arXiv subjects

Götz S. Uhrig

Publications and source records attributed to Götz S. Uhrig.

At least 73 records · Page 4Linked to original sources

arXiv2017

Tunable dispersion of the edge states in the integer quantum Hall effect

Topological aspects represent currently a boosting area in condensed matter physics. Yet there are very few suggestions for technical applications of topological phenomena. Still, the most important is the calibration of resistance standards by means of the integer quantum Hall effect. We propose modifications of samples displaying the integer quantum Hall effect which render the tunability of the Fermi velocity possible by external control parameters such as gate voltages. In this way, so far unexplored possibilities arise to realize devices such as tunable delay lines and interferometers.

cond-mat.mes-hall↗

arXiv2017

Effects of Interactions on Dynamic Correlations of Hard-Core Bosons at Finite Temperatures

We investigate how dynamic correlations of hard-core bosonic excitation at finite temperature are affected by additional interactions besides the hard-core repulsion which prevents them from occupying the same site. We focus especially on dimerized spin systems, where these additional interactions between the elementary excitations, triplons, lead to the formation of bound states, relevant for the correct description of scattering processes. In order to include these effects quantitatively we extend the previously developed Brückner approach to include also nearest-neighbor (NN) and next-nearest neighbor (NNN) interactions correctly in a low-temperature expansion. This leads to the extension of the scalar Bethe-Salpeter equation to a matrix-valued equation. Exemplarily, we consider the Heisenberg spin ladder to illustrate the significance of the additional interactions on the spectral functions at finite temperature which are proportional to inelastic neutron scattering rates.

cond-mat.str-el↗

arXiv2017

Singlet exciton condensation and bond-order-wave phase in the extended Hubbard model

The competition of interactions implies the compensation of standard mechanisms which leads to the emergence of exotic phases between conventional phases. The extended Hubbard model (EHM) is a fundamental example for the competition of the local Hubbard interaction and the nearest-neighbor density-density interaction, which at half-filling and in one dimension leads to a bond order wave (BOW) between a charge density wave (CDW) and a quasi-long-range order Mott insulator (MI). We study the full momentum-resolved excitation spectrum of the one dimensional EHM in the CDW phase and clarify the relation between different elementary energy gaps. We show that the CDW-to-BOW transition is driven by the softening of a singlet exciton at momentum $π$. The BOW is realized as the condensate of this singlet exciton.

cond-mat.str-el↗

arXiv2017

Influence of the nuclear Zeeman effect on mode locking in pulsed semiconductor quantum dots

The coherence of the electron spin in a semiconductor quantum dot is strongly enhanced by mode locking through nuclear focusing, where the synchronization of the electron spin to periodic pulsing is slowly transferred to the nuclear spins of the semiconductor material, mediated by the hyperfine interaction between these. The external magnetic field that drives the Larmor oscillations of the electron spin also subjects the nuclear spins to a Zeeman-like coupling, albeit a much weaker one. For typical magnetic fields used in experiments, the energy scale of the nuclear Zeeman effect is comparable to that of the hyperfine interaction, so that it is not negligible. In this work, we analyze the influence of the nuclear Zeeman effect on mode locking quantitatively. Within a perturbative framework, we calculate the Overhauser-field distribution after a prolonged period of pulsing. We find that the nuclear Zeeman effect can exchange resonant and non-resonant frequencies. We distinguish between models with a single type and with multiple types of nuclei. For the latter case, the positions of the resonances depend on the individual $g$ factors, rather than on the average value.

cond-mat.mes-hall↗

arXiv2017

Efficient algorithms for the dynamics of large and infinite classical central spin models

We investigate the time dependence of correlation functions in the central spin model, which describes the electron or hole spin confined in a quantum dot, interacting with a bath of nuclear spins forming the Overhauser field. For large baths, a classical description of the model yields quantitatively correct results. We develop and apply various algorithms in order to capture the long-time limit of the central spin for bath sizes from 1000 to infinitely many bath spins. Representing the Overhauser field in terms of orthogonal polynomials, we show that a carefully reduced set of differential equations is sufficient to compute the spin correlations of the full problem up to very long times, for instance up to $10^5\hbar/J_\mathrm{Q}$ where $J_\mathrm{Q}$ is the natural energy unit of the system. This technical progress renders an analysis of the model with experimentally relevant parameters possible. We benchmark the results of the algorithms with exact data for a small number of bath spins and we predict how the long-time correlations behave for different effective numbers of bath spins.

