arXiv subjects
Publications and source records attributed to Philipp Werner.
We generalize the recently developed diagrammatic Monte Carlo techniques for quantum impurity models from an imaginary time to a Keldysh formalism suitable for real-time and nonequilibrium calculations. Both weak-coupling and strong-coupling based methods are introduced, analysed and applied to the study of transport and relaxation dynamics in interacting quantum dots.
A three band model containing the essential physics of transition metal oxides with partially filled t_2g shells is solved in the single-site dynamical mean field approximation, using the full rotationally invariant Slater-Kanamori interactions. We compute the metal-Mott insulator phase diagram in the space of chemical potential and interaction strength, determine the response of the different phases to perturbations which break the orbital symmetry, and establish the regimes in which an orbital selective Mott phase occurs. The results are compared to data on titanates, ruthenates, vanadates and C_60.
The four-site DCA method of including intersite correlations in the dynamical mean field theory is used to investigate the metal-insulator transition in the Hubbard model. At half filling a gap-opening transition is found to occur as the interaction strength is increased beyond a critical value. The gapped behavior found in the 4-site DCA approximation is shown to be associated with the onset of strong antiferromagnetic and singlet correlations and the transition is found to be potential energy driven. It is thus more accurately described as a Slater phenomenon (induced by strong short ranged order) than as a Mott phenomenon. Doping the gapped phase leads to a non-Fermi-liquid state with a Fermi surface only in the nodal regions and a pseudogap in the antinodal regions at lower dopings $x \lesssim 0.15$ and to a Fermi liquid phase at higher dopings.
A single-site dynamical mean field study of a three band model with the rotationally invariant interactions appropriate to the t_2g levels of a transition metal oxide reveals a quantum phase transition between a paramagnetic metallic phase and an incoherent metallic phase with frozen moments. The Mott transitions occurring at electron densities n=2,3 per site take place inside the frozen moment phase. The critical line separating the two phases is characterized by a self energy with the frequency dependence Σ(ω)\sim \sqrtω and a broad quantum critical regime. The findings are discussed in the context of the power law observed in the optical conductivity of SrRuO_3.
We present a continuous-time Monte Carlo method for quantum impurity models, which combines a weak-coupling expansion with an auxiliary-field decomposition. The method is considerably more efficient than Hirsch-Fye and free of time discretization errors, and is particularly useful as impurity solver in large cluster dynamical mean field theory (DMFT) calculations.
Impurity solvers play an essential role in the numerical investigation of strongly correlated electrons systems within the "dynamical mean field" approximation. Recently, a new class of continuous-time solvers has been developed, based on a diagrammatic expansion of the partition function in either the interactions or the impurity-bath hybridization. We investigate the performance of these two complementary approaches and compare them to the well-established Hirsch-Fye method. The results show that the continuous-time methods, and in particular the version which expands in the hybridization, provide substantial gains in computational efficiency.
We present a method for solving impurity models with electron-phonon coupling, which treats the phonons efficiently and without approximations. The algorithm is applied to the Holstein-Hubbard model in the dynamical mean field approximation, where it allows access to strong interactions, very low temperatures and arbitrary fillings. We show that a renormalized Migdal-Eliashberg theory provides a reasonlable description of the phonon contribution to the electronic self energy in strongly doped systems, but fails if the quasiparticle energy becomes of order of the phonon frequency.
We study the interplay of crystal field splitting and Hund coupling in a two-orbital model which captures the essential physics of systems with two electrons or holes in the e_g shell. We use single site dynamical mean field theory with a recently developed impurity solver which is able to access strong couplings and low temperatures. The fillings of the orbitals and the location of phase boundaries are computed as a function of Coulomb repulsion, exchange coupling and crystal field splitting. We find that the Hund coupling can drive the system into a novel Mott insulating phase with vanishing orbital susceptibility. Away from half-filling, the crystal field splitting can induce an orbital selective Mott state.
During the last fourteen years several exact results were obtained for the so-called boundary sine-Gordon model. In the case of a conformal bulk this 2D boundary quantum field theory describes the universal scaling behavior of the Caldeira-Leggett model of resistively shunted Josephson junctions. In this work, we use a recently developed Monte Carlo technique to test some of the analytical predictions.
