Spectral functions with the density matrix renormalization group: Krylov-space approach for correction vectors

Transition to the Haldane phase driven by electron-electron correlations

One of the most famous quantum systems with topological properties, the spin [Formula: see text] antiferromagnetic Heisenberg chain, is well-known to display exotic [Formula: see text] edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons - the two-orbital Hubbard model-with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.

Quadrupolar magnetic excitations in an isotropic spin-1 antiferromagnet

The microscopic origins of emergent behaviours in condensed matter systems are encoded in their excitations. In ordinary magnetic materials, single spin-flips give rise to collective dipolar magnetic excitations called magnons. Likewise, multiple spin-flips can give rise to multipolar magnetic excitations in magnetic materials with spin S ≥ 1. Unfortunately, since most experimental probes are governed by dipolar selection rules, collective multipolar excitations have generally remained elusive. For instance, only dipolar magnetic excitations have been observed in isotropic S = 1 Haldane spin systems. Here, we unveil a hidden quadrupolar constituent of the spin dynamics in antiferromagnetic S = 1 Haldane chain material Y₂BaNiO₅ using Ni L₃-edge resonant inelastic x-ray scattering. Our results demonstrate that pure quadrupolar magnetic excitations can be probed without direct interactions with dipolar excitations or anisotropic perturbations. Originating from on-site double spin-flip processes, the quadrupolar magnetic excitations in Y₂BaNiO₅ show a remarkable dual nature of collective dispersion. While one component propagates as non-interacting entities, the other behaves as a bound quadrupolar magnetic wave. This result highlights the rich and largely unexplored physics of higher-order magnetic excitations.

Quantifying and Controlling Entanglement in the Quantum Magnet Cs_{2}CoCl_{4}

The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.

Interaction-induced topological phase transition and Majorana edge states in low-dimensional orbital-selective Mott insulators

Topological phases of matter are among the most intriguing research directions in Condensed Matter Physics. It is known that superconductivity induced on a topological insulator's surface can lead to exotic Majorana modes, the main ingredient of many proposed quantum computation schemes. In this context, the iron-based high critical temperature superconductors are a promising platform to host such an exotic phenomenon in real condensed-matter compounds. The Coulomb interaction is commonly believed to be vital for the magnetic and superconducting properties of these systems. This work bridges these two perspectives and shows that the Coulomb interaction can also drive a canonical superconductor with orbital degrees of freedom into the topological state. Namely, we show that above a critical value of the Hubbard interaction the system simultaneously develops spiral spin order, a highly unusual triplet amplitude in superconductivity, and, remarkably, Majorana fermions at the edges of the system.

Block-spiral magnetism: An exotic type of frustrated order

Competing interactions in quantum materials induce exotic states of matter such as frustrated magnets, an extensive field of research from both the theoretical and experimental perspectives. Here, we show that competing energy scales present in the low-dimensional orbital-selective Mott phase (OSMP) induce an exotic magnetic order, never reported before. Earlier neutron-scattering experiments on iron-based 123 ladder materials, where OSMP is relevant, already confirmed our previous theoretical prediction of block magnetism (magnetic order of the form [Formula: see text]). Now we argue that another phase can be stabilized in multiorbital Hubbard models, the block-spiral state. In this state, the magnetic islands form a spiral propagating through the chain but with the blocks maintaining their identity, namely rigidly rotating. The block-spiral state is stabilized without any apparent frustration, the common avenue to generate spiral arrangements in multiferroics. By examining the behavior of the electronic degrees of freedom, parity-breaking quasiparticles are revealed. Finally, a simple phenomenological model that accurately captures the macroscopic spin spiral arrangement is also introduced, and fingerprints for the neutron-scattering experimental detection are provided.

Magnetic field-induced intermediate quantum spin liquid with a spinon Fermi surface

The Kitaev model with an applied magnetic field in the [Formula: see text] direction shows two transitions: from a nonabelian gapped quantum spin liquid (QSL) to a gapless QSL at [Formula: see text] and a second transition at a higher field [Formula: see text] to a gapped partially polarized phase, where K is the strength of the Kitaev exchange interaction. We identify the intermediate phase to be a gapless U(1) QSL and determine the spin structure function [Formula: see text] and the Fermi surface [Formula: see text] of the gapless spinons using the density matrix renormalization group (DMRG) method for large honeycomb clusters. Further calculations of static spin-spin correlations, magnetization, spin susceptibility, and finite temperature-specific heat and entropy corroborate the gapped and gapless nature of the different field-dependent phases. In the intermediate phase, the spin-spin correlations decay as a power law with distance, indicative of a gapless phase.

Spin dynamics of the block orbital-selective Mott phase

Iron-based superconductors display a variety of magnetic phases originating in the competition between electronic, orbital, and spin degrees of freedom. Previous theoretical investigations of the multi-orbital Hubbard model in one-dimension revealed the existence of an orbital-selective Mott phase (OSMP) with block spin order. Recent inelastic neutron scattering (INS) experiments on the BaFe₂Se₃ ladder compound confirmed the relevance of the block-OSMP. Moreover, the powder INS spectrum revealed an unexpected structure, containing both low-energy acoustic and high-energy optical modes. Here we present the theoretical prediction for the dynamical spin structure factor within a block-OSMP regime using the density-matrix renormalization-group method. In agreement with experiments, we find two dominant features: low-energy dispersive and high-energy dispersionless modes. We argue that the former represents the spin-wave-like dynamics of the block ferromagnetic islands, while the latter is attributed to a novel type of local on-site spin excitations controlled by the Hund coupling.

Exploring the orbital-selective Mott phase (OSMP) addresses the central issue of electron correlations in the iron-based superconductors. Here the authors theoretically study the dynamical spin structure factor in the block-OSMP regime and unveil momentum dependent characteristics for different spin excitation modes.

Computing Resonant Inelastic X-Ray Scattering Spectra Using The Density Matrix Renormalization Group Method

We present a method for computing the resonant inelastic x-ray scattering (RIXS) spectra in one-dimensional systems using the density matrix renormalization group (DMRG) method. By using DMRG to address this problem, we shift the computational bottleneck from the memory requirements associated with exact diagonalization (ED) calculations to the computational time associated with the DMRG algorithm. This approach is then used to obtain RIXS spectra on cluster sizes well beyond state-of-the-art ED techniques. Using this new procedure, we compute the low-energy magnetic excitations observed in Cu L-edge RIXS for the challenging corner shared CuO4 chains, both for large multi-orbital clusters and downfolded t-J chains. We are able to directly compare results obtained from both models defined in clusters with identical momentum resolution. In the strong coupling limit, we find that the downfolded t-J model captures the main features of the magnetic excitations probed by RIXS only after a uniform scaling of the spectra is made.