arXiv subjects

N. Blümer

Publications and source records attributed to N. Blümer.

At least 19 recordsLinked to original sources

arXiv2015

Deciding the fate of the false Mott transition in two dimensions by exact quantum Monte Carlo methods

We present an algorithm for the computation of unbiased Green functions and self-energies for quantum lattice models, free from systematic errors and valid in the thermodynamic limit. The method combines direct lattice simulations using the Blankenbecler Scalapino-Sugar quantum Monte Carlo (BSS-QMC) approach with controlled multigrid extrapolation techniques. We show that the half-filled Hubbard model is insulating at low temperatures even in the weak-coupling regime; the previously claimed Mott transition at intermediate coupling does not exist.

cond-mat.str-el↗

arXiv2014

Fate of the false Mott-Hubbard transition in two dimensions

We have studied the impact of non-local electronic correlations at all length scales on the Mott-Hubbard metal-insulator transition in the unfrustrated two-dimensional Hubbard model. Combining dynamical vertex approximation, lattice quantum Monte-Carlo and variational cluster approximation, we demonstrate that scattering at long-range fluctuations, i.e., Slater-like paramagnons, opens a spectral gap at weak-to-intermediate coupling -- irrespectively of the preformation of localized or short-ranged magnetic moments. This is the reason, why the two-dimensional Hubbard model is insulating at low enough temperatures for any (finite) interaction and no Mott-Hubbard transition is observed.

cond-mat.str-el↗

arXiv2014

Tunable nanomagnetism in moderately cold fermions on optical lattices

Localized defects, unavoidable in real solids, may be simulated in (generically defect-free) cold-atom systems, e.g., via modifications of the optical lattice. We study the Hubbard model on a square lattice with single impurities, pairs of nearby impurities, or lines of impurities using numerically exact determinantal quantum Monte Carlo simulations. In all cases, correlations on the "impurity" sites are enhanced either by larger on-site interactions or by a reduced coupling to the environment. We find highly nontrivial magnetic correlations, which persist at elevated temperatures and should be accessible in cold-atom systems with current experimental techniques. With improved cooling techniques, these features could be followed towards generic quantum antiferromagnetism in the homogeneous limit. More generally, tunable crossing points between different correlation functions could be used, in a quantum steelyard balance setup, as robust thermometers.

cond-mat.quant-gas↗

arXiv2013

Quasi continuous-time impurity solver for the dynamical mean-field theory with linear scaling in the inverse temperature

We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary Hamiltonian, for which the Green function is computed by combining determinantal quantum Monte Carlo (BSS-QMC) calculations with a multigrid extrapolation procedure. The method is numerically exact, i.e., yields results which are free of significant Trotter errors, but retains the BSS advantage, compared to direct QMC impurity solvers, of linear (instead of cubic) scaling with the inverse temperature. The new algorithm is applied to the half-filled Hubbard model close to the Mott transition; detailed comparisons with exact diagonalization, Hirsch-Fye QMC, and continuous-time QMC are provided.

cond-mat.str-el↗

arXiv2013

Orbital-selective Mott transitions in a doped two-band Hubbard model with crystal field splitting

We investigate the effects of crystal field splitting in a doped two-band Hubbard model with different bandwidths within dynamical mean-field theory (DMFT), using a quantum Monte Carlo impurity solver. In addition to an orbital-selective Mott phase (OSMP) of the narrow band, which is adiabatically connected with the well-studied OSMP in the half-filled case without crystal field splitting, we find, for sufficiently strong interaction and a suitable crystal field, also an OSMP of the wide band. We establish the phase diagram (in the absence of magnetic or orbital order) at moderate doping as a function of interaction strength and crystal field splitting and show that also the wide-band OSMP is associated with non-Fermi-liquid behavior in the case of Ising type Hund rule couplings. Our numerical results are supplemented by analytical strong-coupling studies of spin order and spectral functions at integer filling.

cond-mat.str-el↗

arXiv2013

Mott transitions in the half-filled SU(2M) symmetric Hubbard model

The Hubbard model with large orbital degeneracy has recently gained relevance in the context of ultracold earth alkali like atoms. We compute its static properties in the SU(2M) symmetric limit for up to M=8 bands at half filling within dynamical mean-field theory, using the numerically exact multigrid Hirsch-Fye quantum Monte Carlo approach. Based on this unbiased data, we establish scaling laws which predict the phase boundaries of the paramagnetic Mott metal-insulator transition at arbitrary orbital degeneracy M with high accuracy.

