Spinon excitations in the XX chain: spectra, transition rates, observability (original) (raw)
Related papers
Interaction and thermodynamics of spinons in the XX chain
Journal of Physics A: Mathematical and Theoretical, 2008
The mapping between the fermion and spinon compositions of eigenstates in the one-dimensional spin-1/2 XX model on a lattice with N sites is used to describe the spinon interaction from two different perspectives: (i) For finite N the energy of all eigenstates is expressed as a function of spinon momenta and spinon spins, which, in turn, are solutions of a set of Bethe ansatz equations. The latter are the basis of an exact thermodynamic analysis in the spinon representation of the XX model. (ii) For N → ∞ the energy per site of spinon configurations involving any number of spinon orbitals is expressed as a function of reduced variables representing momentum, filling, and magnetization of each orbital. The spins of spinons in a single orbital are found to be coupled in a manner well described by an Ising-like equivalent-neighbor interaction, switching from ferromagnetic to antiferromagnetic as the filling exceeds a critical level. Comparisons are made with results for the Haldane-Shastry model.
Spectrum and transition rates of the XX chain analyzed via Bethe ansatz
Physical Review B, 2004
As part of a study that investigates the dynamics of the s = 1 2 XXZ model in the planar regime |∆| < 1, we discuss the singular nature of the Bethe ansatz equations for the case ∆ = 0 (XX model). We identify the general structure of the Bethe ansatz solutions for the entire XX spectrum, which include states with real and complex magnon momenta. We discuss the relation between the spinon or magnon quasiparticles (Bethe ansatz) and the lattice fermions (Jordan-Wigner representation). We present determinantal expressions for transition rates of spin fluctuation operators between Bethe wave functions and reduce them to product expressions. We apply the new formulas to two-spinon transition rates for chains with up to N = 4096 sites.
Dynamic response of spin-2 bosons in one-dimensional optical lattices
Physical Review A
We investigate the spin-2 chain model corresponding to the small hopping limit of the spin-2 Bose-Hubbard model using density-matrix renormalization-group and time-evolution techniques. We calculate both static correlation functions and the dynamic structure factor. The dynamic structure factor in the dimerized phase differs significantly between parameters near the SU(5)symmetric point and those deeper in the phase where the dimerization is strong. In the former case, most of the spectral weight is concentrated in a single excitation line, while in the latter case, a broad excitation continuum shows up. For the trimerized phase, we find gapless excitations at momenta k = ±2π/3 in agreement with previous results, although the visibility of these excitations in the dynamic spin response depends strongly on the specific parameters. We also consider parameters for specific atoms which may be relevant for future optical-lattice experiments.
Physical Review B, 1998
The exact 2-spinon part of the dynamic spin structure factor Sxx(Q, ω) for the one-dimensional s=1/2 XXZ model at T =0 in the antiferromagnetically ordered phase is calculated using recent advances by Jimbo and Miwa in the algebraic analysis based on (infinite-dimensional) quantum group symmetries of this model and the related vertex models. The 2-spinon excitations form a 2-parameter continuum consisting of two partly overlapping sheets in (Q, ω)-space. The spectral threshold has a smooth maximum at the Brillouin zone boundary (Q = π/2) and a smooth minimum with a gap at the zone center (Q = 0). The 2-spinon density of states has square-root divergences at the lower and upper continuum boundaries. For the 2-spinon transition rates, the two regimes 0 ≤ Q < Qκ (near the zone center) and Qκ < Q ≤ π/2 (near the zone boundary) must be distinguished, where Qκ → 0 in the Heisenberg limit and Qκ → π/2 in the Ising limit. In the regime Qκ < Q ≤ π/2, the 2-spinon transition rates relevant for Sxx(Q, ω) are finite at the lower boundary of each sheet, decrease monotonically with increasing ω, and approach zero linearly at the upper boundary. The resulting 2-spinon part of Sxx(Q, ω) is then square-root divergent at the spectral threshold and vanishes in a square-root cusp at the upper boundary. In the regime 0 < Qκ ≤ π/2, by contrast, the 2-spinon transition rates have a smooth maximum inside the continuum and vanish linearly at either boundary. In the associated 2-spinon line shapes of Sxx(Q, ω), the linear cusps at the continuum boundaries are replaced by square-root cusps. Existing perturbation studies have been unable to capture the physics of the regime Qκ < Q ≤ π/2. However, their line shape predictions for the regime 0 ≤ Q < Qκ are in good agreement with the new exact results if the anisotropy is very strong. For weak anisotropies, the exact line shapes are more asymmetric.
