arXiv subjects

Götz S. Uhrig

Publications and source records attributed to Götz S. Uhrig.

At least 91 records · Page 5Linked to original sources

arXiv2014

Anomalous behavior of control pulses in presence of noise with singular autocorrelation

We report on the anomalous behavior of control pulses for spins under spin-spin relaxation and subject to classical noise with a singular autocorrelation function. This behavior is not detected for noise with analytic autocorrelation functions. The effect is manifest in the different scaling behavior of the deviation of a real pulse to the ideal, instantaneous one. While a standard pulse displays scaling $\propto τ_\mathrm{p}^1$, a first-order refocusing pulse normally shows scaling $\propto τ_\mathrm{p}^2$. But in presence of cusps in the noise autocorrelation the scaling $\propto τ_\mathrm{p}^{3/2}$ occurs. Cusps in the autocorrelation are characteristic for fast fluctuations in the noise with a spectral density of Lorentzian shape. We prove that the anomalous exponent cannot be avoided; it represents a fundamental limit. On the one hand, this redefines the strategies one has to adopt to design refocusing pulses. On the other hand, the anomalous exponent, if found in experiment, provides important information on the noise properties.

quant-ph↗

arXiv2014

Interaction quenches in the two-dimensional fermionic Hubbard model

The generic non-equilibrium evolution of a strongly interacting fermionic system is studied. For strong quenches, a collective collapse-and-revival phenomenon is found extending over the whole Brillouin zone. A qualitatively distinct behavior occurs for weak quenches where only weak wiggling occurs. Surprisingly, no evidence for prethermalization is found in the weak coupling regime. In both regimes, indications for relaxation beyond oscillatory or power law behavior are found and used to estimate relaxation rates without resorting to a probabilistic ansatz. The relaxation appears to be fastest for intermediate values of the quenched interaction.

cond-mat.str-el↗

arXiv2014

Dispersive Excitations in the One-Dimensional Ionic Hubbard Model

A detailed study of the one-dimensional ionic Hubbard model with interaction $U$ is presented. We focus on the band insulating (BI) phase and the spontaneously dimerized insulating (SDI) phase which appears on increasing $U$. By a recently introduced continuous unitary transformation [Krull et al.\ Phys. Rev. B {\bf 86}, 125113 (2012)] we are able to describe the system even close to the phase transition from BI to SDI although the bare perturbative series diverges before the transition is reached. First, the dispersion of single fermionic quasiparticles is determined in the full Brillouin zone. Second, we describe the binding phenomena between two fermionic quasiparticles leading to an $S=0$ and to an $S=1$ exciton. The latter corresponds to the lowest spin excitation and defines the spin gap which remains finite through the transition from BI to SDI. The former becomes soft at the transition indicating that the SDI corresponds to a condensate of these $S=0$ excitons. This view is confirmed by a BCS mean field theory for the SDI phase.

cond-mat.str-el↗

arXiv2013

Dynamics and decoherence in the central spin model in the low-field limit

We present a combination of analytic calculations and a powerful numerical method for large spin baths in the low-field limit. The hyperfine interaction between the central spin and the bath is fully captured by the density matrix renormalization group. The adoption of the density matrix renormalization group for the central spin model is presented and a proper method for calculating the real-time evolution at infinite temperature is identified. In addition, we study to which extent a semiclassical model, where a quantum spin-1/2 interacts with a bath of classical Gaussian fluctuations, can capture the physics of the central spin model. The model is treated by average Hamiltonian theory and by numerical simulation.

cond-mat.mes-hall↗

arXiv2013

One-dimensional fermionic systems after interaction quenches and their description by bosonic field theories

We show that the dynamics of quenches in one dimension far off equilibrium can be described by power laws, but with exponents differing from the fully renormalized ones at lowest energies. Instead they depend on the initial state and its excitation energy. Furthermore, we found that for quenches to strong interactions unexpected similarities between systems in one and in infinite dimensions occur, indicating the dominance of local processes.

cond-mat.str-el↗

arXiv2013

Multi-Particle Spectral Properties in the Transverse Field Ising Model by Continuous Unitary Transformations

The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators which we call string operators. The closure is related to the possibility to map the model by Jordan-Wigner transformation to non-interacting fermions. But it is proven without referring to this mapping. The effective model derived by the continuous unitary transformations is used to compute the contributions of one, two, and three elementary excitations to the diagonal dynamic structure factors. The three-particle contributions have so far not been addressed analytically, except close to the quantum critical point.

cond-mat.str-el↗

arXiv2013

Dynamical Transition in Interaction Quenches of the One-Dimensional Hubbard Model

