We examine spectral properties of doped holes dressed with surrounding spin cloud in the t-J model. These composite-hole excitations well characterize prominent band structures in the angle-resolved photoemission spectrum. In one-dimensional (1D) case at half-filling, we identify the composite operators that separately pick up the spinon and holon branches, respectively. After hole doping, we find that the composite hole excitations with string-like spins tend to be localized at k=π/2 in the momentum space. This means that such composite excitations should be actual electronic excitations, since the spinon and holon branches merge together at this momentum. In 2D case, we find that the composite excitations with more non-local spin fluctuation have stronger intensity near the Fermi level. The composite band structure along diagonal (0,0)-(π,π) direction in 2D has some similarity to that in 1D, and such non-local spin fluctuation plays an important role on the formation of the pseudogap in high-Tc cuprates.
The excitation spectrum of the frustrated spin-$1/2$ Heisenberg chain is reexamined using variational and exact diagonalization calculations. We show that the overlap matrix of the short-range resonating valence bond states basis can be inverted which yields tractable equations for single and two spinons excitations. Older results are recovered and new ones, such as the bond-state dispersion relation and its size with momentum at the Majumdar-Ghosh point are found. In particular, this approach yields a gap opening at $J_2=0.25J_1$ and an onset of incommensurability in the dispersion relation a…
Exact diagonalization calculations of finite antiferromagnetic spin-1 Heisenberg chains at finite temperatures are presented and compared to a recent inelastic neutron scattering experiment for temperatures T up to 7.5 times the intrachain exchange constant J. The calculations show that the excitations at the antiferromagnetic point q=1 and at q=0.5 remain resonant up to at least T=2J, confirming the recent experimental observation of resonant high-temperature domain wall excitations. The predicted first and second moments are in good agreement with experiment, except at temperatures where thr…
Motivated by recent inelastic neutron scattering experiment we examine magnetic properties of LiV2O4. We consider a model which describes the half-filled localized A1g spins interacting via frustrated antiferromagnetic Heisenberg exchange and coupled by local Hund's interaction with the 1/8-filled itinerant Eg band, and study it within an exact diagonalization scheme. In the present study we limited the analysis to the case of the cluster of two isolated tetrahedrons. We obtained that both the ground state structure and low-lying excitations depend strongly on the value of the Hund's coupling …
We investigate the $2k_F$ density-wave instability of non-Fermi liquid states by combining exact diagonalization with renormalization group analysis. At the half-filled zeroth Landau level, we study the fate of the composite Fermi liquid in the presence of the mass anisotropy and mixed Landau level form factors. These two experimentally accessible knobs trigger a phase transition towards a unidirectional charge-density-wave state with a wavevector equal to $2k_F$ of the composite Fermi liquid. Based on exact diagonalization, we identify such a transition by examining both the energy spectra an…
We present a generalization of the composite Fermion picture for a muticomponent quantum Hall plasma which contains particle with different effective charges. The model predicts very well the low-lying states of a $ν=5/2$ quantum Hall state found in numerical diagonalization.
We examine the momentum-dependent excitation spectra of indirect as well as direct resonant inelastic x-ray scattering (RIXS) processes in half-filled (extended) Hubbard rings. We determine the fundamental features of the groundstate RIXS response and discuss the experimental conditions that can allow for the low-energy part of these features to be distinguished in one-dimensional copper-oxide materials, focusing particularly on the different magnetic excitations occurring in indirect and direct RIXS processes. We study the dependence of spin and charge excitations on the choice of and detunin…
The electronic states of the Hubbard model are investigated by use of the Composite Operator Method. In addition to the Hubbard operators, two other operators related with two-site composite excitations are included in the basis. Within the present formulation, higher-order composite excitations are reduced to the chosen operatorial basis by means of a procedure preserving the particle-hole symmetry. The positive comparison with numerical simulations for the double occupancy indicates that such approximation improves over the two-pole approximation.