Exact Edge Singularities and Dynamical Correlations in Spin-1/2 Chains
Physical Review Letters, 2008
Exact formulas for the singularities of the dynamical structure factor, S zz (q, ω), of the S = 1/2 xxz spin chain at all q and any anisotropy and magnetic field in the critical regime are derived, expressing the exponents in terms of the phase shifts which are known exactly from the Bethe ansatz solution. We also study the long time asymptotics of the self-correlation function 0|S z j (t)S z j (0)|0 . Utilizing these results to supplement very accurate time-dependent Density Matrix Renormalization Group (DMRG) for short to moderate times, we calculate S zz (q, ω) to very high precision. PACS numbers: 75.10.Pq, 71.10.Pm
Spin excitations on finite lattices and the discrete Fourier transform
Journal of Magnetism and Magnetic Materials, 2006
The method of discrete Fourier transform (DFT) is applied to obtain the exact one-or bi-magnonic states in several finite onedimensional spin systems. The advantage of DFT method, compared to Bethe ansatz, is that no assumption is made on the form of the wave function and that its limit of infinite system reduces to the standard approach to excitation spectra in condensed matter. So the method has, in principle, no limitation on lattice dimensionality and its physical interpretation is relatively transparent. It is demonstrated that the two approaches (DFT and BA) give identical results for the solution of the Schrodinger equation on the 1D lattice, although the structure of the methods is rather different. The excitation spectrum of the XXZ chain with arbitrary end fields is analyzed in detail and an analogy with atomic wires is briefly discussed. r
Energy Spectrum Analysis of 1D Spin-3/2 Fermionic Chains
Journal of Superconductivity and Novel Magnetism, 2015
We study an ultracold atomic gas of repulsively interacting spin-3/2 fermions loaded into one-dimensional optical lattices. The physics of the lowest band can be described by a Hubbard Hamiltonian that becomes a generalized Heisenberg model for strong enough interactions since the system undergoes into a Mott insulator phase. For few lattice sites (up-to 6 sites), we solve numerically this model by means of the exact diagonalization technique. For larger systems (up-to 9 sites), we use the Lanczos algorithm in order to infer the physics expected in the thermodynamic limit. We present the numerical calculation of the energy spectrum and the energy gap as a function of the lattice sizes, and performing finite-size scaling we show that such small systems are able to recover the main thermodynamiclimit properties of the two distinguished magnetic phases present in this system namely spin liquid and spin Peierls.
Disordered Fermions on Lattices and Their Spectral Properties
Journal of Statistical Physics, 2011
We study Fermionic systems on a lattice with random interactions through their dynamics and the associated KMS states. These systems require a more complex approach compared with the standard spin systems on a lattice, on account of the difference in commutation rules for the local algebras for disjoint regions, between these two systems. It is for this reason that some of the known formulations and proofs in the case of the spin lattice systems with random interactions do not automatically go over to the case of disordered Fermion lattice systems. We extend to the disordered CAR algebra, some standard results concerning the spectral properties exhibited by temperature states for disordered quantum spin systems. We discuss the Arveson spectrum and its connection with the Connes and Borchers Γ-invariants for such W *-dynamical systems. In the case of KMS states exhibiting a natural property of invariance with respect to the spatial translations, some interesting properties, associated with standard spinglass-like behaviour, emerge naturally. It covers infinite-volume limits of finite-volume Gibbs states, that is the quenched disorder for Fermions living on a standard lattice Z d. In particular, we show that a temperature state of the systems under consideration can generate only a type III von Neumann algebra (with the type III 0 component excluded). Moreover, in the case of the pure thermodynamic phase, the associated von Neumann is of type III λ for some λ ∈ (0, 1], independent of the disorder. Such a result is in accordance with the principle of self-averaging which affirms that the physically relevant quantities do not depend on the disorder. The present approach can be viewed as a further step towards fully understanding the very complicated structure of the set of temperature states of quantum spin glasses, and its connection with the breakdown of the symmetry for the replicas.
