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We use the stochastic series expansion quantum Monte Carlo method, together with the eigenstate-to-Hamiltonian construction, to map the localized Bose glass ground state of the disordered two-dimensional Heisenberg model to excited states of new target Hamiltonians. The localized nature of the ground state is established by studying the participation entropy, local entanglement entropy, and local magnetization, all known in the literature to also be identifying characteristics of many-body localized states. Our construction maps the ground state of the parent Hamiltonian to a single excited state of a new target Hamiltonian, which retains the same form as the parent Hamiltonian, albeit with correlated and large disorder. We furthermore provide evidence that the mapped eigenstates are genuine localized states and not special zero-measure localized states like the quantum scar-states. Our results provide concrete evidence for the existence of the many-body localized phase in two dimensions., Comment: (4+\epsilon) pages with 4 figures, and the supplementary material

The Algorithms for Lattice Fermions package provides a general code for the finite-temperature and projective auxiliary-field quantum Monte Carlo algorithm. The code is engineered to be able to simulate any model that can be written in terms of sums of single-body operators, of squares of single-body operators and single-body operators coupled to a bosonic field with given dynamics. The package includes five pre-defined model classes: SU(N) Kondo, SU(N) Hubbard, SU(N) t-V and SU(N) models with long range Coulomb repulsion on honeycomb, square and N-leg lattices, as well as $Z_2$ unconstrained lattice gauge theories coupled to fermionic and $Z_2$ matter. An implementation of the stochastic Maximum Entropy method is also provided. One can download the code from our Git instance at https://git.physik.uni-wuerzburg.de/ALF/ALF/-/tree/ALF-2.4 and sign in to file issues., Comment: 126 pages, 12 figures. v7: update do ALF 2.4. Submission to SciPost. This article supersedes arXiv:1704.00131

The research carried out in this project aims to exactly solve models of correlated electron systems with large-scale fermion quantum Monte Carlo simulations. The goal is to understand the emergent many-body phenomena and critical behaviour. We will first provide an overview of themes and then concentrate on the so-called dimensional crossover phenomena. In this domain, we were able to provide dynamical information about the confinement of fractionalised spinon excitations in weakly coupled Hubbard chains. Such calculations are relevant for the understanding of neutron scattering experiments on KCuF3. From the technical point of view we are using and developing a number of algorithms, including continuous-time interaction expansion and determinantal quantum Monte Carlo methods.

The adiabatic insertion of a ��flux into a quantum spin Hall insulator gives rise to localized spin and charge fluxon states. We demonstrate that ��fluxes can be used in exact quantum Monte Carlo simulations to identify a correlated Z_2 topological insulator using the example of the Kane-Mele-Hubbard model. In the presence of repulsive interactions, a ��flux gives rise to a Kramers doublet of spinon states with a Curie law signature in the magnetic susceptibility. Electronic correlations also provide a bosonic mode of magnetic excitons with tunable energy that act as exchange particles and mediate a dynamical interaction of adjustable range and strength between spinons. ��fluxes can therefore be used to build models of interacting spins. This idea is applied to a three-spin ring and to one-dimensional spin chains. Due to the freedom to create almost arbitrary spin lattices, correlated topological insulators with ��fluxes represent a novel kind of quantum simulator potentially useful for numerical simulations and experiments., 12 pages, 12 figures, published version

Inspired by recent experiments on 3He films between one and two atoms thick, we consider a bilayer Hubbard model on a triangular lattice. Our results are obtained in the framework of a cluster dynamical mean-field calculation with a quantum Monte Carlo impurity solver. For appropriate model parameters, we observe an enhancement of the effective mass as the first layer approaches integer filling and the second remains only partially filled. At finite temperatures, this increase of the effective mass -- or, equivalently, the decrease of the coherence temperature -- leads to a crossover to a state where the first layer fermions localize, drop out of the Luttinger volume, and generate essentially free local moments. This finite temperature behavior is shown to be robust against the cluster size above some critical temperature. The zero temperature phase diagram, however, depends on the cluster topology. In particular, for clusters with an even number of unit cells, the growth of the effective mass is cut off by a first-order, orbital-selective Mott transition., 8 pages, 9 figures

We consider asymmetric spin-1/2 two-leg ladders with non-equal antiferromagnetic (AF) couplings J_|| and \kappa J_|| along legs (\kappa, Comment: 18 pages, 11 figures

18 pages, 11 figures; International audience; We consider asymmetric spin-1/2 two-leg ladders with non-equal antiferromagnetic (AF) couplings J_|| and \kappa J_|| along legs (\kappa

Inspired by recent experiments on bilayer 3He, we consider a bilayer Hubbard model on a triangular lattice. For appropriate model parameters, we observe a band-selective Mott transition at a critical chemical potential, mu_c, corresponding to the solidification of the fermions in the first layer. The growth of the effective mass on the metallic side (mu < mu_c) is cut off by a first order transition in which the first layer fermions drop out of the Luttinger volume and their spin degrees of freedom become locked in a spin singlet state. These results are obtained from a cluster dynamical mean-field calculation on an eight-site cluster with a quantum Monte Carlo cluster solver., 4 + epsilon pages, 6 figures

