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A $K$ and $L_{3}$ -edge RIXS study of the columnar and the staggered quantum dimer phases of the square lattice Heisenberg model

Meiyu He, Trinanjan Datta, Dao‐Xin Yao

Published Jul 2, 2019• 0 citations
OpenAlex

Abstract

We compute the $K$ and $L_{3}$ -edge resonant inelastic x-ray scattering (RIXS) spectrum of the columnar and the staggered quantum dimer states accessible to the square lattice Heisenberg magnet. Utilizing a bond operator representation mean field theory we investigate the RIXS features of the one- and two-triplon excitation spectrum supported by the quantum dimer model in the background of condensed singlet excitation. We find that the two-triplon excitation boundary lies within a 124 (78) meV to (414) 345 meV energy range for the columnar (staggered) phase. We estimated the two-triplon gap to be 124 (78) meV for the columnar (staggered) dimer phase. The highest intensity of the $K$ -edge RIXS spectrum is centralized approximately around the $(\pi/2,\pi/2)$ point for both the columnar and the staggered phases. At the $L_{3}$ -edge we study the one- and two- triplon signal considering experimental scattering geometry, polarization restriction, and experimental resolution effects. Our calculations find an additional contribution to the two-triplon RIXS signal, not previously reported in the literature, that originates from the local hard-core dimer constraint. This leads to a finite non-zero signal at the (0,0) momentum transfer which can offer an explanation for the existing ladder RIXS experiments and also predicts a non-zero signal for the two-dimensional quantum dimer system. We find that the $L_3$ edge RIXS response of the one- and two-triplon signal could exist in antiphase rung modulation for zero and $\pi$ as found in inelastic neutron scattering. We also consider static crystal twinning at the $L_3$ -edge RIXS signal to mimic realistic crystal effects. Since the disordered phase has the potential to harbor a variety of quantum paramagnetic states, our RIXS calculations provide useful signatures to identify the true nature of the ordering pattern.

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Triangular-lattice anisotropic dimerized Heisenberg antiferromagnet: Stability and excitations of the quantum paramagnetic phase