Numerical Block Diagonalization and Linked-Cluster Expansion for Deriving Effective Hamiltonians: Applications to Spin Excitations
RIKEN Center for Emergent Matter Science（理化学研究所物质结构研究中心）；School of Physical and Chemical Sciences, Queen Mary University of London（伦敦大学玛丽女王学院物理与化学科学学院）
We report on exact-diagonalization studies of correlated many-electron states in the half-filled Landau levels of graphene, including pseudospin (valley) degeneracy. We demonstrate that the polarized Fermi sea of non-interacting composite fermions remains stable against a pairing transition in the lowest two Landau levels. However, it undergoes spontaneous depolarization, which is unprotected owing to the lack of single-particle pseudospin splitting. These results suggest the absence of the Pfaffian phase in graphene.
While the integer quantum Hall effect of composite fermions manifests as the prominent fractional quantum Hall effect (FQHE) of electrons, the FQHE of composite fermions produces further, more delicate states, arising from a weak residual interaction between composite fermions. We study the spin phase diagram of these states, motivated by the recent experimental observation by Liu {\em et al.} \cite{Liu14a,Liu14b} of several spin-polarization transitions at 4/5, 5/7, 6/5, 9/7, 7/9, 8/11 and 10/13 in GaAs systems. We show that the FQHE of composite fermions is much more prevalent in multicompon…
Goldstone modes emerge associated with spontaneous breakdown of the continuous symmetry in the two-channel Kondo lattice, which describes strongly correlated f-electron systems with a non-Kramers doublet at each site. This paper derives the spectra of these collective modes by the equation of motion method together with the random phase approximation. The diagonal composite order breaks the SU(2) channel symmetry, and the symmetry-restoring collective mode couples with magnetic field. On the other hand, the off-diagonal or superconducting composite order breaks the gauge symmetry of conduction…
Self-localization of holes in the Holstein t-J model is studied in the adiabatic limit using exact diagonalization and the retraceable path approximation. It is shown that the critical electron-phonon coupling λ_c decreases with increasing J and that this behavior is determined mainly by the incoherent rather than by the coherent motion of the hole. The obtained spin correlation functions in the localized region can be understood within a percolation picture where antiferromagnetic order can persist up to a substantial hole doping. These results restrict the possibility of self-localization of…
Understanding exotic forms of magnetism in quantum spin systems is an emergent topic of modern condensed matter physics. Quantum dynamics can be described by particle-like carriers of information, known-as quasiparticles that appear from the collective behaviour of the underlying system. Spinon excitations, governing the excitations of quantum spin-systems, have been accurately calculated and precisely verified experimentally for the antiferromagnetic chain model. However, identification and characterization of novel quasiparticles emerging from the topological excitations of the spin system h…
The microscopic structure of a charge stripe in an antiferromagnetic insulator is studied within the t-Jz model using analytical and numerical approaches. We demonstrate that a stripe in an antiferromagnet should be viewed as a system of composite holon-spin-polaron excitations condensed at the self-induced antiphase domain wall (ADW) of the antiferromagnetic spins. The properties of such excitations are studied in detail with numerical and analytical results for various quantities being in very close agreement. A picture of the stripe as an effective one-dimensional (1D) band of such excitati…
With the help of analytical and numerical studies of the $t$-$J_z$ model we argue that the charge stripe in an antiferromagnetic insulator should be understood as a system of holon-spin-polaron excitations condensed at the self-induced antiphase domain wall. The structure of such a charge excitation is studied in detail with numerical and analytical results for various quantities being in a very close agreement. An analytical picture of these excitations occupying an effective 1D stripe band is also in a very good accord with numerical data. The emerging concept advocates the primary role of t…
Exact diagonalization studies have revealed that the energy spectrum of interacting electrons in the lowest Landau level splits, non-perturbatively, into bands, which is responsible for the fascinating phenomenology of this system. The theory of nearly free composite fermions has been shown to be valid for the lowest band, and thus to capture the low temperature physics, but it over-predicts the number of states for the excited bands. We explain the state counting of higher bands in terms of composite fermions with an infinitely strong short range interaction between an excited composite-fermi…