We extend the weak-coupling diagrammatic determinantal algorithm to projective schemes as well as to the inclusion of phonon degrees of freedom. The projective approach provides a very efficient algorithm to access zero temperature properties. To implement phonons, we integrate them out in favor of a retarded density-density interaction and simulate the resulting purely electronic action with the weak-coupling diagrammatic determinantal algorithm. Both extensions are tested within the dynamical mean field approximation for the Hubbard and Hubbard-Holstein models., Comment: 8 pages, 4 figures, final version as appeared in PRB

In our reply, we show that the objections put forward in cond-mat/0508763 concerning our paper, Phys. Rev. Lett. 93, 136405 (2004), are not valid: (i) There is no orthogonality catastrophe (OC) for our calculations, and it is also generally not ``unpractical'' to avoid it. (ii) The OC does not affect our results., 1 page, 1 figure, Phys. Rev. Lett. in print; also note cond-mat/0509443

Katsnelson submitted his Comment on our paper "Projective Quantum Monte Carlo Method for the Anderson Impurity Model and its Application to Dynamical Mean Field Theory" to Phys. Rev. Lett. in May 2005. We proved in our report that this comment was incorrect since there is no orthogonality catastrophe for our calculation in Phys. Rev. Lett. 93, 136405 (2004) which is for half-filling. Now in cond-mat/0508763, Katsnelson incorporates our proof of the invalidity of his original Comment, based on Friedel's sum rule. Instead, he now claims that the projective quantum Monte Carlo method is "unpractical" off half-filling, overlooking that our calculations off half-filling (R. Arita and K. Held, LT24 conference proceedings and cond-mat/0508639) employ in practice a noninteracting trial Hamiltonian with the same electron density as the interacting Hamiltonian so that there is again no orthogonality catastrophe. Note added. In the revised version of his comment, Katsnelson gives proper credit to our proof. In our reply, we will present the original proof based on the Friedel sum rule. Moreover, we show that the orthogonality catastrophe does not affect our results. Katsnelson's objection is not valid., no paper, just the clarification. Note added since the comment has been revised

We investigate the phase diagram of the half-filled SU(N) Hubbard-Heisenberg model with hopping t, exchange J and Hubbard U, on a square lattice. In the large-N limit, and as a function of decreasing values of t/J, the model shows a transition from a d-density wave state to a spin dimerized insulator. A similar behavior is observed at N=6 whereas at N=2 a spin density wave insulating ground state is stabilized. The N=4 model, has a d-density wave ground state at large values of t/J which as a function of decreasing values of t/J becomes unstable to an insulating state with no apparent lattice and spin broken symmetries. In this state, the staggered spin-spin correlations decay as a power-law,resulting in gapless spin excitations at q = (pi,pi). Furthermore, low lying spin modes with small spectral weight are apparent around the wave vectors q = (0,pi) and q = (pi,0). This gapless spin liquid state is equally found in the SU(4) Heisenberg model in the self-adjoint antisymmetric representation. An interpretation of this state in terms of a pi-flux phase is offered. Our results stem from projective (T=0) quantum Monte-Carlo simulations on lattice sizes ranging up to 24 X 24., Comment: 10 pages, 12 figures

We consider a two dimensional Kondo lattice model with exchange J and hopping t in which three out of four impurity spins are removed in a regular way. At the particle-hole symmetric point the model may be studied with auxiliary field quantum Monte Carlo methods without sign problems. To achieve the relevant energy scales on finite clusters, we introduce a simple method to reduce size effects by up to an order of magnitude in temperature. In this model, a metallic phase survives up to arbitrarily low temperatures before being disrupted by magnetic fluctuations which open a gap in the charge sector. We study the formation of the heavy-electron state with emphasis on a crossover scale T* defined by the maximum in the resistivity versus temperature curve. The behavior of thermodynamic properties such as specific heat as well as spin and charge uniform susceptibilities are studied as the temperature varies in a wide range across T*. Within our accuracy T* compares well to the Kondo scale of the related single impurity problem. Finally our QMC resuls are compared with mean-field approximations., Comment: 12 pages, 13 figures. Submitted to Phys. Rev. B

Optical reflection measurements within the highly conducting (a,b)-plane of the organic metal (BEDT-TTF)_4[Ni(dto)_2] reveal the gradual development of a sharp feature at around 200 cm as the temperature is reduced below 150 K. Below this frequency a narrow Drude-like response is observed which accounts for the metallic behavior. Since de Haas-von Alphen oscillations at low temperatures confirm band structure calculations of bands crossing the Fermi energy, we assign the observed behavior to a two-dimensional metallic state in the proximity of a correlation induced metal-insulator transition., 4 pages, 2 figures

