Lattice assisted spectroscopy: a generalized scanning tunnelling microscope for ultra-cold atoms

We show that the possibility to address and image single sites of an optical lattice, now an experimental reality, allows to measure the frequency-resolved local particle and hole spectra of a wide variety of one- and two-dimensional systems of lattice-confined strongly correlated ultracold atoms. Combining perturbation theory and time-dependent DMRG, we validate this scheme of lattice-assisted spectroscopy (LAS) on several example systems, such as the 1D superfluid and Mott insulator, with and without a parabolic trap, and finally on edge states of the bosonic Su-Schrieffer-Heeger model. We also highlight extensions of our basic scheme to obtain an even wider variety of interesting and important frequency resolved spectra.Comment: 4 pages, 3 figure

Bound states and entanglement in the excited states of quantum spin chains

We investigate entanglement properties of the excited states of the spin-1/2 Heisenberg (XXX) chain with isotropic antiferromagnetic interactions, by exploiting the Bethe ansatz solution of the model. We consider eigenstates obtained from both real and complex solutions ("strings") of the Bethe equations. Physically, the former are states of interacting magnons, whereas the latter contain bound states of groups of particles. We first focus on the situation with few particles in the chain. Using exact results and semiclassical arguments, we derive an upper bound S_MAX for the entanglement entropy. This exhibits an intermediate behavior between logarithmic and extensive, and it is saturated for highly-entangled states. As a function of the eigenstate energy, the entanglement entropy is organized in bands. Their number depends on the number of blocks of contiguous Bethe-Takahashi quantum numbers. In presence of bound states a significant reduction in the entanglement entropy occurs, reflecting that a group of bound particles behaves effectively as a single particle. Interestingly, the associated entanglement spectrum shows edge-related levels. At finite particle density, the semiclassical bound S_MAX becomes inaccurate. For highly-entangled states S_A\propto L_c, with L_c the chord length, signaling the crossover to extensive entanglement. Finally, we consider eigenstates containing a single pair of bound particles. No significant entanglement reduction occurs, in contrast with the few-particle case.Comment: 39 pages, 10 figure. as published in JSTAT. Invited submission to JSTAT Special Issue: Quantum Entanglement in Condensed Matter Physic

A Strictly Single-Site DMRG Algorithm with Subspace Expansion

We introduce a strictly single-site DMRG algorithm based on the subspace expansion of the Alternating Minimal Energy (AMEn) method. The proposed new MPS basis enrichment method is sufficient to avoid local minima during the optimisation, similarly to the density matrix perturbation method, but computationally cheaper. Each application of $\hat H$ to $|\Psi\rangle$ in the central eigensolver is reduced in cost for a speed-up of $\approx (d + 1)/2$, with $d$ the physical site dimension. Further speed-ups result from cheaper auxiliary calculations and an often greatly improved convergence behaviour. Runtime to convergence improves by up to a factor of 2.5 on the Fermi-Hubbard model compared to the previous single-site method and by up to a factor of 3.9 compared to two-site DMRG. The method is compatible with real-space parallelisation and non-abelian symmetries.Comment: 9 pages, 6 figures; added comparison with two-site DMR

Coulomb interaction effects and electron spin relaxation in the one-dimensional Kondo lattice model

We study the effects of the Coulomb interaction in the one-dimensional Kondo lattice model on the phase diagram, the static magnetic susceptibility, and electron spin relaxation.We show that onsite Coulomb interaction supports ferromagnetic order and nearest-neighbor Coulomb interaction drives, depending on the electron filling, either a paramagnetic or a ferromagnetic order. Furthermore, we calculate electron quasiparticle lifetimes, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate

Scaling of the Thermal Spectral Function for Quantum Critical Bosons in One Dimension

We present an improved scheme for the precise evaluation of finite-temperature response functions of strongly correlated systems in the framework of the time-dependent density matrix renormalization group. The maximum times that we can reach at finite temperatures T are typically increased by a factor of two, when compared against the earlier approaches. This novel scheme, complemented with linear prediction, allows us now to evaluate dynamic correlators for interacting bosons in one dimension. We demonstrate that the considered spectral function in the quantum critical regime with dynamic critical exponent z=2 is captured by the universal scaling form S(k,omega)=(1/T)*Phi(k/sqrt(T),omega/T) and calculate the scaling function precisely.Physic

Spectral functions and time evolution from the Chebyshev recursion

We link linear prediction of Chebyshev and Fourier expansions to analytic continuation. We push the resolution in the Chebyshev-based computation of $T=0$ many-body spectral functions to a much higher precision by deriving a modified Chebyshev series expansion that allows to reduce the expansion order by a factor $\sim\frac{1}{6}$. We show that in a certain limit the Chebyshev technique becomes equivalent to computing spectral functions via time evolution and subsequent Fourier transform. This introduces a novel recursive time evolution algorithm that instead of the group operator $e^{-iHt}$ only involves the action of the generator $H$. For quantum impurity problems, we introduce an adapted discretization scheme for the bath spectral function. We discuss the relevance of these results for matrix product state (MPS) based DMRG-type algorithms, and their use within dynamical mean-field theory (DMFT). We present strong evidence that the Chebyshev recursion extracts less spectral information from $H$ than time evolution algorithms when fixing a given amount of created entanglement.Comment: 12 pages + 6 pages appendix, 11 figure