We show that the non-equilibrium time-evolution after interaction quenches in the one dimensional, integrable Hubbard model exhibits a dynamical transition in the half-filled case. This transition ceases to exist upon doping. Our study is based on systematically extended equations of motion. Thus it is controlled for small and moderate times; no relaxation effects are neglected. Remarkable similarities to the quench dynamics in the infinite dimensional Hubbard model are found suggesting dynamical transitions to be a general feature of quenches in such models.

cond-mat.str-el↗

arXiv2012

Modulated pulses compensating classical noise

We consider pulses of finite duration for coherent control in the presence of classical noise. We derive the corrections to ideal, instantaneous pulses for the case of general decoherence (spin-spin relaxation and spin-lattice relaxation) up to and including the third order in the duration τ_p of the pulses. For pure dephasing (spin-spin relaxation only), we design πand π/2 pulses with amplitude and/or frequency modulation which resemble the ideal ones up to and including the second order in τ_p. For completely general decoherence including spin-lattice relaxation the corrections are computed up to and including the second order in τ_p as well. Frequency modulated pulses are determined which resemble the ideal ones. They are used to design a low-amplitude replacement for XY8 cycles. In comparison with pulses designed to compensate quantum noise less conditions have to be fulfilled. Consequently, we find that the classical pulses can be weaker and simpler than the corresponding pulses in the quantum case.

quant-ph↗

arXiv2012

Frequency modulated pulses for quantum bits coupled to time-dependent baths

We consider the coherent control of a quantum bit by the use of short pulses with finite duration τ_p. By shaping the pulse, we perturbatively decouple the dynamics of the bath from the dynamics of the quantum bit during the pulse. Such shaped pulses provide single quantum bit gates robust against decoherence which are useful for quantum information processing. We extend previous results in two ways: (i) we treat frequency modulated pulses and (ii) we pass from time-independent baths to analytically time-dependent baths. First and second order solutions for π- and π/2-pulses are presented. They are useful in experiments where amplitude modulation is difficult to realize.

quant-ph↗

arXiv2012

Perfect state transfer in XX chains induced by boundary magnetic fields

A recent numerical study of short chains found near-perfect quantum state transfer between the boundary sites of a spin-1/2 XX chain if a sufficiently strong magnetic field acts on these sites. We show that the phenomenon is based on a pair of states strongly localized at the boundaries of the system and provide a simple quantitative analytical explanation.

quant-ph↗

arXiv2011

Microscopic model for Bose-Einstein condensation and quasiparticle decay

Sufficiently dimerized quantum antiferromagnets display elementary S=1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J1=-2.3meV, J2=1.2meV, J3=2.9meV and J4=-0.3meV. These couplings determine IPA-CuCl3 as system of coupled asymmetric S=1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.

cond-mat.str-el↗

arXiv2011

Kinks in the electronic dispersion of the Hubbard model away from half filling

We study kinks in the electronic dispersion of a generic strongly correlated system by dynamic mean-field theory (DMFT). The focus is on doped systems away from particle-hole symmetry where valence fluctuations matter potentially. Three different algorithms are compared to asses their strengths and weaknesses, as well as to clearly distinguish physical features from algorithmic artifacts. Our findings extend a view previously established for half-filled systems where kinks reflect the coupling of the fermionic quasiparticles to emergent collective modes, which are identified here as spin fluctuations. Kinks are observed when strong spin fluctuations are present and, additionally, a separation of energy scales for spin and charge excitations exists. Both criteria are met by strongly correlated systems close to a Mott-insulator transition. The energies of the kinks and their doping dependence fit well to the kinks in the cuprates, which is surprising in view of the spatial correlations neglected by DMFT.

cond-mat.str-el↗

arXiv2011

Self-consistent spin-wave theory for a frustrated Heisenberg model with biquadratic exchange in the columnar phase and its application to iron pnictides

Recent neutron scattering studies revealed the three dimensional character of the magnetism in the iron pnictides and a strong anisotropy between the exchange perpendicular and parallel to the spin stripes. We extend studies of the J1-J2-Jc Heisenberg model with S = 1 using self-consistent spin-wave theory. A discussion of two scenarios for the instability of the columnar phase is provided. The relevance of a biquadratic exchange term between in-plane nearest neighbors is discussed. We introduce mean-field decouplings for biquadratic terms using the Dyson-Maleev and the Schwinger boson representation. Remarkably their respective mean-field theories do not lead to the same results, even at zero temperature. They are gauged in the N'eel phase in comparison to exact diagonalization and series expansion. The J1-J2-Jc model is analyzed under the influence of the biquadratic exchange Jbq and a detailed description of the staggered magnetization and of the magnetic excitations is given. The biquadratic exchange increases the renormalization of the in-plane exchange constants which enhances the anisotropy between the exchange parallel and perpendicular to the spin stripes. Applying the model to iron pnictides, it is possible to reproduce the spin-wave dispersion for CaFe2As2 in the direction perpendicular to the spin stripes and perpendicular to the planes. Discrepancies remain in the direction parallel to the spin stripes which can be resolved by passing from S = 1 to S = 2. In addition, results for the dynamical structure factor within the self-consistent spin-wave theory are provided.