1997
The exact 2-spinon part of the dynamic spin structure factor Sxx(Q,omega)S_{xx}(Q,\omega)Sxx(Q,omega) for the one-dimensional sss=1/2 XXZXXZXXZ model at TTT=0 in the antiferromagnetically ordered phase is calculated using recent advances by Jimbo and Miwa in the algebraic analysis based on (infinite-dimensional) quantum group symmetries of this model and the related vertex models. The 2-spinon excitations form a 2-parameter continuum consisting of two partly overlapping sheets in (Q,omega)(Q,\omega)(Q,omega)-space. The spectral threshold has a smooth maximum at the Brillouin zone boundary (Q=pi/2)(Q=\pi/2)(Q=pi/2) and a smooth minimum with a gap at the zone center (Q=0)(Q=0)(Q=0). The 2-spinon density of states has square-root divergences at the lower and upper continuum boundaries. For the 2-spinon transition rates, the two regimes 0leqQ<Qkappa0 \leq Q < Q_\kappa0leqQ<Qkappa (near the zone center) and Qkappa<Qleqpi/2Q_\kappa < Q \leq \pi/2Qkappa<Qleqpi/2 (near the zone boundary) must be distinguished, where Qkappato0Q_\kappa \to 0Qkappato0 in the Heisenberg limit and Qkappatopi/2Q_\kappa \to \pi/2Qkappatopi/2 in the Ising limit. The resulting 2-spinon part of Sxx(Q,omega)S_{xx}(Q,\omega)Sxx(Q,omega) is then square-root divergent at the spectral threshold and vanishes in a square-root cusp at the upper boundary. In the regime 0<Qkappaleqpi/20 < Q_\kappa \leq \pi/20<Qkappaleqpi/2, by contrast, the 2-spinon transition rates have a smooth maximum inside the continuum and vanish linearly at either boundary. Existing perturbation studies have been unable to capture the physics of the regime Qkappa<Qleqpi/2Q_\kappa < Q \leq \pi/2Qkappa<Qleqpi/2. However, their line shape predictions for the regime 0leqQ<Qkappa0 \leq Q < Q_\kappa0leqQ<Qkappa are in good agreement with the new exact results if the anisotropy is very strong.
Spin dynamics of dimerized Heisenberg chains
Europhysics Letters (EPL), 1997
The user has requested enhancement of the downloaded file. arXiv:cond-mat/9612013v1 [cond-mat.str-el] We study numerically the dimerized Heisenberg model with frustration appropriate for the quasi-1D spin-Peierls compound CuGeO3. We present evidence for a bound state in the dynamical structure factor for any finite dimerization δ and estimate the respective spectral weight. For the homogeneous case (δ = 0) we show that the spin-wave velocity vs is renormalized by the n.n.n. frustration term α as vs = π/2 J(1 − bα) with b ≈ 1.12 78.20.Ls Quantum 1D spin systems may show a variety of instabilities. Of particular interest is the spin-Peierls (SP) phase due to residual magnetoelastic couplings , which leads to the opening of a gap in the spin excitation spectrum. The discovery [2] of the spin-Peierls transition below T SP = 14 K in an inorganic compound, CuGeO 3 , has attracted widespread attention.