Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points

We determine the dynamical dimer correlation functions of quantum dimer models at the Rokhsar-Kivelson point on the bipartite square and cubic lattices and the non-bipartite triangular lattice. Based on an algorithmic idea by Henley, we simulate a stochastic process of classical dimer configurations in continuous time and perform a stochastic analytical continuation to obtain the dynamical correlations in momentum space and the frequency domain. This approach allows us to observe directly the dispersion relations and the evolution of the spectral intensity within the Brillouin zone beyond the single-mode approximation. On the square lattice, we confirm analytical predictions related to soft modes close to the wavevectors (pi,pi) and (pi,0) and further reveal the existence of shadow bands close to the wavevector (0,0). On the cubic lattice the spectrum is also gapless but here only a single soft mode at (pi,pi,pi) is found, as predicted by the single mode approximation. The soft mode has a quadratic dispersion at very long wavelength, but crosses over to a linear behavior very rapidly. We believe this to be the remnant of the linearly dispersing "photon" of the Coulomb phase. Finally the triangular lattice is in a fully gapped liquid phase where the bottom of the dimer spectrum exhibits a rich structure. At the M point the gap is minimal and the spectral response is dominated by a sharp quasiparticle peak. On the other hand, at the X point the spectral function is much broader. We sketch a possible explanation based on the crossing of the coherent dimer excitations into the two-vison continuum.Comment: 16 pages, 7 figures, published versio

Coherence scale of the two-dimensional Kondo Lattice model

A doped hole in the two-dimensional half-filled Kondo lattice model with exchange J and hopping t has momentum (pi,pi) irrespective of the coupling J/t. The quasiparticle residue of the doped hole, Z_{(\pi, \pi)}, tracks the Kondo scale, T_K, of the corresponding single impurity model. Those results stem from high precision quantum Monte Carlo simulations on lattices up to 12 X 12. Accounting for small dopings away from half-filling within a rigid band approximation, this result implies that the effective mass of the charge carriers at the Fermi level tracks 1/T_K or equivalently that the coherence temperature T_{coh} \propto T_K. This results is consistent with the large-N saddle point of the SU(N) symmetric Kondo lattice model.Comment: 4 pages, 4 figure

Metamagnetism and Lifshitz Transitions in Models for Heavy Fermions

We investigate metamagnetic transitions in models for heavy fermions by considering the doped Kondo lattice model in two dimensions. Results are obtained within the framework of dynamical mean field and dynamical cluster approximations. Universal magnetization curves for different temperatures and Kondo couplings develop upon scaling with the lattice coherence temperature. Furthermore, the coupling of the local moments to the magnetic field is varied to take into account the different Land\'e factors of localized and itinerant electrons. The competition between the lattice coherence scale and the Zeeman energy scale allows for two interpretations of the metamagnetism in heavy fermions: Kondo breakdown or Lifshitz transitions. By tracking the single-particle residue through the transition, we can uniquely conclude in favor of the Lifshitz transition scenario. In this scenario, a quasiparticle band drops below the Fermi energy which leads to a change in topology of the Fermi surface.Comment: 8 pages, 7 figure

Critical Exponents of the Metal-Insulator Transition in the Two-Dimensional Hubbard Model

We study the filling-controlled metal-insulator transition in the two-dimensional Hubbard model near half-filling with the use of zero temperature quantum Monte Carlo methods. In the metallic phase, the compressibility behaves as $\kappa \propto |\mu - \mu_c|^{-0.58\pm0.08}$ where $\mu_c$ is the critical chemical potential. In the insulating phase, the localization length follows $\xi_l \propto |\mu - \mu_c|^{-\nu_l}$ with $\nu_l = 0.26 \pm 0.05$. Under the assumption of hyperscaling, the compressibility data leads to a correlation length exponent $\nu_\kappa = 0.21 \pm 0.04$. Our results show that the exponents $\nu_\kappa$ and $\nu_l$ agree within statistical uncertainty. This confirms the assumption of hyperscaling with correlation length exponent $\nu = 1/4$ and dynamical exponent $z = 4$. In contrast the metal-insulator transition in the generic band insulators in all dimensions as well as in the one-dimensional Hubbard model satisfy the hyperscaling assumption with exponents $\nu = 1/2$ and $z = 2$.Comment: Two references added. The DVI file and PS figure files are also available at http://www.issp.u-tokyo.ac.jp/labs/riron/imada/furukawa/; to appear in J. Phys. Soc. Jpn 65 (1996) No.