cond-mat.str-el↗

arXiv2012

Momentum-dependent pseudogaps in the half-filled two-dimensional Hubbard model

We compute unbiased spectral functions of the two-dimensional Hubbard model by extrapolating Green functions, obtained from determinantal quantum Monte Carlo simulations, to the thermodynamic and continuous time limits. Our results clearly resolve the pseudogap at weak to intermediate coupling, originating from a momentum selective opening of the charge gap. A characteristic pseudogap temperature T*, determined consistently from the spectra and from the momentum dependence of the imaginary-time Green functions, is found to match the dynamical mean-field critical temperature, below which antiferromagnetic fluctuations become dominant. Our results identify a regime where pseudogap physics is within reach of experiments with cold fermions in optical lattices.

cond-mat.str-el↗

arXiv2012

Universal probes for antiferromagnetic correlations and entropy in cold fermions on optical lattices

We determine antiferromagnetic (AF) signatures in the half-filled Hubbard model at strong coupling on a cubic lattice and in lower dimensions. Upon cooling, the transition from the charge-excitation regime to the AF Heisenberg regime is signaled by a universal minimum of the double occupancy at entropy s=S/(N k_B)=s*=ln(2) per particle and a linear increase of the next-nearest neighbor (NNN) spin correlation function for s<s*. This crossover, driven by a gain in kinetic exchange energy, appears as the essential AF physics relevant for current cold-atom experiments. The onset of long-range AF order (at low s on cubic lattices) is hardly visible in nearest-neighbor spin correlations versus s, but could be detected in spin correlations at or beyond NNN distances.

cond-mat.quant-gas↗

arXiv2011

Double occupancy as a universal probe for antiferromagnetic correlations and entropy in cold fermions on optical lattices

We verify signatures of antiferromagnetic (AF) correlations in the double occupancy D [Gorelik et al., PRL 105, 065301 (2010)] and study their dimensional dependence using direct quantum Monte Carlo in dimensions d=2,3 and Bethe Ansatz in d=1. We find quantitative agreement with dynamical mean-field theory (DMFT) in the cubic case and qualitative agreement down to d=1. As a function of entropy s=S/(N k_B), D is nearly universal with respect to d; the minimum in D(s) approaches s=log(2) at strong coupling, as predicted by DMFT. Long-range order appears hardly relevant for the current search of AF signatures in cold fermions. Thus, experimentalists need not achieve s<log(2)/2 and should consider lower dimensions, for which the AF effects are larger.

cond-mat.quant-gas↗

arXiv2010

Quantum Monte Carlo simulations of antiferromagnetism in ultracold fermions on optical lattices within real-space dynamical mean-field theory

We present a massively parallel quantum Monte Carlo based implementation of real-space dynamical mean-field theory for general inhomogeneous correlated fermionic lattice systems. As a first application, we study magnetic order in a binary mixture of repulsively interacting fermionic atoms harmonically trapped in an optical lattice. We explore temperature effects and establish signatures of the Néel transition in observables directly accessible in cold-atom experiments; entropy estimates are also provided. We demonstrate that the local density approximation (LDA) fails for ordered phases. In contrast, a "slab" approximation allows us to reach experimental system sizes with O(10^5) atoms without significant loss of accuracy.

cond-mat.quant-gas↗

arXiv2010

Néel transition of lattice fermions in a harmonic trap: a real-space DMFT study

We study the magnetic ordering transition for a system of harmonically trapped ultracold fermions with repulsive interactions in a cubic optical lattice, within a real-space extension of dynamical mean-field theory (DMFT). Using a quantum Monte Carlo impurity solver, we establish that antiferromagnetic correlations are signaled, at strong coupling, by an enhanced double occupancy. This signature is directly accessible experimentally and should be observable well above the critical temperature for long-range order. Dimensional aspects appear less relevant than naively expected.

cond-mat.quant-gas↗

arXiv2009

Mott transitions in ternary flavor mixtures of ultracold fermions on optical lattices