cond-mat.supr-con↗

arXiv2011

Three dimensional generalization of the $J_1$-$J_2$ Heisenberg model on a square lattice and role of the interlayer coupling $J_c$

A possibility to describe magnetism in the iron pnictide parent compounds in terms of the two-dimensional frustrated Heisenberg $J_1$-$J_2$ model has been actively discussed recently. However, recent neutron scattering data has shown that the pnictides have a relatively large spin wave dispersion in the direction perpendicular to the planes. This indicates that the third dimension is very important. Motivated by this observation we study the $J_1$-$J_2$-$J_c$ model that is the three dimensional generalization of the $J_1$-$J_2$ Heisenberg model for $S = 1/2$ and S = 1. Using self-consistent spin wave theory we present a detailed description of the staggered magnetization and magnetic excitations in the collinear state. We find that the introduction of the interlayer coupling $J_c$ suppresses the quantum fluctuations and strengthens the long range ordering. In the $J_1$-$J_2$-$J_c$ model, we find two qualitatively distinct scenarios for how the collinear phase becomes unstable upon increasing $J_1$. Either the magnetization or one of the spin wave velocities vanishes. For $S = 1/2$ renormalization due to quantum fluctuations is significantly stronger than for S=1, in particular close to the quantum phase transition. Our findings for the $J_1$-$J_2$-$J_c$ model are of general theoretical interest, however, the results show that it is unlikely that the model is relevant to undoped pnictides.

cond-mat.supr-con↗

arXiv2010

Truncation errors in self-similar continuous unitary transformations

Effects of truncation in self-similar continuous unitary transformations (S-CUT) are estimated rigorously. We find a formal description via an inhomogeneous flow equation. In this way, we are able to quantify truncation errors within the framework of the S-CUT and obtain rigorous error bounds for the ground state energy and the highest excited level. These bounds can be lowered exploiting symmetries of the Hamiltonian. We illustrate our approach with results for a toy model of two interacting hard-core bosons and the dimerized S=1/2 Heisenberg chain.

cond-mat.str-el↗

arXiv2010

Derivation of the t-J model for finite doping

Mapping complex problems to simpler effective models is a key tool in theoretical physics. One important example in the realm of strongly correlated fermionic systems is the mapping of the Hubbard model to a t-J model which is appropriate for the treatment of doped Mott insulators. Charge fluctuations across the charge gap are eliminated. So far the derivation of the t-J model is only known at half-filling or in its immediate vicinity. Here we present the necessary conceptual advancement to treat finite doping. The results for the ensuing coupling constants are presented. Technically, the extended derivation relies on self-similar continuous unitary transformations (sCUT) and normal-ordering relative to a doped reference ensemble. The range of applicability of the derivation of t-J model is determined as function of the doping $δ$ and the ratio bandwidth W over interaction U.

cond-mat.str-el↗

arXiv2010

Efficient Coherent Control by Optimized Sequences of Pulses of Finite Duration

Reliable long-time storage of arbitrary quantum states is a key element for quantum information processing. In order to dynamically decouple a spin or quantum bit from a dephasing environment, we introduce an optimized sequence of $N$ control pulses of finite durations $τ\pp$ and finite amplitudes. The properties of this sequence of length $T$ stem from a mathematically rigorous derivation. Corrections occur only in order $T^{N+1}$ and $τ\pp^3$ without mixed terms such as $T^Nτ\pp$ or $T^Nτ\pp^2$. Based on existing experiments, a concrete setup for the verification of the properties of the advocated realistic sequence is proposed.

quant-ph↗

arXiv2010

Adapted continuous unitary transformation to treat systems with quasiparticles of finite lifetime

An improved generator for continuous unitary transformations is introduced to describe systems with unstable quasiparticles. Its general properties are derived and discussed. To illustrate this approach we investigate the asymmetric antiferromagnetic spin-1/2 Heisenberg ladder which allows for spontaneous triplon decay. We present results for the low energy spectrum and the momentum resolved spectral density of this system. In particular, we show the resonance behavior of the decaying triplon explicitly.

cond-mat.str-el↗