The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature o…
We study the two-dimensional electron gas in a magnetic field at filling fraction $ν=\frac{1}{2}$. At this filling the system is in a gapless state which can be interpreted as a Fermi liquid of composite fermions. We construct trial wave functions for the system on a torus, based on this idea, and numerically compare these to exact wave functions for small systems found by exact diagonalization. We find that the trial wave functions give an excellent description of the ground state of the system, as well as its charged excitations, in all momentum sectors. We analyze the dispersion of the comp…
We propose that a composite fermion operator $f_{iσ}(2n_{i{\bar σ}}-1)$ could have coherent excitations, where $f_{iσ}$ is the fermion operator for interacting electrons and $n_{i{\bar σ}}$ is the number operator of the opposite spin. In the two-impurity Anderson model, it is found that the excitation of this composite fermion has a pseudogap in the Kondo regime, and has a finite spectral weight in the regime where the excitation of the regular fermion $f_{iσ}$ has a pseudogap. In the latter regime, the self-energy of $f_{iσ}$ is found to be singular near Fermi energy. We argue that this compo…
A proposed ground state for the Kagome Lattice Heisenberg Model (KLHM) consists of a Valence Bond Crystal (VBC) with a 36-site unit cell. We calculate the low-lying triplet and singlet excitations in the VBC phase for the infinite-lattice model and for the 36-site cluster. For the infinite lattice, the lowest triplet excitation is found to have a spin gap of approximately $0.08 \pm 0.02 J$ and a bandwidth of only about $0.01 J$. For the 36-site cluster, consisting of a single unit cell with periodic boundary conditions, there are substantial finite-size effects: the spin gap there is estimated…
We study the effect of electron-electron interaction on the charge and spin structures at the edge of integer quantum Hall liquids, under three different kinds of confining potentials. Our exact diagonalization calculation for small systems indicates that the low energy excitations of ν=1 ferromagnetic state are bosonic edge spin waves. Instabilities of the ferromagnetic state with altering confinement strength result from the softening of these edge spin waves, and formation of edge spin textures. In ν\lesssim 2 regime, exact diagonalization on edge electron systems indicates that compact Har…
The optical conductivity σ(ω) in the two-dimensional Hubbard model is examined by applying the exact diagonalization technique to small square clusters with periodic boundary conditions up to \sqrt{20} X \sqrt{20} sites. Spectral-weight distributions at half filling and their doping dependence in the 20-site cluster are found to be similar to those in a \sqrt{18} X \sqrt{18} cluster, but different from 4 X 4 results. The results for the 20-site cluster enable us to perform a systematic study of the doping dependence of the spectral-weight transfer from the region of the Mott-gap excitation to …
We propose a method to calculate the charge dynamical structure factors for the ground states of correlated electron systems based on the variational Monte Carlo method. Our benchmarks for the one- and two-dimensional Hubbard models show that inclusion of composite-fermion excitations in the basis set greatly improves the accuracy, in reference to the exact charge dynamical structure factors for clusters. Together with examination for larger systems beyond tractable sizes by the exact diagonalization, our results indicate that the variational Monte Carlo method is a promising way for studies o…
The excitations of the 7/3 fractional Hall state, one of the most prominent states in the second Landau level, are not understood. We study the effect of screening by composite fermion excitons and find that it causes a strong renormalization at 7/3, thanks to a relatively small exciton gap and a relatively large residual interaction between composite fermions. The excitations of the 7/3 state are to be viewed as composite fermions dressed by a large exciton cloud. Their wide extent has implications for experiments as well as for analysis of finite system exact diagonalization studies.
We study the nature of the superconducting state, the origin of d-wave pairing, and elementary excitations of a resonating valence bond (RVB) superconductor. We show that the phase string formulation of the t-J model leads to confinement of bare spinon and holon excitations in the superconducting state, though the vacuum is described by the RVB state. Nodal quasiparticles are obtained as composite excitations of spinon and holon excitations. The d-wave pairing symmetry is shown to arise from short range antiferromagnetic correlations.
