arXiv subjects

Hans Gerd Evertz

Publications and source records attributed to Hans Gerd Evertz.

At least 19 recordsLinked to original sources

arXiv2019

Comparison of MPS based real time evolution algorithms for Anderson Impurity Models

We perform a detailed comparison of two Matrix Product States (MPS) based time evolution algorithms for Anderson Impurity Models. To describe the bath, we use both the star-geometry as well as the commonly employed Wilson chain geometry. For each bath geometry, we use either the Time Dependent Variational Principle (TDVP) or the Time Evolving Block Decimation (TEBD) to perform the time evolution. To apply TEBD for the star-geometry, we use a specially adapted algorithm that can deal with the long-range coupling terms. Analyzing the major sources of errors, one expects them to be proportional to the system size for all algorithms. Surprisingly, we find errors independent of system size except for TEBD in chain geometry. Additionally, we show that the right combination of bath representation and time evolution algorithm is important. While TDVP in chain geometry is a very precise approach, TEBD in star geometry is much faster, such that for a given accuracy it is superior to TDVP in chain geometry. This makes the adapted version of TEBD in star geometry the most efficient method to solve impurity problems.

cond-mat.str-el↗

arXiv2018

Dynamical Mean-Field Theory on the Real-Frequency Axis: p-d Hybridizations and Atomic Physics in SrMnO$_3$

We investigate the electronic structure of SrMnO$_3$ with Density Functional Theory (DFT) plus Dynamical Mean-Field Theory (DMFT). Within this scheme the selection of the correlated subspace and the construction of the corresponding Wannier functions is a crucial step. Due to the crystal field splitting of the Mn-$3d$ orbitals and their separation from the O-2$p$ bands, SrMnO$_3$ is a material where on first sight a 3-band $d$-only model should be sufficient. However, in the present work we demonstrate that the resulting spectrum is considerably influenced by the number of correlated orbitals and the number of bands included in the Wannier function construction. For example, in a $d$-$dp$ model we observe a splitting of the \tg lower Hubbard band into a more complex spectral structure, not observable in $d$-only models. To illustrate these high-frequency differences we employ the recently developed Fork Tensor Product State (FTPS) impurity solver, as it provides the necessary spectral resolution on the real-frequency axis. We find that the spectral structure of a 5-band $d$-$dp$ model is in good agreement with PES and XAS experiments. Our results demonstrate that the FTPS solver is capable of performing full 5-band DMFT calculations directly on the real-frequency axis.

cond-mat.str-el↗

arXiv2017

Fork Tensor Product States - Efficient Three Orbital Real Time DMFT Solver

We present a tensor network especially suited for multi-orbital Anderson impurity models and as an impurity solver for multi-orbital dynamical mean-field theory (DMFT). The solver works directly on the real-frequency axis and yields very high spectral resolution at all frequencies. We use a large number $\left(\mathcal{O}(100)\right)$ of bath sites, and therefore achieve an accurate representation of the bath. The solver can treat full rotationally invariant interactions with reasonable numerical effort. We show the efficiency and accuracy of the method by a benchmark for the testbed material SrVO$_3$. There we observe multiplet structures in the high-energy spectrum which are almost impossible to resolve by other multi-orbital methods. The resulting structure of the Hubbard bands can be described as a broadened atomic spectrum with rescaled interaction parameters. Additional features emerge when $U$ is increased. The impurity solver offers a new route to the calculation of precise real-frequency spectral functions of correlated materials.

cond-mat.str-el↗

arXiv2017

Interaction effects in a microscopic quantum wire model with strong spin-orbit interaction

We investigate the effect of strong interactions on the spectral properties of quantum wires with strong Rashba spin-orbit interaction in a magnetic field, using a combination of Matrix Product State and bosonization techniques. Quantum wires with strong Rashba spin-orbit interaction and magnetic field exhibit a partial gap in one-half of the conducting modes. Such systems have attracted wide-spread experimental and theoretical attention due to their unusual physical properties, among which are spin-dependent transport, or a topological superconducting phase when under the proximity effect of an s-wave superconductor. As a microscopic model for the quantum wire we study an extended Hubbard model with spin-orbit interaction and Zeeman field. We obtain spin resolved spectral densities from the real-time evolution of excitations, and calculate the phase diagram. We find that interactions increase the pseudo gap at $k = 0$ and thus also enhance the Majorana-supporting phase and stabilize the helical spin order. Furthermore, we calculate the optical conductivity and compare it with the low energy spiral Luttinger Liquid result, obtained from field theoretical calculations. With interactions, the optical conductivity is dominated by an excotic excitation of a bound soliton-antisoliton pair known as a breather state. We visualize the oscillating motion of the breather state, which could provide the route to their experimental detection in e.g. cold atom experiments.