THE EFFECT OF TEACHER'S EXAMPLE ON THE MORALS OF MADRASAH STUDENTS ALIYAH NURUL AS'ADIYAH CALLACCU SENGKANG, WAJO REGENCY

This study discusses the effect of the teacher's example on the morals of the students of Madrasah Aliyah Nurul As'adiyah Callaccu Sengkang, Wajo Regency. The type of research used in this research is ex-post facto quantitative. Ex-post facto research is research in which the independent variables have been treated, or treatment was not carried out at the time of the research, so this research is usually separated from experimental research. This quantitative research aims to find out how much influence between variables. In this study, the research will examine the effect of teacher's example on the morals of the students of Madrasah Aliyah Nurul As'adiyah Callaccu Sengkang, Wajo Regency. The example of the teacher is very influential on the morals of students, therefore a teacher is required to continue to show good examples, the example of the teacher is needed with the aim that students have good morals.This study discusses the effect of the teacher's example on the morals of the students of Madrasah Aliyah Nurul As'adiyah Callaccu Sengkang, Wajo Regency. The type of research used in this research is ex-post facto quantitative. Ex-post facto research is research in which the independent variables have been treated, or treatment was not carried out at the time of the research, so this research is usually separated from experimental research. This quantitative research aims to find out how much influence between variables. In this study, the research will examine the effect of teacher's example on the morals of the students of Madrasah Aliyah Nurul As'adiyah Callaccu Sengkang, Wajo Regency. The example of the teacher is very influential on the morals of students, therefore a teacher is required to continue to show good examples, the example of the teacher is needed with the aim that students have good morals

Spin nematic phases in models of correlated electron systems: a numerical study

Strongly interacting systems are known to often spontaneously develop exotic ground states under certain conditions. For instance, spin nematic phases have been discovered in various magnetic models. Such phases, which break spin symmetry but have no net local magnetization, have also been proposed by Nersesyan et al. (J. Phys.: Cond. Matt. 3, 3353 (1991)) in the context of electronic models. We introduce a N-flavor microscopic model that interpolates from the large-N limit, where mean-field is valid and such a nematic phase occurs, to the more realistic N=1 case. By using a sign-free quantum Monte-Carlo, we show the existence of a spin nematic phase (analogous to a spin flux phase) for finite N; when N decreases, quantum fluctuations increase and this phase ultimately disappears in favor of an s-wave superconducting state. We also show that this nematic phase extends up to a finite critical charge doping. Dynamical studies allow us to clarify the Fermi surface property: in the nematic phase at half-filling, it consists of 4 points and the low-energy structure has a Dirac cone-like shape. Under doping, we observe clear signatures of Fermi pockets around these points. This is one of the few examples where numerical simulations show how quantum fluctuations can destroy a large-N phase.Comment: 9 pages, 19 figures. Problem with figures has been fixe

Finite-temperature properties of hard-core bosons confined on one-dimensional optical lattices

We present an exact study of the finite-temperature properties of hard-core bosons (HCB's) confined on one-dimensional optical lattices. Our solution of the HCB problem is based on the Jordan-Wigner transformation and properties of Slater determinants. We analyze the effects of the temperature on the behavior of the one-particle correlations, the momentum distribution function, and the lowest natural orbitals. In addition, we compare results obtained using the grand-canonical and canonical descriptions for systems like the ones recently achieved experimentally. We show that even for such small systems, as small as 10 HCB's in 50 lattice sites, there are only minor differences between the energies and momentum distributions obtained within both ensembles.Comment: RevTex file, 12 pages, 16 figures, published versio

Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method

Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for fermions with positive weights. In the example of the Hubbard model close to half filling it fails to reproduce all the symmetries of the ground state leading to systematic errors at low temperatures. In a previous work [Phys. Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by projecting the density matrix obtained from the simulation onto the ground state symmetry sector. For ground state properties, the accuracy of this method depends on a {\it large overlap} between the GQMC and exact density matrices. Thus, the method is not rigorously exact. We present the limits of the approach by a systematic study of the method for 2 and 3 leg Hubbard ladders for different fillings and on-site repulsion strengths. We show several indications that the systematic errors stem from non-vanishing boundary terms in the partial integration step in the derivation of the Fokker-Planck equation. Checking for spiking trajectories and slow decaying probability distributions provides an important test of the reliability of the results. Possible solutions to avoid boundary terms are discussed. Furthermore we compare results obtained from two different sampling methods: Reconfiguration of walkers and the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl

Systematic errors in Gaussian Quantum Monte Carlo and a systematic study of the symmetry projection method

Gaussian Quantum Monte Carlo (GQMC) is a stochastic phase space method for fermions with positive weights. In the example of the Hubbard model close to half filling it fails to reproduce all the symmetries of the ground state leading to systematic errors at low temperatures. In a previous work [Phys. Rev. B {\bf 72}, 224518 (2005)] we proposed to restore the broken symmetries by projecting the density matrix obtained from the simulation onto the ground state symmetry sector. For ground state properties, the accuracy of this method depends on a {\it large overlap} between the GQMC and exact density matrices. Thus, the method is not rigorously exact. We present the limits of the approach by a systematic study of the method for 2 and 3 leg Hubbard ladders for different fillings and on-site repulsion strengths. We show several indications that the systematic errors stem from non-vanishing boundary terms in the partial integration step in the derivation of the Fokker-Planck equation. Checking for spiking trajectories and slow decaying probability distributions provides an important test of the reliability of the results. Possible solutions to avoid boundary terms are discussed. Furthermore we compare results obtained from two different sampling methods: Reconfiguration of walkers and the Metropolis algorithm.Comment: 11 pages, 14 figures, revised version, new titl