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A KKK and L3L_{3}L3​ -edge RIXS study of the columnar and the staggered quantum dimer phases of the square lattice Heisenberg model
We compute the KKK and L3L_{3}L3​ -edge resonant inelastic x-ray scattering (RIXS) spectrum of the columnar and the staggered quantum dimer states accessible to the square lattice Heisenberg magnet. Utilizing a bond operator representation mean field theory we investigate the RIXS features of the one- and two-triplon excitation spectrum supported by the quantum dimer model in the background of condensed singlet excitation. We find that the two-triplon excitation boundary lies within a 124 (78) meV to (414) 345 meV energy range for the columnar (staggered) phase. We estimated the two-triplon gap to be 124 (78) meV for the columnar (staggered) dimer phase. The highest intensity of the KKK -edge RIXS spectrum is centralized approximately around the (π/2,π/2)(\pi/2,\pi/2)(π/2,π/2) point for both the columnar and the staggered phases. At the L3L_{3}L3​ -edge we study the one- and two- triplon signal considering experimental scattering geometry, polarization restriction, and experimental resolution effects. Our calculations find an additional contribution to the two-triplon RIXS signal, not previously reported in the literature, that originates from the local hard-core dimer constraint. This leads to a finite non-zero signal at the (0,0) momentum transfer which can offer an explanation for the existing ladder RIXS experiments and also predicts a non-zero signal for the two-dimensional quantum dimer system. We find that the L3L_3L3​ edge RIXS response of the one- and two-triplon signal could exist in antiphase rung modulation for zero and π\piπ as found in inelastic neutron scattering. We also consider static crystal twinning at the L3L_3L3​ -edge RIXS signal to mimic realistic crystal effects. Since the disordered phase has the potential to harbor a variety of quantum paramagnetic states, our RIXS calculations provide useful signatures to identify the true nature of the ordering pattern.
We compute the KKK- and L3{L}_{3}L3​-edge resonant inelastic x-ray-scattering (RIXS) spectrum of the columnar and the staggered quantum dimer states accessible to the square lattice Heisenberg magnet. Utilizing a bond-operator representation mean-field theory we investigate the RIXS features of the one- and two-triplon excitation spectrum supported by the quantum dimer model in the background of condensed singlet excitation. We find that the two-triplon excitation boundary lies within an energy range of 2.7J2(1.7J2)2.7{J}_{2}\phantom{\rule{0.28em}{0ex}}(1.7{J}_{2})2.7J2​(1.7J2​) to 9J2(7.5J2)9{J}_{2}\phantom{\rule{0.28em}{0ex}}(7.5{J}_{2})9J2​(7.5J2​) for the columnar (staggered) phase, where J2{J}_{2}J2​ is the interbond coupling strength. We estimated the two-triplon gap to be 2.7J22.7{J}_{2}2.7J2​ (1.7J2)(1.7{J}_{2})(1.7J2​) for the columnar (staggered) dimer phase. The highest intensity of the KKK-edge RIXS spectrum is localized approximately around the $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ point for both the columnar and the staggered phases. At the L3{L}_{3}L3​ edge we study the one- and two-triplon signal considering experimental scattering geometry, polarization restriction, and experimental resolution effects. Our calculations find a contribution to the two-triplon RIXS signal that originates from the local hard-core dimer constraint. This leads to a finite nonzero signal at the (0,0) momentum transfer which can offer an explanation for the existing ladder RIXS experiments and also predicts a nonzero signal for the two-dimensional quantum dimer system. We find that the L3{L}_{3}L3​-edge RIXS response of the one- and two-triplon signal could exist in antiphase rung modulation for zero and $\ensuremath{\pi}$ as found in inelastic neutron scattering. Since the disordered phase has the potential to harbor a variety of quantum paramagnetic states, our RIXS calculations provide useful signatures to identify the true nature of the ordering pattern.
Abstract We investigate the spin dynamics of a 1D spin-1/2 Heisenberg tetramer chain. Employing a combination of density matrix renormalization group, quantum renormalization group, and perturbation theory techniques, we compute the energy levels and the quantum phase diagram, analyze the phase transitions, and evaluate the dynamical structure factor (DSF), which is related to the inelastic neutron scattering (INS) spectrum and the resonant inelastic x-ray scattering (RIXS) spectrum of fractionalized and collective excitations. Our calculations suggest that the chain can transition between a hidden Z 2 × Z 2 discrete symmetry preserving tetramer phase and a Haldane phase with non-vanishing string order that breaks the hidden symmetry. These two gapped phases are intervened by an intermediate deconfined quantum critical state comprising of free spins and three-site doublets, which is a gapless critical phase with deconfined spinons that can be detected either by INS or L -edge RIXS. We find that the tetramer chain can support fractionalized (spinon) and collective (triplon and quinton) excitations. In the ferromagnetic intra-tetramer limit, the chain can support a quinton excitation which has a five-fold degenerate excited state. String order parameter calculations suggest CuInVO 5 should be in a Haldane-like phase whose INS or L -edge RIXS spectrum can support observable single-spin excitations including triplon and quinton excitations. We also identify possible two-particle excitations (two-singlon, two-triplon, triplon-quinton, and two-quinton excitations) resulting from the double spin-flip effect in the K -edge RIXS spectrum.
