We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the π-flux lattice, which exhibits a direct transition from a Dirac semimetal to an antiferromagnetically ordered Mott insulator. We use projective auxiliary-field quantum Monte Carlo simulations and a careful finite-size scaling analysis that exploits approximately improved renormalization-group-invariant observables. This approach, which is successfully verified for the three-dimensional XY transition of the Kane-Mele-Hubbard model, allows us to extract estimates for the critical couplings and the critical exponents. The results confirm that the critical behavior for the semimetal to Mott insulator transition in the Hubbard model belongs to the Gross-Neveu-Heisenberg universality class on both lattices.

We present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behavior of these systems is affected by slowly-decaying scaling corrections which make the accurate determination of their universal asymptotic behavior quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class.The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents, ν = 0.683(2), η = 0.036(1), α = −0.049(6), γ = 1.341(4), β = 0.354(1), δ = 4.792(6), and of the leading and next-to-leading correction-to-scaling exponents, ω = 0.33(3) and ω 2 = 0.82(8).

Appendix A. Analysis of the high-temperature series 39 Appendix B. Monte Carlo simulations 43 References 45

Recent experiments have measured the critical Casimir force acting on a colloid immersed in a binary liquid mixture near its continuous demixing phase transition and exposed to a chemically structured substrate. Motivated by these experiments, we study the critical behavior of a system, which belongs to the Ising universality class, for the film geometry with one planar wall chemically striped, such that there is a laterally alternating adsorption preference for the two species of the binary liquid mixture, which is implemented by surface fields. For the opposite wall we employ alternatively a homogeneous adsorption preference or homogeneous Dirichlet boundary conditions, which within a lattice model are realized by open boundary conditions. By means of mean-field theory, Monte Carlo simulations, and finite-size scaling analysis we determine the critical Casimir force acting on the two parallel walls and its corresponding universal scaling function. We show that in the limit of stripe widths small compared with the film thickness, on the striped surface the system effectively realizes Dirichlet boundary conditions, which generically do not hold for actual fluids. Moreover, the critical Casimir force is found to be attractive or repulsive, depending on the width of the stripes of the chemically patterned surface and on the boundary condition applied to the opposing surface.

We consider the three-dimensional ±J model defined on a simple cubic lattice and study its behavior close to the multicritical Nishimori point where the paramagnetic-ferromagnetic, the paramagnetic-glassy, and the ferromagnetic-glassy transition lines meet in the T -p phase diagram (p characterizes the disorder distribution and gives the fraction of ferromagnetic bonds). For this purpose we perform Monte Carlo simulations on cubic lattices of size L ≤ 32 and a finitesize scaling analysis of the numerical results. The magnetic-glassy multicritical point is found at p * = 0.76820(4), along the Nishimori line given by 2p − 1 = Tanh(J/T ). We determine the renormalization-group dimensions of the operators that control the renormalization-group flow close to the multicritical point, y 1 = 1.02(5), y 2 = 0.61(2), and the susceptibility exponent η = −0.114(3). The temperature and crossover exponents are ν = 1/y 2 = 1.64(5) and φ = y 1 /y 2 = 1.67(10), respectively. We also investigate the model-A dynamics, obtaining the dynamic critical exponent z = 5.0(5).

We formulate a pseudofermion functional renormalization group (PFFRG) scheme to address frustrated quantum magnetism in three dimensions. In a scenario where many numerical approaches fail due to sign problem or small system size, three-dimensional (3D) PFFRG allows for a quantitative investigation of the quantum spin problem and its observables. We illustrate 3D PFFRG for the simple cubic J1-J2-J3 quantum Heisenberg antiferromagnet, and benchmark it against other approaches, if available.Introduction. Frustrated quantum magnetism has established broad experimental and theoretical interest in condensed matter [1,2]. In particular, from the viewpoint of quantum paramagnets as potential hosts of unconventional quantum states of matter [3,4], this field has persisted until today, and keeps generating manifold connections to other areas of contemporary research such as topological phases and quantum information.From a methodological perspective, the microscopic investigation of three-dimensional (3D) frustrated quantum magnetism constitutes one of the biggest challenges, which to a large extent remains unresolved. Mean-field approaches for quantum magnetism such as Schwinger bosons [5], along with spin waves, and linked cluster expansions [6] are often efficient to describe magnetic order in 3D but tend not to accurately capture paramagnetic behavior. While density-matrix renormalization group (DMRG) [7] is the method of choice for one-dimensional spin systems, and extensions to two dimensions (2D) have proven useful in many cases [8], applications in 3D are unfeasible due to system size and entanglement scaling. The application of variational Monte Carlo (VMC) [9,10] methods, equipped with an efficient mean-field description of magnetic and paramagnetic states including spin liquids [11], has likewise been predominantly constrained to 2D [12]: While an increase in the number of wave function parameters to be optimized is in principle no issue, VMC still suffers from system size limitation when computing expectation values of observables. Whereas sufficient system size can be reached by quantum Monte Carlo approaches [13,14], they are constrained to bipartite lattices with nonfrustrating spin interactions, and as such mostly do not allow access to the domains of interest.In this Rapid Communication, we propose a pseudofermion functional renormalization group (PFFRG) scheme to describe frustrated quantum magnetism in 3D. While methodologically the 3D PFFRG is similar to previous formulations in 2D [15,16], it remedies some short-