Ternary flavor mixtures of ultracold fermionic atoms in an optical lattice are studied in the case of equal, repulsive on-site interactions U>0. The corresponding SU(3) invariant Hubbard model is solved numerically exactly within dynamical mean-field theory using multigrid Hirsch-Fye quantum Monte Carlo simulations. We establish Mott transitions close to integer filling at low temperatures and show that the associated signatures in the compressibility and pair occupancy persist to high temperatures, i.e., should be accessible to experiments. In addition, we present spectral functions and discuss the properties of a ``semi-compressible'' state observed for large U near half filling.

cond-mat.quant-gas↗

arXiv2008

Multigrid Hirsch-Fye quantum Monte Carlo method for dynamical mean-field theory

We present a new algorithm which allows for direct numerically exact solutions within dynamical mean-field theory (DMFT). It is based on the established Hirsch-Fye quantum Monte Carlo (HF-QMC) method. However, the DMFT impurity model is solved not at fixed imaginary-time discretization Delta_tau, but for a range of discretization grids; by extrapolation, unbiased Green functions are obtained in each DMFT iteration. In contrast to conventional HF-QMC, the multigrid algorithm converges to the exact DMFT fixed points. It extends the useful range of Delta_tau, is precise and reliable even in the immediate vicinity of phase transitions and is more efficient, also in comparison to continuous-time methods. Using this algorithm, we show that the spectral weight transfer at the Mott transition has been overestimated in a recent density matrix renormalization group study.

cond-mat.str-el↗

arXiv2007

Numerically exact Green functions from Hirsch-Fye quantum Monte Carlo simulations

We present a new method for extracting numerically exact imaginary-time Green functions from standard Hirsch-Fye quantum Monte Carlo (HF-QMC) simulations within dynamical mean-field theory. By analytic continuation, angular resolved spectra are obtained without the discretization bias previously associated with HF-QMC results. The method is shown to be accurate even at very low temperatures (T=W/800 for bandwidth W) in the strongly correlated regime.

cond-mat.str-el↗

arXiv2007

Efficiency of quantum Monte Carlo impurity solvers for dynamical mean-field theory

Since the inception of the dynamical mean-field theory, numerous numerical studies have relied on the Hirsch-Fye quantum Monte Carlo (HF-QMC) method for solving the associated impurity problem. Recently developed continuous-time algorithms (CT-QMC) avoid the Trotter discretization error and allow for faster configuration updates, which makes them candidates for replacing HF-QMC. We demonstrate, however, that a state-of-the-art implementation of HF-QMC (with extrapolation of discretization delta_tau -> 0) is competitive with CT-QMC. A quantitative analysis of Trotter errors in HF-QMC estimates and of appropriate delta_tau values is included.

cond-mat.str-el↗

arXiv2006

Orbital-selective Mott transitions in two-band Hubbard models

The anisotropic two-orbital Hubbard model is investigated at low temperatures using high-precision quantum Monte Carlo (QMC) simulations within dynamical mean-field theory (DMFT). We demonstrate that two distinct orbital-selective Mott transitions (OSMTs) occur for a bandwidth ratio of 2 even without spin-flip contributions to the Hund exchange, and we quantify numerical errors in earlier QMC data which had obscured the second transition. The limit of small inter-orbital coupling is introduced via a new generalized Hamiltonian and studied using QMC and Potthoff's self-energy functional method, yielding insight into the nature of the OSMTs and the non-Fermi-liquid OSM phase and opening the possibility for a new quantum-critical point.

cond-mat.str-el↗

arXiv2005

Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice

We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity which maps the problem onto the case of only nearest-neighbor hopping. We find in particular that hopping between next-nearest neighbors leads to an asymmetric spectrum with additional van-Hove singularities.

cond-mat.str-el↗

arXiv2005

Orbital-selective Mott transitions in the 2-band J_z-model: a high-precision quantum Monte Carlo study

Using high-precision quantum Monte Carlo (QMC) simulations within the framework of dynamical mean field theory (DMFT), we show that the anisotropic degenerate two-orbital Hubbard model contains two consecutive orbital-selective Mott transitions (OSMTs) even in the absence of spin-flip terms and pair-hopping processes. In order to reveal the second transition we carefully analyze the low-frequency part of the self-energy and the local spectral functions. This paper extends our previous work to lower temperatures. We discuss the nature - in particular the order - of both Mott transitions and list various possible extensions.

cond-mat.str-el↗