cond-mat.mes-hall↗

arXiv2017

Massive spinons in $S=1/2$ spin chains: spinon-pair operator representation

Spinons are among the generic excitations in one-dimensional spin systems, they can be massless or massive. The quantitative description of massive spinons poses a considerable challenge in spite of various variational approaches. We show that a representation in terms of hopping and Bogoliubov spinon processes, which we call "spinon-pair" operators, and their combination is possible. We refer to such a representation as second quantized form. Neglecting terms which change the number of spinons yields the variational results. Treating the bilinear and quartic terms by continuous unitary transformations leads to considerably improved results. Thus, we provide the proof-of-principle that systems displaying massive spinons as elementary excitations can be treated in second quantization based on spinon-pair representation.

cond-mat.str-el↗

arXiv2016

Minimal model for the frustrated spin ladder system BiCu$_2$PO$_6$

To establish the microscopic model of the compound BiCu$_2$PO$_6$ is a challenging task. Inelastic neutron scattering experiments showed that the dispersion of this material is non-degenerate suggesting the existence of anisotropic interactions. Here we present a quantitative description of the excitation spectrum for BiCu$_2$PO$_6$ on the one-particle level. The solution of the isotropic frustrated spin ladder by continuous unitary transformations is the starting point of our approach. Further couplings such as isotropic interladder couplings and anisotropic interactions are included on the mean-field level. Our aim is to establish a minimal model built on the symmetry allowed interactions and to find a set of parameters, which allow us to describe the low-energy part of the dispersion without assuming unrealistic couplings.

cond-mat.str-el↗

arXiv2016

Persisting correlations of a central spin coupled to large spin baths

The decohering environment of a quantum bit is often described by the coupling to a large bath of spins. The quantum bit itself can be seen as a spin $S=1/2$ which is commonly called the central spin. The resulting central spin model describes an important mechanism of decoherence. We provide mathematically rigorous bounds for a persisting magnetization of the central spin in this model with and without magnetic field. In particular, we show that there is a well defined limit of infinite number of bath spins. Only if the fraction of very weakly coupled bath spins tends to 100\% does no magnetization persist.

quant-ph↗

arXiv2016

Increased coherence time in narrowed bath states in quantum dots

We study the influence of narrowed distributions of the nuclear Overhauser field on the decoherence of a central electron spin in quantum dots. We describe the spin dynamics in quantum dots by the central spin model. We use analytic solutions for uniform couplings and the time dependent density-matrix renormalization group (tDMRG) for nonuniform couplings. With these tools we calculate the dynamics of the central spin for large baths of nuclear spins with or without external magnetic field applied to the central spin. The focus of our study is the influence of initial mixtures with narrowed distributions of the Overhauser field and of applied magnetic fields on the decoherence of the central spin.

cond-mat.mes-hall↗

arXiv2016

Tunable and direction-dependent group velocities in topologically protected edge states

Topological effects continue to fascinate physicists since more than three decades. One of their main applications are high-precision measurements of the resistivity. We propose to make also use of the spatially separated edge states. It is possible to realize strongly direction-dependent group velocities. They can also be tuned over orders of magnitude so that robust delay lines and interference devices are within reach.

cond-mat.mes-hall↗

arXiv2016

Orientational bond and Néel order in the two-dimensional ionic Hubbard model

Unconventional phases often occur where two competing mechanisms compensate. An excellent example is the ionic Hubbard model where the alternating local potential $δ$, favoring a band insulator (BI), competes with the local repulsion $U$, favoring a Mott insulator (MI). By continuous unitary transformations we derive effective models in which we study the softening of various excitons. The softening signals the instability towards new phases that we describe on the mean-field level. On increasing $U$ from the BI in two dimensions, we find a bond-ordered phase breaking orientational symmetry due to a d-wave component. Then, antiferromagnetic order appears coexisting with the d-wave bond order. Finally, the d-wave order vanishes and a Néel-type MI persists.

cond-mat.str-el↗

arXiv2016

Topologically non-trivial Hofstadter bands on the kagome lattice

We investigate how the multiple bands of fermions on a crystal lattice evolve if a magnetic field is added which does not increase the number of bands. The kagome lattice is studied as generic example for a lattice with loops of three bonds. Finite Chern numbers occur as non-trivial topological property in presence of the magnetic field. The symmetries and periodicities as function of the applied field are discussed. Strikingly, the dispersions of the edge states depend crucially on the precise shape of the boundary. This suggests that suitable design of the boundaries helps to tune physical properties which may even differ between upper and lower edge. Moreover, we suggest a promising gauge to realize this model in optical lattices.

cond-mat.quant-gas↗

arXiv2015

Low temperature thermodynamics of multi-flavored hardcore bosons by the Brückner approach

