The real part of optical conductivity, $text{Re}sigma(omega)$, of the Mott insulators has a large amount of information on how spin and charge degrees of freedom interact with each other. By using the time-dependent density-matrix renormalization gro
up, we study $text{Re}sigma(omega)$ of the two-dimensional Hubbard model on a square lattice at half filling. We find an excitonic peak at the Mott-gap edge of $text{Re}sigma(omega)$ not only for the two-dimensional square lattice but also for two- and four-leg ladders. For the square lattice, however, we do not clearly find a gap between an excitonic peak and continuum band, which indicates that a bound state is not well-defined. The emergence of an excitonic peak in $text{Re}sigma(omega)$ implies the formation of a spin polaron. Examining the dependence of $text{Re}sigma(omega)$ on the on-site Coulomb interaction and next-nearest neighbor hoppings, we confirm that an excitonic peak is generated from a magnetic effect. Electron scattering due to an electron-phonon interaction is expected to easily suppress an excitonic peak since spectral width of an excitonic peak is very narrow. Introducing a large broadening in $text{Re}sigma(omega)$ by modeling the electron-phonon coupling present in La$_{2}$CuO$_{4}$ and Nd$_{2}$CuO$_{4}$, we obtain $text{Re}sigma(omega)$ comparable with experiments.
Frustrated one-dimensional quantum spin systems are known to exhibit a variety of quantum ground states due to the effects of quantum fluctuations and frustrations. In a spin-1/2 kagome-strip chain, which is one of the frustrated one-dimensional spin
systems, many quantum phases have been found. However, the magnetic phase diagrams of the kagome-strip chain under magnetic field have not been fully understood. We construct magnetic phase diagrams at 0, 1/5, 3/10, 1/3, 2/5, 7/15, 3/5, and 4/5 magnetization ratio in the kagome-strip chain and investigate magnetic properties in each phase using the density matrix renormalization group method. We find fifteen magnetization-plateau phases, one of which is equivalent to the spin-1 Haldane phase.
The role of non-stoquasticity in the field of quantum annealing and adiabatic quantum computing is an actively debated topic. We study a strongly-frustrated quasi-one-dimensional quantum Ising model on a two-leg ladder to elucidate how a first-order
phase transition with a topological origin is affected by interactions of the $pm XX$-type. Such interactions are sometimes known as stoquastic (negative sign) and non-stoquastic (positive sign) catalysts. Carrying out a symmetry-preserving real-space renormalization group analysis and extensive density-matrix renormalization group computations, we show that the phase diagrams obtained by these two methods are in qualitative agreement with each other and reveal that the first-order quantum phase transition of a topological nature remains stable against the introduction of both $XX$-type catalysts. This is the first study of the effects of non-stoquasticity on a first-order phase transition between topologically distinct phases. Our results indicate that non-stoquastic catalysts are generally insufficient for removing topological obstacles in quantum annealing and adiabatic quantum computing.
Optical measurements in doped Mott insulators have discovered the emergence of spectral weights at mid-infrared (MIR) upon chemical doping and photodoping. MIR weights may have a relation to string-type excitation of spins, which is induced by a dope
d hole generating misarranged spins with respect to their sublattice. There are two types of string effects: one is an $S^z$ string that is repairable by quantum spin flips and the other is a phase string irreparable by the spin flips. We investigate the effect of $S^{z}$ and phase strings on MIR weights. Calculating the optical conductivity of the single-hole Hubbard model in the strong-coupling regime and the $t$-$J$ model on two-leg ladders by using time-dependent Lanczos and density-matrix renormalization group, we find that phase strings make a crucial effect on the emergence of MIR weights as compared with $S^{z}$ strings. Our findings indicate that a mutual Chern-Simons gauge field acting between spin and charge degrees of freedom, which is the origin of phase strings, is significant for obtaining MIR weights. Conversely, if we remove this gauge field, no phase is picked up by a doped hole. As a result, a spin-polaron accompanied by a local spin distortion emerges and a quasiparticle with a cosine-like energy dispersion is formed in single-particle spectral function. Furthermore, we suggest a Floquet engineering to examine the phase-string effect in cold atoms.
Highly frustrated spin systems such as the kagome lattice (KL) are a treasure trove of new quantum states with large entanglements. We thus study the spin-$frac{1}{2}$ Heisenberg model on a kagome-strip chain (KSC), which is one-dimensional KL, using
the density-matrix renormalization group (DMRG) method. Calculating central charge and entanglement spectrum for the KSC, we find a novel gapless spin liquid state with doubly degenerate entanglement spectra in a 1/5 magnetization plateau. We also obtain a gapless low-lying continuum in the dynamic spin structure calculated by dynamical DMRG method. We propose a resonating dimer-monomer liquid state that would meet these features.
Motivated by the magnetic phase transition of a proximate Kitaev system $alpha$-RuCl$_3$ in the presence of a magnetic field, we study the simplest but essential quantum spin model with the ferromagnetic nearest neighboring (NN) Kitaev interaction an
d additional antiferromagnetic third NN Heisenberg interaction. Employing both exact diagonalization and density matrix renormalization group methods, we demonstrate that the model shows the magnetic phase transition from the zigzag order phase to the spin polarized phase through an intermediate phase in both cases when an in-plane magnetic field is applied perpendicular to the NN bond direction and when an out-of-plane field is applied, in good agreement with experimental observations. Furthermore, we verify that additional symmetric off-diagonal $Gamma$ interaction and ferromagnetic Heisenberg interaction between NN spins can both suppress the intermediate phase with the in-plane field. Our result gives important clues on determining relevant interactions in the field-induced magnetic phase transition of proximate Kiteav systems.
The ground state of a hole-doped t-t-J ladder with four legs favors a striped charge distribution. Spin excitation from the striped ground state is known to exhibit incommensurate spin excitation near q=(pi,pi) along the leg direction (qx direction).
However, an outward dispersion from the incommensurate position toward q=(0,pi) is strong in intensity, inconsistent with inelastic neutron scattering (INS) experiment in hole-doped cuprates. Motivated by this inconsistency, we use the t-t-J model with m x n=96 lattice sites by changing lattice geometry from four-leg (24x4) to rectangle (12x8) shape and investigate the dynamical spin structure factor by using the dynamical density matrix renormalization group. We find that the outward dispersion has weak spectral weights in the 12x8 lattice, accompanied with the decrease of excitation energy close to q=(pi,pi), being consistent with the INS data. In the 12x8 lattice, weakening of incommensurate spin correlation is realized even in the presence of the striped charge distribution. For further investigation of geometry related spin dynamics, we focus on direction dependent spin excitation reported by recent resonant inelastic x-ray scattering (RIXS) for cuprate superconductors and obtain a consistent result with RIXS by examining an 8x8 t-t-J square lattice.
Magnetization plateaux emerging in quantum spin systems due to spontaneously breaking of translational symmetry have been reported both theoretically and experimentally. The broken symmetry can induce reconstruction of elementary excitations such as
Goldstone and Higgs modes, whereas its microscopic mechanism and reconstructed quasi-particle in magnetization-plateau phases have remained unclear so far. Here we theoretically study magnetic excitations in the magnetization-plateau phases of a frustrated spin ladder by using dynamical density-matrix renormalization-group method. Additionally, analytical approaches with perturbation theory are performed to obtain intuitive view of magnetic excitations. Comparison between numerical and analytical results indicates the presence of a reconstructed quasi-particle originating from spontaneously broken translational symmetry, which is realized as a collective mode of spin trimer called trimeron.
