We investigate how entanglement entropy behaves in a non-conformal scalar field system with a quantum phase transition, by the replica method. We study the σ-model in 3+1 dimensions which is O(N) symmetric as the mass squared parameter μ² is positive, and undergoes spontaneous symmetry breaking while μ² becomes negative. The area law leading divergence of the entanglement entropy is preserved in both of the symmetric and the broken phases. The spontaneous symmetry breaking changes the subleading divergence from log to log squared, due to the cubic interaction on the cone. At the leading order of the coupling constant expansion, the entanglement entropy reaches a cusped maximum at the quantum phase transition point μ² = 0, and decreases while μ² is tuned away from 0 into either phase.

我们通过复制方法研究纠缠熵在具有量子相变的非共形标量场系统中的行为。我们研究了3+1 维的σ 模型，它是O ( N ) 对称的，因为质量平方参数μ ²为正，并且在μ ^{2 时}发生自发对称性破缺变得消极。在对称相和破碎相中都保留了主导纠缠熵散度的面积定律。由于锥体上的三次相互作用，自发对称性破缺改变了对数平方的次导散度。在耦合常数扩展的前导阶，纠缠熵在量子相变点μ ² = 0处达到峰值，并在μ ²从 0 调谐到任一相时减小。