Francesco Parisen Toldin

Fermionic quantum criticality in honeycomb and π-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

Entanglement Spectra of Interacting Fermions in Quantum Monte Carlo Simulations

\pi

Critical behavior of the three-dimensional +/- J Ising model at the paramagnetic-ferromagnetic transition line

-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.

The critical equation of state of the three-dimensional O(N) universality class: N>4

Department of Physics, Boston University, Boston, MA 02215, USA(Dated: November 25, 2013)In a recent article T. Grover [Phys. Rev. Lett. 111, 130402 (2013)] introduced a simple methodto compute Renyi entanglement entropies in the realm of the auxiliary eld quantum Monte Carloalgorithm. Here, we further develop this approach and provide a stabilization scheme to computehigher order Renyi entropies and an extension to access the entanglement spectrum. The methodis tested on systems of correlated topological insulators.

Functional renormalization group for three-dimensional quantum magnetism

We study the critical behavior of the three-dimensional ±J Ising model [with a random-exchange probability P (Jxy) = pδ(Jxy−J)+(1−p)δ(Jxy +J)] at the transition line between the paramagnetic and ferromagnetic phase, which extends from p = 1 to a multicritical (Nishimori) point at p = pN ≈ 0.767. By a finite-size scaling analysis of Monte Carlo simulations at various values of p in the region pN < p < 1, we provide strong numerical evidence that the critical behavior along the ferromagnetic transition line belongs to the same universality class as the three-dimensional randomly-dilute Ising model. We obtain the results ν = 0.682(3) and η = 0.036(2) for the critical exponents, which are consistent with the estimates ν = 0.683(2) and η = 0.036(1) at the transition of randomly-dilute Ising models. PACS numbers: 75.10.Nr, 75.40.Cx, 75.40.Mg, 64.60.Fr

Strong-disorder paramagnetic-ferromagnetic fixed point in the square-lattice +- J Ising model

Abstract We determine the scaling equation of state of the three-dimensional O ( N ) universality class, for N = 5 , 6 , 32 , 64 . The N = 5 model is relevant for the SO ( 5 ) theory of high- T c superconductivity, while the N = 6 model is relevant for the chiral phase transition in two-color QCD with two flavors. We first obtain the critical exponents and the small-field, high-temperature, expansion of the effective potential (Helmholtz free energy) by analyzing the available perturbative series, in both fixed-dimension and e-expansion schemes. Then, we determine the critical equation of state by using a systematic approximation scheme, based on polynomial representations valid in the whole critical region, which satisfy the known analytical properties of the equation of state, take into account the Goldstone singularities at the coexistence curve and match the small-field, high-temperature, expansion of the effective potential. This allows us also to determine several universal amplitude ratios. We also compare our approximate solutions with those obtained in the large- N expansion, up to order 1 / N , finding good agreement for N ≳ 32 .

Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model

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

Line contribution to the critical Casimir force between a homogeneous and a chemically stepped surface

{J}_{1}\text{\ensuremath{-}}{J}_{2}\text{\ensuremath{-}}{J}_{3}

Universality of the glassy transitions in the two-dimensional +/- J Ising model

quantum Heisenberg antiferromagnet, and benchmark it against other approaches, if available.

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

We consider the random-bond ±J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the critical behavior along the paramagnetic-ferromagnetic transition line at low temperatures, below the temperature of the multicritical Nishimori point at T*=0.9527(1), p*=0.89083(3). We present finite-size scaling analyses of Monte Carlo results at two temperature values, T≈0.645 and T=0.5. The results show that the paramagnetic-ferromagnetic transition line is reentrant for T<T*, that the transitions are continuous and controlled by a strong-disorder fixed point with critical exponents ν=1.50(4), η=0.128(8), and β=0.095(5). This fixed point is definitely different from the Ising fixed point controlling the paramagnetic-ferromagnetic transitions for T>T*. Our results for the critical exponents are consistent with the hyperscaling relation 2β/ν−η=d−2=0.