cond-mat.str-el↗

arXiv2016

Universal front propagation in the quantum Ising chain with domain-wall initial states

We study the melting of domain walls in the ferromagnetic phase of the transverse Ising chain, created by flipping the order-parameter spins along one-half of the chain. If the initial state is excited by a local operator in terms of Jordan-Wigner fermions, the resulting longitudinal magnetization profiles have a universal character. Namely, after proper rescalings, the profiles in the noncritical Ising chain become identical to those obtained for a critical free-fermion chain starting from a step-like initial state. The relation holds exactly in the entire ferromagnetic phase of the Ising chain and can even be extended to the zero-field XY model by a duality argument. In contrast, for domain-wall excitations that are highly non-local in the fermionic variables, the universality of the magnetization profiles is lost. Nevertheless, for both cases we observe that the entanglement entropy asymptotically saturates at the ground-state value, suggesting a simple form of the steady state.

cond-mat.stat-mech↗

arXiv2015

Auxiliary master equation approach within matrix product states: Spectral properties of the nonequilibrium Anderson impurity model

Within the recently introduced auxiliary master equation approach it is possible to address steady state properties of strongly correlated impurity models, small molecules or clusters efficiently and with high accuracy. It is particularly suited for dynamical mean field theory in the nonequilibrium as well as in the equilibrium case. The method is based on the solution of an auxiliary open quantum system, which can be made quickly equivalent to the original impurity problem. In its first implementation a Krylov space method was employed. Here, we aim at extending the capabilities of the approach by adopting matrix product states for the solution of the corresponding auxiliary quantum master equation. This allows for a drastic increase in accuracy and permits us to access the Kondo regime for large values of the interaction. In particular, we investigate the nonequilibrium steady state of a single impurity Anderson model and focus on the spectral properties for temperatures T below the Kondo temperature T_K and for small bias voltages phi. For the two cases considered, with T=T_K/4 and T=T_K/10 we find a clear splitting of the Kondo resonance into a two-peak structure for phi close above T_K. In the equilibrium case (phi=0) and for T=T_K/4, the obtained spectral function essentially coincides with the one from numerical renormalization group.

cond-mat.str-el↗

arXiv2015

Efficient DMFT impurity solver using real-time dynamics with Matrix Product States

We propose to calculate spectral functions of quantum impurity models using the Time Evolving Block Decimation (TEBD) for Matrix Product States. The resolution of the spectral function is improved by a so-called linear prediction approach. We apply the method as an impurity solver within the Dynamical Mean Field Theory (DMFT) for the single- and two-band Hubbard model on the Bethe lattice. For the single-band model we observe sharp features at the inner edges of the Hubbard bands. A finite size scaling shows that they remain present in the thermodynamic limit. We analyze the real time-dependence of the double occupation after adding a single electron and observe oscillations at the same energy as the sharp feature in the Hubbard band, indicating a long-lived coherent superposition of states that correspond to the Kondo peak and the side peaks. For a two-band Hubbard model we observe an even richer structure in the Hubbard bands, which cannot be related to a multiplet structure of the impurity, in addition to sharp excitations at the band edges of a type similar to the single-band case.

cond-mat.str-el↗

arXiv2015

Quasi-soliton scattering in quantum spin chains

The quantum scattering of magnon bound states in the anisotropic Heisenberg spin chain is shown to display features similar to the scattering of solitons in classical exactly solvable models. Localized colliding Gaussian wave packets of bound magnons are constructed from string solutions of the Bethe equations and subsequently evolved in time, relying on an algebraic Bethe ansatz based framework for the computation of local expectation values in real space-time. The local magnetization profile shows the trajectories of colliding wave packets of bound magnons, which obtain a spatial displacement upon scattering. Analytic predictions on the displacements for various values of anisotropy and string lengths are derived from scattering theory and Bethe ansatz phase shifts, matching time evolution fits on the displacements. The time evolved block decimation (TEBD) algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.

cond-mat.str-el↗

arXiv2015

Nonequilibrium, spatio-temporal formation of the Kondo screening-cloud on a lattice

