Spin-exchange dynamical structure factor of the S=1/2 Heisenberg chain

We determine the spin-exchange dynamical structure factor of the Heisenberg spin chain, as is measured by indirect resonant inelastic x-ray scattering (RIXS). We find that two-spin RIXS excitations nearly entirely fractionalize into two-spinon states. These share the same continuum lower bound as single-spin neutron scattering excitations, even if the relevant final states belong to orthogonal symmetry sectors. The RIXS spectral weight is mainly carried by higher-energy excitations, and is beyond the reach of the low-energy effective theories of Luttinger liquid type.     

Calculation of correlation functions in the Heisenberg spin-1/2 antiferromagnetic model

We derive the exact expression of the four-spinon contribution S ₄ to the dynamical correlation function S of the spin 1/2 isotropic (XXX) He isenberg model in the antiferromagnetic regime using the quantum group symmetry of the model. We first give the exact expression for the n-spinon contribution in the form of contour integrals and display known results regarding the two-spinon contribution S ₂. Then we specialize the n-spinon formula to the case n = 4 and compute three sum rules for S ₄ that the total S is known to satisfy exactly. These are: the total integrated intensity, the first frequency moment and the nearest-neighbor correlation function. We find that S ₄ corrects only by a small amount the contribution from S ₂. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.     

Inozemtsev's hyperbolic spin model and its related spin chain

In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane–Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm–Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane–Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.     

Entanglement control in one-dimensional s= 1/2 random XY spin chain

The entanglement in one-dimensional random XY spin systems where the impurities of exchange couplings and the external magnetic fields are considered as random variables is investigated by solving the different spin-spin correlation functions and the average magnetization per spin. The entanglement dynamics near particular locations of the system is also studied when the exchange couplings （or the external magnetic fields） satisfy three different distributions （the Gaussian distribution, double-Gaussian distribution, and bimodal distribution）. We find that the entanglement can be controlled by varying the strength of external magnetic field and the distributions of impurities. Moreover, the entanglement of some nearest-neighbouring qubits can be increased for certain parameter values of the three different distributions.     

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures (T/J=10^-24) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given. Received: 12 February 1998 / Received in final form: 15 March 1998 / Accepted: 17 March 1998     

Quantum Monte Carlo investigation of the 2D Heisenberg model with S=1/2

The two-dimensional (2D) Heisenberg model with anisotropic exchange (Δ = 1−J _x /J _z ) and S=1/2 is investigated by the quantum Monte Carlo method. The energy, susceptibility, specific heat, spin-spin correlation functions, and correlation radius are calculated. The sublattice magnetization (σ) and the Néel temperature of the anisotropic antiferromagnet are logarithmic functions of the exchange anisotropy: 1/σ+1+0.13(1)ln(1/Δ). Crossover of the static magnetic structural factor as a function of temperature from power-law to exponential occurs for T _c /J≈0.4. The correlation radius can be approximated by 1/ξ=2.05T ^1.0(6)/exp(1.0(4)/T). For La₂CuO₄ the sublattice magnetization is calculated as σ=0.45, the exchange is J=(1125–1305) K; for Er₂CuO₄ J∼625 K and the exchange anisotropy Δ∼0.003. The temperature dependence of the static structural magnetic factor and the correlation radius above the Néel temperature in these compounds can be explained by the formation of topological excitations (spinons). Fiz. Tverd. Tela (St. Petersburg) 41, 116–121 (January 1999)     

Magnetic properties of the spin S = 1/2 Heisenberg chain with hexamer modulation of exchange

We consider the spin-1/2 Heisenberg chain with alternating spin exchange in the presence of additional modulation of exchange on odd bonds with period 3. We study the ground state magnetic phase diagram of this hexamer spin chain in the limit of very strong antiferromagnetic (AF) exchange on odd bonds using the numerical Lanczos method and bosonization approach. In the limit of strong magnetic field commensurate with the dominating AF exchange, the model is mapped onto an effective XXZ Heisenberg chain in the presence of uniform and spatially modulated fields, which is studied using the standard continuum-limit bosonization approach. In the absence of additional hexamer modulation, the model undergoes a quantum phase transition from a gapped phase into the only one gapless Lüttinger liquid (LL) phase by increasing the magnetic field. In the presence of hexamer modulation, two new gapped phases are identified in the ground state at magnetization equal to [Formula: see text] and [Formula: see text] of the saturation value. These phases reveal themselves also in the magnetization curve as plateaus at corresponding values of magnetization. As a result, the magnetic phase diagram of the hexamer chain shows seven different quantum phases, four gapped and three gapless, and the system is characterized by six critical fields which mark quantum phase transitions between the ordered gapped and the LL gapless phases.     

Analytic evidence of the equivalence of the alternating Heisenberg spin chain to the mixed spin (1, 1/2) Heisenberg chain

We investigated the properties of the spin-1/2 ferromagnetic-antiferromagnetic-antiferromagnetic alternating Heisenberg chain using the spin-wave theory. The spin-wave excitation spectra, the sublattice magnetizations and the local bond energies of the model are calculated to be compared with the corresponding properties of the mixed spin (1, 1/2) chain for a range of α. The results demonstrate that all the properties show similar behaviours in the small α limit, so the properties of the mixed spin (1, 1/2) chain can be described using the spin-1/2 ferromagnetic-antiferromagnetic-antiferromagnetic alternating Heisenberg chain.     

Bipartite entanglement in spin-1/2 Heisenberg model

The bipartite entanglement of the two- and three-spin Heisenberg model was investigated by using the concept of negativity. It is found that for the ground-state entanglement of the two-spin model, the negativity always decreases as B increases if Δ<γ－1, and it may keep a steady value of 0.5 in the region of B2－γ²]^1/2 if Δ>γ－1, while for that of the three-spin model, the negativity exhibits square wave structures if γ=0 or Δ=0. For thermal states, there are two areas showing entanglement, namely, the main region and the sub-region. The main region exists only when Δ>Δ_c (Δ_c=γ－1 and (γ²－1)/2 for the 2- and 3-spin model respectively) and extends in terms of B and T as Δ increases, while the sub-region survives only when γ≠0 and shrinks in terms of B and T as Δ increases.     

Bipartite entanglement in spin-1/2Heisenberg model

The bipartite entanglement of the two-and three-spin Heisenberg model was investigated by using the concept of negativity.It is found that for the ground-state entanglement of the two-spin model,the negativity always decreases as B increases if A Δ＜y-1,and it may keep a steady value of 0.5in the region of B＜J[(Δ+1)2-y2]1/2if Δ＞y-1,while for that of the three-spin model,the negativity exhibits square wave structures if y=0 or Δ=0.For thermal states,there are two areas showing entanglement,namely,the main region and the sub-region.The main region exists only when Δ＞Δc(Δc1=and(y2-1)/2for the 2-and 3-spin model respectively)and extends in terms of B and T as Δ increases,while the sub-region survives only when y≠0 and shrinks in terms of B and T as Δ increases.