We investigate the excitation spectra of a spin-1/2 antiferromagnetic Heisenberg trimer spin chain by employing a combination of numerical and theoretical techniques. Utilizing the Krylov-space correction-vector method in density matrix renormalization group (DMRG), we calculate both the direct and indirect resonant inelastic x-ray scattering (RIXS) spectra for the trimer spin chain. To interpret the observed features in the RIXS spectra, we perform a theoretical perturbative analysis to compute the energy dispersions, which are then utilized to determine the density of states (DOS) for both the single-particle and the two-particle excitation spectra. Our results show that the single-particle continua of the direct RIXS spectrum align with the energy levels observed in the DOS spectra of spinon, doublon, and quarton excitations. Furthermore, the two-particle continua are revealed in the indirect RIXS process, where all possible single-particle excitations combine to form the various two-particle excitations of the trimer spin chain. Based on our calculations, we propose the RIXS mechanism of generating the fractionalized (spinon) and collective (doublon and quarton) excitations in the trimer spin chain at both the LLL edge and the KKK edge, including discussing the interplay of these excitations in the RIXS spectrum for various trimer coupling strength. The computed energy range of the excitations suggest the possibility of experimental detection at both the LLL edge and the KKK edge within the current capabilities of RIXS instrumentation resolution.
Resonant inelastic x-ray scattering (RIXS) has become an important tool for studying elementary excitations in correlated materials. Here, we present a systematic theoretical investigation of the Cu LLL-edge RIXS spectra of undoped and doped cuprate two-leg spin-ladders in both the non-spin-conserving (NSC) and spin-conserving (SC) channels. The spectra are rich and host many exotic excitations. In the NSC channel of the undoped case, we identify one-triplon and bound triplet two-triplon excitations in the strong rung coupling limit, as well as confined spinons in the weak rung coupling limit. In the doped case, we observe a quasiparticle excitation formed from a bound charge and spin-1/21/21/2 in the strong rung coupling limit. In the SC channel, we also identify several new features, including bound singlet two-triplon excitations and confined spinons in the undoped ladders in the strong and weak rung coupling limits, respectively. Conversely, in the doped case, the SC channel primarily probes both gapless and gapped charge excitations. Finally, we revisit the available data for the ladder compound Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ in the context of our results.
Abstract Studying multi-particle elementary excitations has provided unique access to understand collective many-body phenomena in correlated electronic materials, paving the way towards constructing microscopic models. In this work, we perform O K-edge resonant inelastic X-ray scattering (RIXS) on the quasi-one-dimensional cuprate Sr14Cu24O41{{{{{{\rm{Sr}}}}}}}_{14}{{{{{{\rm{Cu}}}}}}}_{24}{{{{{{\rm{O}}}}}}}_{41}Sr14​Cu24​O41​ Sr 14 Cu 24 O 41 with weakly-doped spin ladders. The RIXS signal is dominated by a dispersing sharp mode ~ 270 meV on top of a damped incoherent component ~ 400-500 meV. Comparing with model calculations using the perturbative continuous unitary transformations method, the two components resemble the spin-conserving ΔS = 0 two-triplon bound state and continuum excitations in the spin ladders. Such multi-spin response with long-lived ΔS = 0 excitons is central to several exotic magnetic properties featuring Majorana fermions, yet remains unexplored given the generally weak cross-section with other experimental techniques. By investigating a simple spin-ladder model system, our study provides valuable insight into low-dimensional quantum magnetism.
Motivated by experiments on nonmagnetic triangular-lattice Mott insulators, we study one candidate paramagnetic phase, namely the columnar dimer (or valence-bond) phase. We apply variants of the bond-operator theory to a dimerized and spatially anisotropic spin-1/2 Heisenberg model and determine its zero-temperature phase diagram and the spectrum of elementary triplet excitations (triplons). Depending on model parameters, we find that the minimum of the triplon energy is located at either a commensurate or an incommensurate wave vector. Condensation of triplons at this commensurate-incommensurate transition defines a quantum Lifshitz point, with effective dimensional reduction that possibly leads to nontrivial paramagnetic (e.g., spin-liquid) states near the closing of the triplet gap. We also discuss the two-particle decay of high-energy triplons, and we comment on the relevance of our results for the organic Mott insulator EtMe3{}_{3}3​P[Pd(dmit)2{}_{2}2​]2{}_{2}2​.