We study the nonequilibrium formation of a spin screening cloud that accompanies the quenching of a local magnetic moment immersed in a Fermi sea at zero temperature. Based on high precision density matrix renormalization group results for the interacting single impurity Anderson model we discuss the real time evolution after a quantum quench in the impurity-reservoir hybridization using time evolving block decimation. We report emergent length and time scales in the spatiotemporal structure of non-local correlation functions in the spin- and the charge density channel. At equilibrium, our data for the correlation functions and the extracted length-scales show good agreement with existing results, as do local time dependent observables at the impurity. In the time-dependent data, we identify a major signal which defines a "light cone" moving at the Fermi velocity and a ferromagnetic component in its wake. Inside the light cone we find that the structure of the nonequilibrium correlation functions emerges on two time scales. Initially, the qualitative structure of the correlation functions develops rapidly at the lattice Fermi velocity. Subsequently the spin correlations converge to the equilibrium results on a much larger time scale. This process sets a dynamic energy scale, which we identify to be proportional to the Kondo temperature. Outside the light cone we observe two different power law decays of the correlation functions in space, with time and interaction strength independent exponents.

cond-mat.str-el↗

arXiv2014

Chebyshev expansion for Impurity Models using Matrix Product States

We improve a recently developed expansion technique for calculating real frequency spectral functions of any one-dimensional model with short-range interactions, by postprocessing computed Chebyshev moments with linear prediction. This can be achieved at virtually no cost and, in sharp contrast to existing methods based on the dampening of the moments, improves the spectral resolution rather than lowering it. We validate the method for the exactly solvable resonating level model and the single impurity Anderson model. It is capable of resolving sharp Kondo resonances, as well as peaks within the Hubbard bands when employed as an impurity solver for dynamical mean-field theory (DMFT). Our method works at zero temperature and allows for arbitrary discretization of the bath spectrum. It achieves similar precision as the dynamical density matrix renormalization group (DDMRG), at lower cost. We also propose an alternative expansion, of 1-exp(-tau H) instead of the usual H, which opens the possibility of using established methods for the time evolution of matrix product states to calculate spectral functions directly.

cond-mat.str-el↗

arXiv2013

Quantum Monte Carlo Simulations for Stacked Spin Ladder Systems Containing Low Concentrations of Non-Magnetic Impurities; Application to the Low Temperature Broadening of NMR-Spectra in SrCu2O3

We present a Quantum Monte Carlo study for Heisenberg spin-1/2 two leg ladder systems doped with non magnetic impurities. The simulations are applied to the doped spin ladder compound SrCu2O3 doped with Zn, where a large broadening of the 65Cu NMR lines has been observed in experiment at low temperatures but far above the Neel temperature. We find that interladder-couplings with a sizeable coupling in stacking direction are required to describe the line broadening, which can not be explained by considering a single ladder only. Around a single impurity, spin correlations cause an exponentially decaying antiferromagnetic local magnetization in a magnetic field. We develop an effective model for the local magnetization of systems with many randomly distributed impurities, with few parameters which can be extracted out of QMC calculations with a single impurity. The broadening arises from a drag effect, where the magnetization around an impurity works as an effective field for spins on the neighboring ladders, causing a non-exponentially decaying magnetization cloud around the impurity. Our results show that even for impurity concentrations as small as x = 0.001 and x = 0.0025, the broadening effect is large, in good quantitative agreement with experiment. We also develop a simple model for the effective interaction of two impurity spins.

cond-mat.str-el↗

arXiv2013

Steady-state and quench dependent relaxation of a quantum dot coupled to one-dimensional leads

We study the time evolution and steady state of the charge current in a single-impurity Anderson model, using matrix product states techniques. A nonequilibrium situation is imposed by applying a bias voltage across one-dimensional tight-binding leads. Focusing on particle-hole symmetry, we extract current-voltage characteristics from universal low-bias up to high-bias regimes, where band effects start to play a dominant role. We discuss three quenches, which after strongly quench-dependent transients yield the same steady-state current. Among these quenches we identify those favorable for extracting steady-state observables. The period of short-time oscillations is shown to compare well to real-time renormalization group results for a simpler model of spinless fermions. We find indications that many-body effects play an important role at high-bias voltage and finite bandwidth of the metallic leads. The growth of entanglement entropy after a certain time scale (proportional to the inverse of Delta) is the major limiting factor for calculating the time evolution. We show that the magnitude of the steady-state current positively correlates with entanglement entropy. The role of high-energy states for the steady-state current is explored by considering a damping term in the time evolution.

