论文标题
通过量子纠缠在纯基态的子系统中的热平衡的出现
Emergence of a thermal equilibrium in a subsystem of a pure ground state by quantum entanglement
论文作者
论文摘要
通过在小簇上的Spin-1/2抗磁性Heisenberg模型的数值确切计算，我们证明了子系统$ A $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a+b $ a+b $的量子纠缠可以在子系统$ a $ a $中诱导热平衡。在这里，整个系统都用纠缠剪切的纠缠剪切，该系统涵盖了子系统$ a $的全部卷。温度$ {\ cal t} _ {a}子系统$ a $不是参数，但可以从纠缠von neumann entropy $ {\ cal s} _ {a} $中确定，总能量$ {\ cal e} _} _ {a} $ a} $ a $ a $ a $ a $ a $ a $ a $ a $的状态的状态。我们表明，可以通过最大程度地减少子系统$ a $ $ a $的密度密度矩阵操作员的相对熵和吉布斯州（即热力学密度矩阵操作员）的相对于couplingsuptians usepling of ueplingsepters $ a $ a $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ b $ $ b $ $ b $ $ b $ $ b $ $。温度$ {\ cal t} _ {a} $与热力学温度实质上相同，在该温度下，使用统计机制中的规范机制评估的熵和内部能量，用于孤立子系统$ A $数值与纠缠熵$ {\ cal s} _ {\ cal a} $ { $ .FIDELITY计算确定子系统的密度矩阵$ a $的密度矩阵运算符，用于整个系统的纯但纠缠基$ a+b $匹配，在有限尺寸的群集中最大的$ 1.5 \％$错误，研究了热力学密度矩阵$ a $ a $的热力学密度矩阵运算符$} $ a} $} $}。我们认为，在纠缠的纯状态下的量子波动可以模仿子系统中的热波动。我们还提供了两个简单但非平凡的分析示例，这些示例是免费的，这些陈述是准确的。我们进一步讨论了我们发现的含义和可能的应用。
By numerically exact calculations of spin-1/2 antiferromagnetic Heisenberg models on small clusters, we demonstrate that quantum entanglement between subsystems $A$ and $B$ in a pure ground state of a whole system $A+B$ can induce thermal equilibrium in subsystem $A$. Here, the whole system is bipartitoned with the entanglement cut that covers the entire volume of subsystem $A$. Temperature ${\cal T}_{A}$ of subsystem $A$ is not a parameter but can be determined from the entanglement von Neumann entropy ${\cal S}_{A}$ and the total energy ${\cal E}_{A}$ of subsystem $A$ calculated for the ground state of the whole system. We show that temperature ${\cal T}_{A}$ can be derived by minimizing the relative entropy for the reduced density matrix operator of subsystem $A$ and the Gibbs state (i.e., thermodynamic density matrix operator) of subsystem $A$ with respect to the coupling strength between subsystems $A$ and $B$. Temperature ${\cal T}_{A}$ is essentially identical to the thermodynamic temperature, for which the entropy and the internal energy evaluated using the canonical ensemble in statistical mechanics for the isolated subsystem $A$ agree numerically with the entanglement entropy ${\cal S}_{A}$ and the total energy ${\cal E}_{A}$ of subsystem $A$.Fidelity calculations ascertain that the reduced density matrix operator of subsystem $A$ for the pure but entangled ground state of the whole system $A+B$ matches, within a maximally $1.5\%$ error in the finite size clusters studied, the thermodynamic density matrix operator of subsystem $A$ at temperature ${\cal T}_{A}$. We argue that quantum fluctuation in an entangled pure state can mimic thermal fluctuation in a subsystem. We also provide two simple but nontrivial analytical examples of free bosons and free fermions for which these statements are exact. We furthermore discuss implications and possible applications of our finding.
