Critical behavior of the three-dimensional bond-diluted Ising spin glass: Finite-size scaling functions and Universality

We study the three-dimensional (3D) bond-diluted Edwards-Anderson (EA) model with binary interactions at a bond occupation of 45% by Monte Carlo (MC) simulations. Using an efficient cluster MC algorithm we are able to determine the universal finite-size scaling (FSS) functions and the critical exponents with high statistical accuracy. We observe small corrections to scaling for the measured observables. The critical quantities and the FSS functions indicate clearly that the bond-diluted model for dilutions above the critical dilution p*, at which a spin glass (SG) phase appears, lies in the same universality class as the 3D undiluted EA model with binary interactions. A comparison with the FSS functions of the 3D site-diluted EA model with Gaussian interactions at a site occupation of 62.5% gives very strong evidence for the universality of the SG transition in the 3D EA model.Comment: Revised version. 10 pages, 9 figures, 2 table

Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations

In a recent article T. Grover [Phys. Rev. Lett. 111, 130402 (2013)] introduced a simple method to compute Renyi entanglement entropies in the realm of the auxiliary field quantum Monte Carlo algorithm. Here, we further develop this approach and provide a stabilization scheme to compute higher order Renyi entropies and an extension to access the entanglement spectrum. The method is tested on systems of correlated topological insulators.Comment: 7+ pages, 5 figure

Multicritical Nishimori point in the phase diagram of the +- J Ising model on a square lattice

We investigate the critical behavior of the random-bond +- J Ising model on a square lattice at the multicritical Nishimori point in the T-p phase diagram, where T is the temperature and p is the disorder parameter (p=1 corresponds to the pure Ising model). We perform a finite-size scaling analysis of high-statistics Monte Carlo simulations along the Nishimori line defined by $2p-1={\rm Tanh}(1/T)$, along which the multicritical point lies. The multicritical Nishimori point is located at p^*=0.89081(7), T^*=0.9528(4), and the renormalization-group dimensions of the operators that control the multicritical behavior are y_1=0.655(15) and y_2 = 0.250(2); they correspond to the thermal exponent \nu= 1/y_2=4.00(3) and to the crossover exponent \phi= y_1/y_2=2.62(6).Comment: 23 page

Phase diagram of the SU(NN) antiferromagnet of spin SS on a square lattice

We investigate the ground state phase diagram of an SU($N$)-symmetric antiferromagnetic spin model on a square lattice where each site hosts an irreducible representation of SU($N$) described by a square Young tableau of $N/2$ rows and $2S$ columns. We show that negative sign free fermion Monte Carlo simulations can be carried out for this class of quantum magnets at any $S$ and even values of $N$. In the large-$N$ limit, the saddle point approximation favors a four-fold degenerate valence bond solid phase. In the large $S$-limit, the semi-classical approximation points to N\'eel state. On a line set by $N=8S + 2$ in the $S$ versus $N$ phase diagram, we observe a variety of phases proximate to the N\'eel state. At $S = 1/2$ and $3/2$ we observe the aforementioned four fold degenerate valence bond solid state. At $S=1$ a two fold degenerate spin nematic state in which the C$_4$ lattice symmetry is broken down to C$_2$ emerges. Finally at $S=2$ we observe a unique ground state that pertains to a two-dimensional version of the Affleck-Kennedy-Lieb-Tasaki state. For our specific realization, this symmetry protected topological state is characterized by an SU(18), $S=1/2$ boundary state, that has a dimerized ground state. These phases that are proximate to the N\'eel state are consistent with the notion of monopole condensation of the antiferromagnetic order parameter. In particular one expects spin disordered states with degeneracy set by $\text{mod}(4,2S)$.Comment: 18 pages, 21 figures; adapted title to APS style and included minor correction

Fermionic quantum criticality in honeycomb and π\pi-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo

We numerically investigate the critical behavior of the Hubbard model on the honeycomb and the $\pi$-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.Comment: 19 pages, 16 figures; v2: replaced Fig. 5, corrected typo in Uc for the Kane-Mele-Hubbard model, 19 pages, 16 figure

Zero-temperature behavior of the random-anisotropy model in the strong-anisotropy limit

We consider the random-anisotropy model on the square and on the cubic lattice in the strong-anisotropy limit. We compute exact ground-state configurations, and we use them to determine the stiffness exponent at zero temperature; we find $\theta = -0.275(5)$ and $\theta \approx 0.2$ respectively in two and three dimensions. These results show that the low-temperature phase of the model is the same as that of the usual Ising spin-glass model. We also show that no magnetic order occurs in two dimensions, since the expectation value of the magnetization is zero and spatial correlation functions decay exponentially. In three dimensions our data strongly support the absence of spontaneous magnetization in the infinite-volume limit

An ab initio Calculation of the Universal Equation of State for the O(N) Model

Using an Environmentally Friendly Renormalization Group we derive an ab initio universal scaling form for the equation of state for the O(N) model, y=f(x), that exhibits all required analyticity properties in the limits $x\to 0$, $x\to\infty$ and $x\to -1$. Unlike current methodologies based on a phenomenological scaling ansatz the scaling function is derived solely from the underlying Landau-Ginzburg-Wilson Hamiltonian and depends only on the three Wilson functions $\gamma_\lambda$, $\gamma_\phi$ and $\gamma_{\phi^2}$ which exhibit a non-trivial crossover between the Wilson-Fisher fixed point and the strong coupling fixed point associated with the Goldstone modes on the coexistence curve. We give explicit results for N=2, 3 and 4 to one-loop order and compare with known results.Comment: 12 pages, to appear in Journal of Physics