标题： 在 Lifshitz 费米子理论中的纠缠 显示英文标题

标题： Entanglement in Lifshitz Fermion Theories

摘要： 我们研究具有Lifshitz对称性和任意整数动力学临界指数的(1+1)维自由狄拉克费米子理论中的静态纠缠结构。该模型与[Hartmann等，SciPost Phys. 11, no.2, 031 (2021)]中引入的模型不同，这是由于对平方拉普拉斯算子进行了正确的处理。狄拉克费米子Lifshitz理论是局部的，而其标量对应物则不是，这对其纠缠结构有显著影响。我们表明，对于任意整数的动力学临界指数，该理论的各种纯态（包括真空）和混合态中存在跨任意子区域的量子纠缠。我们的数值研究显示，该理论中的量子纠缠受到严格的上限限制。这种界限和其他量子纠缠的物理特性从这些理论的相关结构中得到了仔细解释。还讨论了到(2+1)维的推广，其中纠缠结构存在严重差异。 显示英文摘要

摘要： We study the static entanglement structure in (1+1)-dimensional free Dirac-fermion theory with Lifshitz symmetry and arbitrary integer dynamical critical exponent. This model is different from the one introduced in [Hartmann et al., SciPost Phys. 11, no.2, 031 (2021)] due to a proper treatment of the square Laplace operator. Dirac fermion Lifshitz theory is local as opposed to its scalar counterpart which strongly affects its entanglement structure. We show that there is quantum entanglement across arbitrary subregions in various pure (including the vacuum) and mixed states of this theory for arbitrary integer values of the dynamical critical exponent. Our numerical investigations show that quantum entanglement in this theory is tightly bounded from above. Such a bound and other physical properties of quantum entanglement are carefully explained from the correlation structure in these theories. A generalization to (2+1)-dimensions where the entanglement structure is seriously different is addressed.