The dispersion relation of a doped hole in the half-filled 2D Hubbard model is shown to follow a k^4 law around the (0,pi) and (pi,0) points in the Brillouin zone. Upon addition of pair-hopping processes this dispersion relation is unstable towards a k^2 law. The above follows from T=0 Quantum Monte calculations of the single particle spectral function A(k, omega) on 16 X 16 lattices. We discuss finite dopings and argue that the added term restores coherence to charge dynamics and drives the system towards a d_x^2 - y^2 superconductor., 5 pages including 5 figures

We consider the repulsive Hubbard model on a square lattice with an additional term, W, which depends upon the square of a single-particle nearest-neighbor hopping. At half-band filling, constant W, we show that enhancing U/t drives the system from a d-wave superconductor to an antiferromagnetic Mott insulator. At zero temperature in the superconducting phase, spin-spin correlations follow a powerlaw: exp(-i r Q) |r|^(-alpha). Here Q = (pi, pi) and alpha is in the range 1 < alpha < 2 and depends upon the coupling constants W and U. This results is reached on the basis of large scale quantum Monte-Carlo simulations on lattices up to 24 times 24, and is shown to be independent on the choice of the boundary conditions. We define a pairing (magnetic) scale by the temperature below which short range d-wave pairing correlations (antiferromagnetic fluctuations) start growing. With finite temperature quantum Monte Carlo simulations, we demonstrate that both scales are identical over a large energy range. Those results show the extreme compatibility and close interplay of antiferromagnetic fluctuations and d-wave superconductivity., 4 pages including 6 figures in encapsulated postscript format

Auxiliary field quantum Monte Carlo methods for Hubbard models are generally based on a Hubbard-Stratonovitch transformation where the field couples to the z-component of the spin. This transformation breaks SU(2) spin invariance. The symmetry is restored only after summation over the auxiliary fields. Here, we analyze an alternative decomposition, which conserves SU(2) spin invariance, but requires the use of complex numbers. We show that this algorithm gets rid of the very large fluctuations observed in imaginary time displaced correlation functions of quantities which do not commute with the z-component of the total spin. The algorithm prooves to be efficient for the study of spin dynamics., Comment: 5 pages including 2 figures in encapsulated postscript format

We show numerically that the nature of the doping induced metal-insulator transition in the two-dimensional Hubbard model is radically altered by the inclusion of a term, $W$, which depends upon a square of a single-particle nearest-neighbor hopping. This result is reached by computing the localization length, $\xi_l$, in the insulating state. At finite values of $W$ we find results consistent with $\xi_l \sim | \mu - \mu_c|^{- 1/2} $ where $\mu_c$ is the critical chemical potential. In contrast, $\xi_l \sim | \mu - \mu_c|^{-1/4}$ for the Hubbard model. At finite values of $W$, the presented numerical results imply that doping the antiferromagnetic Mott insulator leads to a $d_{x^2 - y ^2}$ superconductor., Comment: 19 pages (latex) including 7 figures in encapsulated postscript format. Submitted for publication in Phys. Rev. B

To the Hubbard model on a square lattice we add an interaction, $W$, which depends upon the square of a near-neighbor hopping. We use zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$, to show that at half-filling and constant value of the Hubbard repulsion, the interaction $W$ triggers a quantum transition between an antiferromagnetic Mott insulator and a $d_{x^2 -y^2}$ superconductor. With a combination of finite temperature quantum Monte Carlo simulations and the Maximum Entropy method, we study spin and charge degrees of freedom in the superconducting state. We give numerical evidence for the occurrence of a finite temperature Kosterlitz-Thouless transition to the $d_{x^2 -y^2}$ superconducting state. Above and below the Kosterlitz-Thouless transition temperature, $T_{KT}$, we compute the one-electron density of states, $N(\omega)$, the spin relaxation rate $1/T_1$, as well as the imaginary and real part of the spin susceptibility $\chi(\vec{q},\omega)$. The spin dynamics are characterized by the vanishing of $1/T_1$ and divergence of $Re \chi(\vec{q} = (\pi,\pi), \omega = 0)$ in the low temperature limit. As $T_{KT}$ is approached $N(\omega)$ develops a pseudo-gap feature and below $T_{KT}$ $Im \chi(\vec{q} = (\pi,\pi), \omega)$ shows a peak at finite frequency., Comment: 46 pages (latex) including 14 figures in encapsulated postscript format. Submitted for publication in Phys. Rev. B

We consider a Hubbard model on a square lattice with an additional interaction, $W$, which depends upon the square of a near-neighbor hopping. At half-filling and a constant value of the Hubbard repulsion, increasing the strength of the interaction $W$ drives the system from an antiferromagnetic Mott insulator to a $d_{x^2 -y^2}$ superconductor. This conclusion is reached on the basis of zero temperature quantum Monte Carlo simulations on lattice sizes up to $16 \times 16$., 4 pages (latex) and 4 postscript figures

Excitation spectra in Hubbard models from quantum Monte Carlo simulations / A. Muramatsu ... - In: Computer simulation studies in condensed matter physics / ed.: D. P. Landau ... - Berlin u.a. : Springer. - Vol. 7. (1994). - S. 113-124. - (Springer proceedings in physics ; 78)