Martin Ganahl

Quantum Flutter: Signatures and Robustness

We investigate the motion of an impurity particle injected with finite velocity into an interacting one-dimensional quantum gas. Using large-scale numerical simulations based on matrix product states, we observe and quantitatively analyze long-lived oscillations of the impurity momentum around a nonzero saturation value, called quantum flutter. We show that the quantum flutter frequency is equal to the energy difference between two branches of collective excitations of the model. We propose an explanation of the finite saturation momentum of the impurity based on the properties of the edge of the excitation spectrum. Our results indicate that quantum flutter exists away from integrability and provide parameter regions in which it could be observed in experiments with ultracold atoms using currently available technology.

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. 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, 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 the spectral functions directly.

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.

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

The non-equilibrium Anderson impurity model is solved to an unprecedented accuracy to obtain its spectral properties in the steady state using a recently developed approach.

Time evolution within a comoving window: scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains

We present a modification of Matrix Product State time evolution to simulate the propagation of signal fronts on infinite one-dimensional systems. We restrict the calculation to a window moving along with a signal, which by the Lieb-Robinson bound is contained within a light cone. Signal fronts can be studied unperturbed and with high precision for much longer times than on finite systems. Entanglement inside the window is naturally small, greatly lowering computational effort. We investigate the time evolution of the transverse field Ising (TFI) model and of the S  =  1/2 XXZ antiferromagnet in their symmetry broken phases after several different local quantum quenches. In both models, we observe distinct magnetisation plateaus at the signal front for very large times, resembling those previously observed for the particle density of tight binding (TB) fermions. We show that the normalised difference to the magnetisation of the ground state exhibits similar scaling behaviour as the density of TB fermions. In the XXZ model there is an additional internal structure of the signal front due to pairing, and wider plateaus with tight binding scaling exponents for the normalised excess magnetisation. We also observe parameter dependent interaction effects between individual plateaus, resulting in a slight spatial compression of the plateau widths. In the TFI model, we additionally find that for an initial Jordan-Wigner domain wall state, the complete time evolution of the normalised excess longitudinal magnetisation agrees exactly with the particle density of TB fermions.

Continuous Matrix Product States for Quantum Fields: an Energy Minimization Algorithm

The generalization of matrix product states (MPS) to continuous systems, as proposed in the breakthrough Letter of Verstraete and Cirac [Phys. Rev. Lett. 104, 190405 (2010).PRLTAO0031-900710.1103/PhysRevLett.104.190405], provides a powerful variational ansatz for the ground state of strongly interacting quantum field theories in one spatial dimension. A continuous MPS (cMPS) approximation to the ground state can be obtained by simulating a Euclidean time evolution. In this Letter we propose a cMPS optimization algorithm based instead on energy minimization by gradient methods and demonstrate its performance by applying it to the Lieb-Liniger model (an integrable model of an interacting bosonic field) directly in the thermodynamic limit. We observe a very significant computational speed-up, of more than 2 orders of magnitude, with respect to simulating a Euclidean time evolution. As a result, a much larger cMPS bond dimension D can be reached (e.g., D=256 with moderate computational resources), thus helping unlock the full potential of the cMPS representation for ground state studies.

Thermoelectric response of a correlated impurity in the nonequilibrium Kondo regime

We study nonequilibrium thermoelectric transport properties of a correlated impurity connected to two leads for temperatures below the Kondo scale. At finite bias, for which a current flows across the leads, we investigate the differential response of the current to a temperature gradient. In particular, we compare the influence of a bias voltage and of a finite temperature on this thermoelectric response. This is of interest from a fundamental point of view to better understand the two different decoherence mechanisms produced by a bias voltage and by temperature. Our results show that in this respect the thermoelectric response behaves differently from the electric conductance. In particular, while the latter displays a similar qualitative behavior as a function of voltage and temperature, both in theoretical and experimental investigations, qualitative differences occur in the case of the thermoelectric response. In order to understand this effect, we analyze the different contributions in connection to the behavior of the impurity spectral function versus temperature. Especially in the regime of strong interactions and large enough bias voltages we obtain a simple picture based on the asymmetric suppression or enhancement of the split Kondo peaks as a function of the temperature gradient. Besides the academic interest, these studies could additionally provide valuable information to assess the applicability of quantum dot devices as responsive nanoscale temperature sensors.

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 algorithm allows for the study of scattering displacements from spin-block states, showing similar scattering displacement features.

Lieb-Liniger model with exponentially decaying interactions: A continuous matrix product state study

The Lieb-Liniger model describes one-dimensional bosons interacting through a repulsive contact potential. In this work, we introduce an extended version of this model by replacing the contact potential with a decaying exponential. Using the recently developed continuous matrix product states techniques, we explore the ground state phase diagram of this model by examining the superfluid and density correlation functions. At weak coupling superfluidity governs the ground state, in a similar way as in the Lieb-Liniger model. However, at strong coupling quasi-crystal and super-Tonks-Girardeau regimes are also found, which are not present in the original Lieb-Liniger case. Therefore the presence of the exponentially-decaying potential leads to a superfluid/super-Tonks-Girardeau/quasi-crystal crossover, when tuning the coupling strength from weak to strong interactions. This corresponds to a Luttinger liquid parameter in the range

Steady-state spectra, current, and stability diagram of a quantum dot: A nonequilibrium variational cluster approach

K \in (0, \infty)