We determine the phase diagram of the Kane-Mele model with a long-range Coulomb interaction using an exact quantum Monte Carlo method. Long-range interactions are expected to play a role in honeycomb materials because the vanishing density of states in the semimetallic weak-coupling phase suppresses screening. According to our results, the Kane-Mele-Coulomb model supports the same phases as the Kane-Mele-Hubbard model. The nonlocal part of the interaction promotes short-range sublattice charge fluctuations, which compete with antiferromagnetic order driven by the onsite repulsion. Consequently, the critical interaction for the magnetic transition is significantly larger than for the purely local Hubbard repulsion. Our numerical data are consistent with SU (2) GrossNeveu universality for the semimetal to antiferromagnet transition, and with 3D XY universality for the quantum spin Hall to antiferromagnet transition.

Based on large-scale quantum Monte Carlo simulations, we examine the correlations along the edges of two-dimensional semi-infinite quantum critical Heisenberg spin-1/2 systems. In particular, we consider coupled quantum spin-dimer systems at their bulk quantum critical points, including the columnar-dimer model and the plaquette-square lattice. The alignment of the edge spins strongly affects these correlations and the corresponding scaling exponents, with remarkably similar values obtained for various quantum spin-dimer systems. We furthermore observe subtle effects on the scaling behavior from perturbing the edge spins that exhibit the genuine quantum nature of these edge states. Our observations furthermore challenge recent attempts that relate the edge spin criticality to the presence of symmetry-protected topological phases in such quantum spin systems.Quantum criticality in quantum many-body systems is a central aspect of current research in condensed matter physics [1]. In this respect, quantum spin systems in particular allow for a detailed comparison of experimental results to a quantitative computational modeling and analytical calculations of critical properties. Prominent examples are dimerized antiferromagnets, in which an explicit dimerization of the exchange couplings can be varied (e.g., by applying pressure [2-5]) in order to induce quantum phase transitions between quantum disordered phases and conventional antiferromagnetic order. In the absence of frustration, the quantum critical properties of such systems in d spatial dimensions are generally considered to be in accord with the universality class of the (d + 1)-dimensional classical Heisenberg model at its finite temperature critical point, described by the Wilson-Fisher fixed point of the three-component φ 4 theory [6]. This rationale is supported also by large-scale numerical studies of coupled spin dimer models on various twodimensional (2D) lattices [1,7,8,[10][11][12]. Within the nonlinear σ-model description of quantum antiferromagnets [13][14][15][16][17][18][19][20][21], such an agreement with the critical φ 4 theory suggests that for this purpose spin Berry-phase contributions [22] can be neglected in the effective action for 2D dimerized quantum antiferromagnets [21] (they may however give rise to additional scaling corrections from cubic terms in coupled dimer systems with reduced spatial symmetries [23]). As is well known, this is in stark contrast to the one-dimensional (1D) Heisenberg spin-1/2 chain, for which uncompensated spin Berry phases lead to a nonvanishing topological θ-term in the effective continuum action, associated with a gapless, quantum critical ground state [13][14][15][16][17][18]. Such a topological term can also emerge for a one-dimensional edge of 2D quantum spin systems: by appropriately cutting a 2D quantum antiferromagnet to a semi-infinite system, an effective 1D edge spin-1/2 system with similarly uncompensated Berry phases is generated. Such edge spins are further-more susceptible to effective interact...