Using exact diagonalization, we study the projected Hamiltonian with Coulomb interaction in the 8 flat bands of first magic angle twisted bilayer graphene. Employing the U(4) (U(4)$\times$U(4)) symmetries in the nonchiral (chiral) flat band limit, we reduced the Hilbert space to an extent which allows for study around $ν=\pm 3,\pm2,\pm1$ fillings. In the first chiral limit $w_0/w_1=0$ where $w_0$ ($w_1$) is the $AA$ ($AB$) stacking hopping, we find that the ground-states at these fillings are extremely well-described by Slater determinants in a so-called Chern basis, and the exactly solvable c…
A fully self-consistent calculation of the bosonic dynamics of the Hubbard model is developed within the Composite Operator Method. From one side we consider a basic set of fermionic composite operators (Hubbard fields) and calculate the retarded propagators. On the other side we consider a basic set of bosonic composite operators (charge, spin and pair) and calculate the causal propagators. The equations for the Green's functions (GF) (retarded and causal), studied in the polar approximation, are coupled and depend on a set of parameters not determined by the dynamics. First, the pair sector …
Using quantum Monte Carlo, exact diagonalization and perturbation theory, we study the spectrum of the $S=1/2$ antiferromagnetic Heisenberg trimer chain by varying the ratio $g=J_2/J_1$ of the intertrimer and intratrimer coupling strengths. The doublet ground states of trimers form effective interacting $S=1/2$ degrees of freedom described by a Heisenberg chain. Therefore, the conventional two-spinon continuum of width $\propto J_1$ when $g=1$ evolves into to a similar continuum of width $\propto J_2$ when $g\to 0$. The intermediate-energy and high-energy modes are termed \emph{doublons} and \…
The spin-wave excitation spectrum, the magnetization, and the Néel temperature for the quasi-two-dimensional spin-1/2 antiferromagnetic Heisenberg model with compass-model interaction in the plane proposed for iridates are calculated in the random phase approximation. The spin-wave spectrum agrees well with data of Lanczos diagonalization. We find that the Neel temperature is enhanced by the compass-model interaction and is close to the experimental value for Ba2IrO4.
The spin-excitations of a fractional quantum Hall system are evaluated within a bosonization approach. In a first step, we generalize Murthy and Shankar's Hamiltonian theory of the fractional quantum Hall effect to the case of composite fermions with an extra discrete degree of freedom. Here, we mainly investigate the spin degrees of freedom, but the proposed formalism may be useful also in the study of bilayer quantum-Hall systems, where the layer index may formally be treated as an isospin. In a second step, we apply a bosonization scheme, recently developed for the study of the two-dimensio…
Magnetic field effects on the one-dimensional frustrated ferromagnetic chain are studied by means of effective field theory approaches in combination with numerical calculations utilizing Lanczos diagonalization and the density matrix renormalization group method. The nature of the ground state is shown to change from a spin-density-wave region to a nematic-like one upon approaching the saturation magnetization. The excitation spectrum is analyzed and the behavior of the single spin-flip excitation gap is studied in detail, including the emergent finite-size corrections.
We investigate the influence of biquadratic exchange interactions on the low-lying excitations of a S=1/2-ladder using perturbation theory, numerical diagonalization of finite systems and exact results for ladders with matrix product ground states. We consider in particular the combination of biquadratic exchange interactions corresponding to ring exchange on the basic ladder plaquette. We find that a moderate amount of ring exchange reduces the spin gap substantially and makes equal bilinear exchange on legs and rungs consistent with experimentally observed spectra.
The particle-hole (PH) symmetry of {\em electrons} is an exact symmetry of the electronic Hamiltonian confined to a specific Landau level, and its interplay with the formation of composite fermions has attracted much attention of late. This article investigates an emergent symmetry in the fractional quantum Hall effect, namely the PH symmetry of {\em composite fermions}, which relates states at composite fermion filling factors $ν^*=n+\barν$ and $ν^*=n+1-\barν$, where the integer $n$ is the $Λ$ level index and $0\leq \barν\leq 1$. Detailed calculations using the microscopic theory of composite…
We report the neutron scattering results on magnetic orderings and excitations in $\mathrm{Ba}_2\mathrm{CoTeO}_6$ composed of two almost isolated subsystems A and B, which are described as an $S\,{=}\,1/2$ triangular Heisenberg-like antiferromagnet and a frustrated honeycomb Ising-like antiferromagnet, respectively. Stripy ordering of subsystem B was confirmed below $T_{\rm N1}\,{=}\,12.0$ K, whereas sharp streaks were observed along $(1/3, 1/3, L)$ and $(2/3, 2/3, L)$ at 0.3 K (${\ll}\,T_{\rm N2}\,{=}\,3.0$ K). This indicates the two-dimensional nature of ordering in subsystem A. It was found…
The Rydberg blockade induces strongly correlated many-body effects in Rydberg atom arrays, including rich ground-state phases and many-body scar states in the excitation spectrum. In this letter, we propose a composite spin representation that can provide a unified description for major features in this system. The composite spin combines Rydberg excitation and the auxiliary fermions, which are introduced to implement the Rydberg blockade constraint automatically. First, we focus on the PXP model describing one-dimensional arrays with the Rydberg blocking radius being a lattice spacing. Using …
We have used exact numerical diagonalization to study the excitation spectrum and the dynamic spin correlations in the $s=1/2$ next-next-nearest neighbor Heisenberg antiferromagnet on the square lattice, with additional 4-spin ring exchange from higher order terms in the Hubbard expansion. We have varied the ratio between Hubbard model parameters, $t/U$, to obtain different relative strengths of the exchange parameters, while keeping electrons localized. The Hubbard model parameters have been parametrized via an effective ring exchange coupling, $J_r$, which have been varied between 0$J$ and 1…
We report on exact diagonalization studies for fully spin polarized 5/2 fractional quantum Hall effect, incorporating Landau level mixing through the Bishara-Nayak effective interaction. We find that there is an experimentally accessible region in the phase diagram where the Pfaffian model accurately describes not only the ground state but also the neutral and charged excitations. These results are consistent with the observed persistence of the 5/2 Hall effect down to very low magnetic fields; they are also relevant to the experimental attempts to detect nonabelian braid statistics.