cond-mat.str-el↗

arXiv2012

Steady-state spectra, current and stability diagram of a quantum dot: a non-equilibrium Variational Cluster Approach

We calculate steady-state properties of a strongly correlated quantum dot under voltage bias by means of non-equilibrium Cluster Perturbation Theory and the non-equilibrium Variational Cluster Approach, respectively. Results for the steady-state current are benchmarked against data from accurate Matrix Product State based time evolution. We show that for low to medium interaction strength, non-equilibrium Cluster Perturbation Theory already yields good results, while for higher interaction strength the self-consistent feedback of the non-equilibrium Variational Cluster Approach significantly enhances the accuracy. We report the current-voltage characteristics for different interaction strengths. Furthermore we investigate the non-equilibrium local density of states of the quantum dot and illustrate that within the variational approach a linear splitting and broadening of the Kondo resonance is predicted which depends on interaction strength. Calculations with applied gate voltage, away from particle hole symmetry, reveal that the maximum current is reached at the crossover from the Kondo regime to the doubly-occupied or empty quantum dot. Obtained stability diagrams compare very well to recent experimental data [Phys. Rev. B, 84, 245316 (2011)].

cond-mat.str-el↗

arXiv2012

Worm algorithms for the 3-state Potts model with magnetic field and chemical potential

We discuss worm algorithms for the 3-state Potts model with external field and chemical potential. The complex phase problem of this system can be overcome by using a flux representation where the new degrees of freedom are dimer and monomer variables. Working with this representation we discuss two different generalizations of the conventional Prokof'ev-Svistunov algorithm suitable for Monte Carlo simulations of the model at arbitrary chemical potential and evaluate their performance.

hep-lat↗

arXiv2011

Observing complex bound states in the spin-1/2 Heisenberg XXZ chain using local quantum quenches

We consider the non-equilibrium evolution in the spin-1/2 XXZ Heisenberg chain for fixed magnetization after a local quantum quench. This model is equivalent to interacting spinless fermions. Initially an infinite magnetic field is applied to n consecutive sites and the ground state is calculated. At time t=0 the field is switched off and the time evolution of observables such as the z-component of spin is computed using the Time Evolving Block Decimation (TEBD) algorithm. We find that the observables exhibit strong signatures of linearly propagating spinon and bound state excitations. These persist even when integrability-breaking perturbations are included. Since bound states ("strings") are notoriously difficult to observe using conventional probes such as inelastic neutron scattering, we conclude that local quantum quenches are an ideal setting for studying their properties. We comment on implications of our results for cold atom experiments.

cond-mat.str-el↗

arXiv2011

The QCD Phase Diagram with Effective Theories

We study two effective theories for QCD at non-zero temperature and finite chemical potential, using local Polyakov loops as the degrees of freedom. The sign problem is solved by exactly mapping the partition function to a sum over flux and monomer variables with only real and positive weights, making the two models accessible to Monte Carlo simulation techniques. We use generalized worm algorithms and a local Metropolis update to perform the simulations and determine the phase diagram as a function of the temperature and the chemical potential.

hep-lat↗

arXiv2011

Solving the Complex Phase Problem in a QCD Related Model

We discuss an effective theory for QCD at finite chemical potential and non-zero temperature, where QCD is reduced to its center degrees of freedom. The effective action can be mapped to a flux representation, where the complex phase problem is solved and the theory accessible to Monte Carlo techniques. In this work, we use a generalized Prokof'ev-Svistunov worm algorithm to perform the simulations and determine the phase diagram as a function of temperature, quark mass and chemical potential. It turns out that the transition is qualitatively as expected for QCD.

hep-lat↗

arXiv2011

The QCD phase diagram according to the center group

We study an effective theory for QCD at finite temperature and density which contains the leading center symmetric and center symmetry breaking terms. The effective theory is studied in a flux representation where the complex phase problem is absent and the model becomes accessible to Monte Carlo techniques also at finite chemical potential. We simulate the system using a generalized Prokof'ev-Svistunov worm algorithm and compare the results to a low temperature expansion. The phase diagram is determined as a function of temperature, chemical potential and quark mass. Shape and quark mass dependence of the phase boundaries are as expected for QCD. The transition into the deconfined phase is smooth throughout, without any discontinuities or critical points.

hep-lat↗