Low-energy excitations and transport functions of the one-dimensional Kondo insulator

Using variational matrix product states, we analyze the finite temperature behavior of a half-filled periodic Anderson model in one dimension, a prototypical model of a Kondo insulator. We present an extensive analysis of single-particle Green's functions, two-particle Green's functions, and transport functions creating a broad picture of the low-temperature properties. We confirm the existence of energetically low-lying spin excitations in this model and study their energy-momentum dispersion and temperature dependence. We demonstrate that charge-charge correlations at the Fermi energy exhibit a different temperature dependence than spin-spin correlations. While energetically low-lying spin excitations emerge approximately at the Kondo temperature, which exponentially depends on the interaction strength, charge correlations vanish already at high temperatures. Furthermore, we analyze the charge and thermal conductivity at finite temperatures by calculating the time-dependent current-current correlation functions. While both charge and thermal conductivity can be fitted for all interaction strengths by gapped systems with a renormalized band gap, the gap in the system describing the thermal conductivity is generally smaller than the system describing the charge conductivity. Thus, two-particle correlations affect the charge and heat conductivities in a different way resulting in a temperature region where the charge conductivity of this one-dimensional Kondo insulator is already decreasing while the heat conductivity is still increasing

Topological phases arising from attractive interaction and pair hopping in the Extended Hubbard Model

The extended Hubbard model with an attractive density-density interaction, positive pair hopping, or both, is shown to host topological phases, with a doubly degenerate entanglement spectrum and interacting edge spins. This constitutes a novel instance of topological order which emerges from interactions. When the interaction terms combine in a charge-SU(2) symmetric fashion, a novel partially polarized pseudospin phase appears, in which the topological features of the spin degrees of freedom coexist with long-range $\eta$-wave superconductivity. Thus, our system provides an example of an interplay between spontaneous symmetry breaking and symmetry-protected topological order that leads to novel and unexpected properties

Matrix-product state approach to the generalized nuclear pairing Hamiltonian

We show that from the point of view of the generalized pairing Hamiltonian, the atomic nucleus is a system with small entanglement and can thus be described efficiently using a one-dimensional tensor network (matrix-product state) despite the presence of long-range interactions. The ground state can be obtained using the density-matrix renormalization group (DMRG) algorithm, which is accurate up to machine precision even for large nuclei, is numerically as cheap as the widely used BCS approach, and does not suffer from any mean-field artefacts. We apply this framework to compute the even-odd mass differences of all known lead isotopes from $^{178}$Pb to $^{220}$Pb in a very large configuration space of 13 shells between the neutron magic numbers 82 and 184 (i.e., two major shells) and find good agreement with the experiment. To go beyond the ground state, we calculate the first 100 excited states, as well as the two-neutron removal spectral function of $^{210}$Pb which relates to a two-neutron pickup experiment. Finally, we treat pairing with non-zero angular momentum and determine the lowest excited states in the full configuration space of one major shell, which we demonstrate for the $N=126$, $Z\geq 82$ isotones

Non-collinear spin states in bottom-up fabricated atomic chains

Non-collinear spin states with unique rotational sense, such as chiral spin-spirals, are recently heavily investigated because of advantages for future applications in spintronics and information technology and as potential hosts for Majorana Fermions when coupled to a superconductor. Tuning the properties of such spin states, e.g., the rotational period and sense, is a highly desirable yet difficult task. Here, we experimentally demonstrate the bottom-up assembly of a spin-spiral derived from a chain of Fe atoms on a Pt substrate using the magnetic tip of a scanning tunneling microscope as a tool. We show that the spin-spiral is induced by the interplay of the Heisenberg and Dzyaloshinskii-Moriya components of the Ruderman-Kittel-Kasuya-Yosida interaction between the Fe atoms. The relative strengths and signs of these two components can be adjusted by the interatomic Fe distance, which enables tailoring of the rotational period and sense of the spin-spiral.Comment: 16 pages, 5 figure

Quantum spin spiral ground state of the ferrimagnetic sawtooth chain

The ferrimagnetic phase of the sawtooth chain with mixed ferromagnetic nearest-neighbour interactions $J$ and antiferromagnetic next-nearest-neighbour interactions $J'$ (within the isotropic Heisenberg model) was previously characterized as a phase with commensurate order. In this paper, we demonstrate that the system in fact exhibits an incommensurate quantum spin spiral. Even though the ground state is translationally invariant in terms of the local spin expectations \avg{\vec{S}_i}, the spiral can be detected via the connected spin-spin correlations \avg{\vec{S}_i\cdot\vec{S}_j}-\avg{\vec{S}_i}\cdot\avg{\vec{S}_j} between the apical spins. It has a long wavelength that grows with $J'$ and that soon exceeds finite-system sizes typically employed in numerical simulations. A faithful treatment thus requires the use of state-of-the-art simulations for large, periodic systems. In this work, we are able to accurately treat up to $L=400$ sites (200 unit cells) with periodic boundary conditions using the density-matrix renormaliztion group (DMRG). Exploiting the SU(2) symmetry allows us to directly compute the lowest-energy state for a given total spin. Our results are corroborated by variational uniform matrix product state (VUMPS) calculations, which work directly in the thermodynamic limit at the cost of a lower accuracy

Minimal one-dimensional model of bad metal behavior from fast particle-hole scattering

A strongly interacting plasma of linearly dispersing electron and hole excitations in two spatial dimensions (2D), also known as a Dirac fluid, can be captured by relativistic hydrodynamics and shares many universal features with other quantum critical systems. We propose a one-dimensional (1D) model to capture key aspects of the 2D Dirac fluid while including lattice effects and being amenable to non-perturbative computation. When interactions are added to the Dirac-like 1D dispersion without opening a gap, we show that this kind of irrelevant interaction is able to preserve Fermi-liquid-like quasi-particle features while relaxing a zero-momentum charge current via collisions between particle-hole excitations, leading to resistivity that is linear in temperature via a mechanism previously discussed for large-diameter metallic carbon nanotubes. We further provide a microscopic lattice model and obtain numerical results via density-matrix renormalization group (DMRG) simulations, which support the above physical picture. The limits on such fast relaxation at strong coupling are of considerable interest because of the ubiquity of bad metals in experiments.Comment: 7 pages, 3 figures plus supplemental material