Dynamic correlations of quantum magnets provide valuable information. However, especially at finite temperature, many observations, e.g., by inelastic neutron scattering experiments, are not yet quantitatively understood. Generically, the elementary excitations of gapped quantum magnets are hardcore bosons because no two of them can occupy the same site. The previously introduced diagrammatic Brückner approach dealt with hardcore bosons of a single flavor at finite temperature. Here, this approach is extended to hardcore bosons of several kinds (flavors). The approach based on ladder diagrams is gauged with so far unknown rigorous results for the thermal occupation function of multiflavored hardcore bosons in one dimension with nearest-neighbor hopping. For low temperatures, it works very well. Furthermore, we study to which extent the approach is a conserving approximation. Empirical evidence shows that this is true only in the single-flavor case.

cond-mat.str-el↗

arXiv2015

Effective One-Dimensional Models from Matrix Product States

In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of the creation operator of single quasi-particles in both real and momentum space can be extracted from the dispersion calculation. The method is tested for the analytically solvable Ising model in a transverse magnetic field. Properties of the matrix product representation of the creation operator are discussed and validated by calculating the one-particle contribution to the spectral weight. Results are also given for the ground state energy and the dispersion.

cond-mat.str-el↗

arXiv2015

Effective Models for the Anderson Impurity and the Kondo Model from Continuous Unitary Transformations

The method of continuous unitary transformations (CUTs) is applied to the Anderson impurity and the Kondo model aiming at the systematic derivation of convergent effective models. If CUTs are applied in a conventional way, diverging differential equations occur. Similar to poor man's scaling the energy scale, below which the couplings diverge, corresponds to the Kondo temperature $T_K$. We present a way to apply CUTs to the Kondo and to the Anderson impurity model so that no divergences occur but a converged effective low-energy model is derived with small fnite parameters at arbitrarily small energies. The ground state corresponds to a bound singlet with a binding energy given by the Kondo temperature $T_K$.

cond-mat.str-el↗

arXiv2014

From Gapped Excitons to Gapless Triplons in One Dimension

Often, exotic phases appear in the phase diagrams between conventional phases. Their elementary excitations are of particular interest. Here, we consider the example of the ionic Hubbard model in one dimension. This model is a band insulator (BI) for weak interaction and a Mott insulator (MI) for strong interaction. Inbetween, a spontaneously dimerized insulator (SDI) occurs which is governed by energetically low-lying charge and spin degrees of freedom. Applying a systematically controlled version of the continuous unitary transformations (CUTs) we are able to determine the dispersions of the elementary charge and spin excitations and of their most relevant bound states on equal footing. The key idea is to start from an externally dimerized system using the relative weak interdimer coupling as small expansion parameter which finally is set to unity to recover the original model.

cond-mat.str-el↗

arXiv2014

From quantum-mechanical to classical dynamics in the central-spin model

We discuss the semiclassical and classical character of the dynamics of a single spin 1/2 coupled to a bath of noninteracting spins 1/2. On the semiclassical level, we extend our previous approach presented in D. Stanek, C. Raas, and G. S. Uhrig, Phys. Rev. B 88, 155305 (2013) by the explicit consideration of the conservation of the total spin. On the classical level, we compare the results of the classical equations of motions in absence and presence of an external field to the full quantum result obtained by density-matrix renormalization (DMRG). We show that for large bath sizes and not too low magnetic field the classical dynamics, averaged over Gaussian distributed initial spin vectors, agrees quantitatively with the quantum-mechanical one. This observation paves the way for an efficient approach for certain parameter regimes.

cond-mat.mes-hall↗

arXiv2014

Finite temperature line-shapes of hard-core bosons in quantum magnets: A diagrammatic approach tested in one dimension

The dynamics in quantum magnets can often be described by effective models with bosonic excitations obeying a hard-core constraint. Such models can be systematically derived by renormalization schemes such as continuous unitary transformations or by variational approaches. Even in the absence of further interactions the hard-core constraint makes the dynamics of the hard-core bosons nontrivial. Here we develop a systematic diagrammatic approach to the spectral properties of hard-core bosons at finite temperature. Starting from an expansion in the density of thermally excited bosons in a system with an energy gap, our approach leads to a summation of ladder diagrams. Conceptually, the approach is not restricted to one dimension, but the one-dimensional case offers the opportunity to gauge the method by comparison to exact results obtained via a mapping to Jordan-Wigner fermions. In particular, we present results for the thermal broadening of single-particle spectral functions at finite temperature. The line-shape is found to be asymmetric at elevated temperatures and the band-width of the dispersion narrows with increasing temperature. Additionally, the total number of thermally excited bosons is calculated and compared to various approximations and analytic results. Thereby, a flexible approach is introduced which can also be applied to more sophisticated and higher dimensional models.

cond-mat.str-el↗