作用当模特儿借助于格林的功能理论被调查。当四纺纱的相互作用不在时，扎根的状态由于多重旋转相互作用和磁场介绍丰富的量阶段。二地点的纠纷熵是量阶段转变(QPT ) 的好指示物，这被显示出。另外，轮流出现的相互作用能破坏磁化高原并且外面洗低刺激的纺纱差距。面对四纺纱的相互作用，除了第二顺序 QPT ，然而，系统在 tricritical 点和称为“旋转波浪”的一个另外的新阶段表明第一顺序 QPT ，它由于四纺纱的相互作用为大三纺纱的 couplings 调制的连续像塔的低刺激的倒塌。

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通过 JordanWigner 转变，确切可解决的纺纱的纠纷熵和地面状态阶段图与轮流出现和多重旋转交换相互作用当模特儿借助于格林的功能理论被调查。当四纺纱的相互作用不在时，扎根的状态由于多重旋转相互作用和磁场介绍丰富的量阶段。二地点的纠纷熵是量阶段转变(QPT ) 的好指示物，这被显示出。另外，轮流出现的相互作用能破坏磁化高原并且外面洗低刺激的纺纱差距。面对四纺纱的相互作用，除了第二顺序 QPT ，然而，系统在 tricritical 点和称为“旋转波浪”的一个另外的新阶段表明第一顺序 QPT ，它由于四纺纱的相互作用为大三纺纱的 couplings 调制的连续像塔的低刺激的倒塌。
Through the Jordan—Wigner transformation, the entanglement entropy and ground state phase diagrams of exactly solvable spin model with alternating and multiple spin exchange interactions are investigated by means of Green's function theory. In the absence of four-spin interactions, the ground state presents plentiful quantum phases due to the multiple spin interactions and magnetic fields. It is shown that the two-site entanglement entropy is a good indicator of quantum phase transition (QPT). In addition, the alternating interactions can destroy the magnetization plateau and wash out the spin-gap of low-lying excitations. However, in the presence of four-spin interactions, apart from the second order QPTs, the system manifests the first order QPT at the tricritical point and an additional new phase called “spin waves”, which is due to the collapse of the continuous tower-like low-lying excitations modulated by the four-spin interactions for large three-spin couplings.
We study the spin-boson model (SBM) with two spins in staggered biases by a numerically exact method based on variational matrix product states. Several observables such as the magnetization, the entanglement entropy between the two spins and the bosonic environment, the ground-state energy, as well as the correlation function for two spins are calculated exactly. The characteristics of these observables suggest that the staggered biases can drive the second-order quantum phase transition (QPT) to the first-order QPT in the sub-Ohmic SBM, while the Kosterlitz-Thouless QPT in the Ohmic SBM goes directly to the first-order one. A quantum tricritical point, where the continuous QPT meets the first-order one, can then be detected. It is found that the staggered biases would not change the universality of the phase transition in this model below the quantum tricritical point.
Entanglement entropy (EE), a fundamental concept in quantum information for characterizing entanglement, has been extensively employed to explore quantum phase transitions (QPTs). Although the conventional single-site mean-field (MF) approach successfully predicts the emergence of QPTs, it fails to include any entanglement. Here, in the framework of a cluster MF treatment, we extract the signature of EE in bosonic superfluid-insulator (SI) transitions. We consider a trimerized Kagom\'e lattice of interacting bosons, in which each trimer is treated as a cluster, and implement the cluster MF treatment by decoupling all intertrimer hopping. In addition to superfluid and integer insulator phases, we find that fractional insulator phases appear when the tunneling is dominated by the intratrimer part. To quantify the residual bipartite entanglement in a cluster, we calculate the second-order R\'enyi entropy, which can be experimentally measured by quantum interference of many-body twins. The second-order R\'enyi entropy itself is continuous everywhere, however, the continuousness of its first-order derivative breaks down at the phase boundary. This means that the bosonic SI transitions can still be efficiently captured by the residual entanglement in our cluster MF treatment. Besides to the bosonic SI transitions, our cluster MF treatment may also be used to capture the signature of EE for other QPTs in quantum superlattice models.