Motivated by recent experiments that reveal expansive fractional quantum Hall states in the $n=1$ graphene Landau level and suggest a nontrivial role of the spin degree of freedom [Amet {\em et al.}, Nat. Common. {\bf 6}, 5838 (2014)], we perform accurate quantitative study of the the competition between fractional quantum Hall states with different spin polarizations. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the $n=0$ Landau level. In particular, for the states at filling fact…
We construct model wavefunctions for a family of single-quasielectron states supported by the $ν=1/3$ fractional quantum Hall (FQH) fluid. The charge $e^*$ = $e/3$ quasielectron state is identified as a composite of a charge-$2e^*$ quasiparticle and a $-e^*$ quasihole, orbiting around their common center of charge with relative angular momentum $n\hbar > 0$, and corresponds precisely to the "composite fermion" construction based on a filled $n=0$ Landau level plus an extra particle in level $n > 0$. An effective three-body model (one $2e^*$ quasiparticle and two $-e^*$ quasiholes) is introduce…
In this paper, we found a new type of insulator - composite spin liquid which can be regarded as a short range B-type topological spin-density-wave. Composite spin liquid is topological ordered state beyond the classification of traditional spin liquid states. The elementary excitations are the "composite electrons" with both spin degree of freedom and charge degree of freedom, together with topological spin texture. This topological state supports chiral edge mode but no topological degeneracy.
Exact diagonalization of a two-dimensional electron gas in a strong magnetic field in the disk geometry shows that there exists a filling factor range in the second Landau level where the states significantly differ from those in the lowest Landau level. We show that the difference arises because the interaction between composite fermions is not negligible in higher Landau levels, as indicated by a substantial mixing between composite-fermion Landau-like levels, or lambda levels. We find that the exact ground state is well reproduced by composite fermion theory with lambda level mixing incorpo…
The $S=1/2$ kagome- and triangular-lattice Heisenberg antiferromagnets are investigated using the numerical exact diagonalization and the finite-size scaling analysis. The behaviour of the field derivative at zero magnetization is examined for both systems. The present result indicates that the spin excitation is gapless for each system.
We study the system size dependence of the singlet-triplet excitation gap in the $S=1/2$ kagome-lattice Heisenberg antiferromagnet by numerical diagonalization. We successfully obtain a new result of a cluster of 42 sites. The two sequences of gaps of systems with even-number sites and that with odd-number sites are separately analyzed. Careful examination clarifies that there is no contradiction when we consider the system to be gapless.
Magnetic excitations in the quasi-one-dimensional antiferromagnet IPA-CuCl3 are studied by cold neutron inelastic scattering. Strongly dispersive gap excitations are observed. Contrary to previously proposed models, the system is best described as an asymmetric quantum spin ladder. The observed spectrum is interpreted in terms of ``composite'' Haldane spin chains. The key difference from actual S=1 chains is a sharp cutoff of the single-magnon spectrum at a certain critical wave vector.
