Title: Tunable quantum criticality and pseudocriticality across the fixed-point annihilation in the anisotropic spin-boson model Show Chinese title

Title: 各向异性自旋-玻色模型中固定点湮灭处的可调量子临界性和拟临界性

Abstract: Spin-boson models are simple examples of quantum dissipative systems, but also serve as effective models in quantum magnetism and exhibit nontrivial quantum criticality. Recently, they have been established as a platform to study the nontrivial renormalization-group (RG) scenario of fixed-point annihilation, in which two intermediate-coupling RG fixed points collide and generate an extremely slow RG flow near the collision. For the Bose Kondo model, a single $S=1/2$ spin where each spin component couples to an independent bosonic bath with power-law spectrum $\propto \omega^s$ via dissipation strengths $\alpha_i$, $i\in\{x,y,z\}$, such phenomena occur sequentially for the U(1)-symmetric model at $\alpha_z=0$ and the SU(2)-symmetric case at $\alpha_z = \alpha_{xy}$, as the bath exponent $s<1$ is tuned. Here we use an exact wormhole quantum Monte Carlo method to show how fixed-point annihilations within symmetry-enhanced parameter manifolds affect the anisotropy-driven criticality across them. We find a tunable transition between two long-range-ordered localized phases that can be continuous or strongly first-order, and even becomes weakly first-order in an extended regime close to the fixed-point collision. We extract critical exponents at the continuous transition, but also find scaling behavior at the symmetry-enhanced first-order transition, for which the inverse correlation-length exponent is given by the bath exponent $s$. In particular, we provide direct numerical evidence for pseudocritical scaling on both sides of the fixed-point collision, which manifests in an extremely slow drift of the correlation-length exponent. In addition, we also study the crossover behavior away from the SU(2)-symmetric case and determine the phase boundary of an extended U(1)-symmetric critical phase for $\alpha_z < \alpha_{xy}$. Show Chinese abstract

Abstract: 自旋-玻色模型是量子耗散系统的简单例子，同时也作为量子磁性中的有效模型，并表现出非平凡的量子临界性。 最近，它们已被确立为研究固定点湮灭的非平凡重正化群（RG）场景的平台，在此过程中两个中间耦合的RG固定点发生碰撞，并在碰撞附近产生极慢的RG流。 对于玻色Kondo模型，一个$S=1/2$自旋，每个自旋分量通过耗散强度$\alpha_i$、$i\in\{x,y,z\}$耦合到具有幂律谱$\propto \omega^s$的独立玻色浴，这些现象在 U(1)-对称模型的$\alpha_z=0$和 SU(2)-对称情况的$\alpha_z = \alpha_{xy}$依次出现，当浴指数$s<1$被调节时。 在这里，我们使用精确的虫洞量子蒙特卡罗方法来展示在对称性增强的参数流形内的固定点湮灭如何影响跨流形的各向异性驱动临界性。 我们发现两种长程有序局域相之间存在可调节的相变，可以是连续的或强一阶的，甚至在接近固定点碰撞的扩展区域内变为弱一阶的。 我们在连续相变处提取临界指数，还发现在对称性增强的一阶相变中的标度行为，其中反关联长度指数由浴态指数$s$给出。 特别是，我们提供了固定点碰撞两侧伪临界标度的直接数值证据，这表现为关联长度指数的极慢漂移。 此外，我们还研究了远离SU(2)对称情况的交叉行为，并确定了扩展U(1)对称临界相的相边界对于$\alpha_z < \alpha_{xy}$。