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    Anisotropic swim stress in active matter with nematic order

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    Active Brownian Particles (ABPs) transmit a swim pressure Πswim=nζDswim\Pi^{swim}=n\zeta D^{swim} to the container boundaries, where ζ\zeta is the drag coefficient, DswimD^{swim} is the swim diffusivity and nn is the uniform bulk number density far from the container walls. In this work we extend the notion of the isotropic swim pressure to the anisotropic tensorial swim stress σswim=nζDswim\mathbf{\sigma}^{swim} = - n \zeta \mathbf{D}^{swim}, which is related to the anisotropic swim diffusivity Dswim\mathbf{D}^{swim}. We demonstrate this relationship with ABPs that achieve nematic orientational order via a bulk external field. The anisotropic swim stress is obtained analytically for dilute ABPs in both 2D and 3D systems, and the anisotropy is shown to grow exponentially with the strength of the external field. We verify that the normal component of the anisotropic swim stress applies a pressure Πswim=(σswimn)n\Pi^{swim}=-(\mathbf{\sigma}^{swim}\cdot\mathbf{n})\cdot\mathbf{n} on a wall with normal vector n\mathbf{n}, and, through Brownian dynamics simulations, this pressure is shown to be the force per unit area transmitted by the active particles. Since ABPs have no friction with a wall, the difference between the normal and tangential stress components -- the normal stress difference -- generates a net flow of ABPs along the wall, which is a generic property of active matter systems

    Sweeping cluster algorithm for quantum spin systems with strong geometric restrictions

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    Quantum spin systems with strong geometric restrictions give rise to rich quantum phases such as valence bond solids and spin liquid states. However, the geometric restrictions often hamper the application of sophisticated numerical approaches. Based on the stochastic series expansion method, we develop an efficient and exact quantum Monte Carlo "sweeping cluster" algorithm which automatically satisfies the geometrical restrictions. Here we use the quantum dimer model as a benchmark to demonstrate the reliability and power of this algorithm. Comparing to existing numerical methods, we can obtain higher accuracy results for a wider parameter region and much more substantial system sizes