Composite fermion metal states emerge in quantum Hall bilayers at total Landau level filling factor $ν_T$=1 when the tunneling gap collapses by application of in-plane components of the external magnetic field. Evidence of this transformation is found in the continua of spin excitations observed by inelastic light scattering below the spin-wave mode at the Zeeman energy. The low-lying spin modes are interpreted as quasiparticle excitations with simultaneous changes in spin orientation and composite fermion Landau level index.
It is shown, with the help of exact diagonalization studies on systems with up to sixteen electrons, in the presence of up to two delta function impurities, that the Pfaffian model is inadequate for the actual quasiholes and quasiparticles of the 5/2 fractional quantum Hall effect. Implications for non-Abelian statistics are discussed.
The fractional quantum Hall effect (FQHE) is extensively studied, but the explanation for Hall plateau widths and excitation energy gaps remains elusive. We study the effective theory of FQHE built upon experimental inputs of Hall current distribution, edge dynamics, and many-body correlations. We argue that correlated composites of integer spin, comprising electrons and their images, localized at the edge of the incompressible strip are the basic transport entity. We show in the lowest Landau level that Zeeman interactions of these composites produce all odd denominator plateaus and effective…
$s$-wave paired composite-fermion electron-hole trial state for quantum Hall bilayers with $ν=1$
Kavli Institute for Theoretical Physics, University of California Santa Barbara（卡弗里理论物理研究所，加州大学圣塔芭芭拉分校）；Brown Theoretical Physics Center, Brown University（布朗理论物理中心，布朗大学）；Department of Physics, Harvard University（物理学系，哈佛大学）
本文提出一种新的变分波函数，用于量子反铁磁双层体系中$ν=1$的情况，基于$ s $-波BCS配对复合费米子电子与复合费米子空穴。通过精确对角化计算，发现该试态与基态的重叠在不同层间距离与磁长度比范围内具有良好一致性。
We present numerical exact results for the ground state and the low-lying excitations for the spin-1/2 J1-J2 Heisenberg antiferromagnet on finite square lattices of up to N=40 sites. Using finite-size extrapolation we determine the ground-state energy, the magnetic order parameters, the spin gap, the uniform susceptibility, as well as the spin-wave velocity and the spin stiffness as functions of the frustration parameter J2/J1. In agreement with the generally excepted scenario we find semiclassical magnetically ordered phases for J2 < J2^{c1} and J2 > J2^{c2} separated by a gapful quantum para…
A fully self-consistent calculation of the bosonic dynamics of the Hubbard model is developed within the Composite Operator Method. From one side we consider a basic set of fermionic composite operators (Hubbard fields) and calculate the retarded propagators. On the other side we consider a basic set of bosonic composite operators (charge, spin and pair) and calculate the causal propagators. The equations for the Green's functions (GF) (retarded and causal), studied in the polar approximation, are coupled and depend on a set of parameters not determined by the dynamics. First, the pair sector …
We introduce (3+1) dimensional models of short-range-interacting electrons that form a strongly correlated many-body state whose low-energy excitations are relativistic neutral fermions coupled to an emergent gauge field, $\text{QED}_{4}$. We discuss the properties of this critical state and its instabilities towards exotic phases such as a gapless `composite' Weyl semimetal and fully gapped topologically ordered phases that feature anyonic point-like as well as line-like excitations. These fractionalized phases describe electronic insulators. They may be further enriched by symmetries which r…
We report inelastic light scattering experiments in the fractional quantum Hall regime at filling factors $ν\lesssim1/3$. A spin mode is observed below the Zeeman energy. The filling factor dependence of the mode energy is consistent with its assignment to spin flip excitations of composite fermions with four attached flux quanta ($ϕ$=4). Our findings reveal a composite fermion Landau level structure in the $ϕ$=4 sequence.
The multitude of excitations of the fractional quantum Hall state are very accurately understood, microscopically, as excitations of composite fermions across their Landau-like $Λ$ levels. In particular, the dispersion of the composite fermion exciton, which is the lowest energy spin conserving neutral excitation, displays filling-factor-specific minima called "magnetoroton" minima. Simon and Halperin employed the Chern-Simons field theory of composite fermions [Phys. Rev. B {\bf 48}, 17368 (1993)] to predict the magnetoroton minima positions. Recently, Golkar \emph{et al.} [Phys. Rev. Lett. {…