A powerful new impurity solver is shown to permit a systematic study of the doping driven Mott transition in a one-band Hubbard model within the framework of single-site dynamical mean field theory. At small dopings and large interaction strengths we are able access low enough temperatures that a reliable extrapolation to temperature T=0 may be performed, and ground state energies of insulating and metallic states may be compared. We find that the T=0 doping-driven transition is of second order and is characterized by an interaction-strength dependent electronic compressibility, which vanishes at the critical interaction strength of the half filled model. Over wide parameter ranges the compressibility is substantially reduced relative to the non-interacting system. The metal insulator transition is characterized by the appearance of in-gap states, but these are relevant only for very low dopings of less than 3%.
We perform a numerical analysis of recently proposed scaling functions for the single electron box. Specifically, we study the ``magnetic'' susceptibility as a function of tunneling conductance and gate charge, and the effective charging energy at zero gate charge as a function of tunneling conductance in the strong tunneling limit. Our Monte Carlo results confirm the accuracy of the theoretical predictions.
A recently developed continuous time solver based on an expansion in hybridization about an exactly solved local limit is reformulated in a manner appropriate for general classes of quantum impurity models including spin exchange and pair hopping terms. The utility of the approach is demonstrated via applications to the dynamical mean field theory of the Kondo lattice and two-orbital models. The algorithm can handle low temperatures and strong couplings without encountering a sign problem.
We study the stability of topological order against local perturbations by considering the effect of a magnetic field on a spin model -- the toric code -- which is in a topological phase. The model can be mapped onto a quantum loop gas where the perturbation introduces a bare loop tension. When the loop tension is small, the topological order survives. When it is large, it drives a continuous quantum phase transition into a magnetic state. The transition can be understood as the condensation of `magnetic' vortices, leading to confinement of the elementary `charge' excitations. We also show how the topological order breaks down when the system is coupled to an Ohmic heat bath and discuss our results in the context of quantum computation applications.
We present a new continuous time solver for quantum impurity models such as those relevant to dynamical mean field theory. It is based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter. Comparisons to quantum Monte Carlo and exact diagonalization calculations confirm the accuracy of the new approach, which allows very efficient simulations even at low temperatures and for strong interactions. As examples of the power of the method we present results for the temperature dependence of the kinetic energy and the free energy, enabling an accurate location of the temperature-driven metal-insulator transition.
Using a new cluster Monte Carlo algorithm, we study the phase diagram and critical properties of an interacting pair of resistively shunted Josephson junctions. This system models tunneling between two electrodes through a small superconducting grain, and is described by a double sine-Gordon model. In accordance with theoretical predictions, we observe three different phases and crossover effects arising from an intermediate coupling fixed point. On the superconductor-to-metal phase boundary, the observed critical behavior is within error-bars the same as in a single junction, with identical values of the critical resistance and a correlation function exponent which depends only on the strength of the Josephson coupling. We explain these critical properties on the basis of a renormalization group (RG) calculation. In addition, we propose an alternative new mean-field theory for this transition, which correctly predicts the location of the phase boundary at intermediate Josephson coupling strength.
We review efficient Monte Carlo methods for simulating quantum systems which couple to a dissipative environment. A brief introduction of the Caldeira-Leggett model and the Monte Carlo method will be followed by a detailed discussion of cluster algorithms and the treatment of long-range interactions. Dissipative quantum spins and resistively shunted Josephson junctions will be considered.
We use Monte Carlo simulations to study chains of Ising- and XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed previously, and here we consider a universal ratio of susceptibilities. We furthermore present the phase diagram and exponents of the dissipative XY-chain, which exhibits a second order phase transition. All our results compare well with the predictions from a dissipative $ϕ^4$ field theory.
We present numerical results on electron tunneling in a single-electron box at low temperature. The effective action of this device is equivalent to the Hamiltonian of a classical XY spin chain with long ranged interactions. Using an efficient cluster algorithm and a new transition matrix Monte Carlo approach, we are able to compute the effective charging energy $E_C^*$ in the limit of very small tunneling resistance. While previous Monte Carlo simulations were restricted to the weak and intermediate tunneling regimes, our method extends the range of $E_C^*$-values by more than 30 orders of magnitude. This allows us to clearly observe the exponential suppression of $E_C^*$ with increasing tunneling conductance $α$. For large, but fixed $α$, the correction to the leading exponential behavior exhibits a crossover from an intermediate temperature behavior at $βE_C^* \ll 1$, to zero temperature behavior at $βE_C^*\gg 1$. We determine this correction in both regimes and compare the numerical results to the numerous and controversial theoretical predictions for the strong tunneling limit.