Generalized Pauli principle for particles with distinguishable traits

The s=3/2 Ising spin chain with uniform nearest-neighbor coupling, quadratic single-site potential, and magnetic field is shown to be equivalent to a system of 17 species of particles with internal structure. The same set of particles (with different energies) is shown to generate the spectrum of the s=1/2 Ising chain with dimerized nearest-neighbor coupling. The particles are free of interaction energies even at high densities. The mutual exclusion statistics of particles from all species is determined by their internal structure and encoded in a generalized Pauli principle. The exact statistical mechanical analysis can be performed for thermodynamically open or closed systems and with arbitrary energies assigned to all particle species. Special circumstances make it possible to merge two or more species into a single species. All traits that distinguish the original species become ignorable. The particles from the merged species are effectively indistinguishable and obey modified exclusion statistics. Different mergers may yield the same endproduct, implying that the inverse process (splitting any species into subspecies) is not unique. In a macroscopic system of two merged species at thermal equilibrium, the concentrations of the original species satisfy a functional relation governed by their mutual statistical interaction. That relation is derivable from an extremum principle. In the Ising context the system is open and the particle energies depend on the Hamiltonian parameters. Simple models of polymerization and solitonic paramagnetism each represent a closed system of two species that can transform into each other. Here they represent distinguishable traits with different energies of the same physical particle.Comment: 12 pages, 7 figures, 6 table

Spin Chains as Perfect Quantum State Mirrors

Quantum information transfer is an important part of quantum information processing. Several proposals for quantum information transfer along linear arrays of nearest-neighbor coupled qubits or spins were made recently. Perfect transfer was shown to exist in two models with specifically designed strongly inhomogeneous couplings. We show that perfect transfer occurs in an entire class of chains, including systems whose nearest-neighbor couplings vary only weakly along the chain. The key to these observations is the Jordan-Wigner mapping of spins to noninteracting lattice fermions which display perfectly periodic dynamics if the single-particle energy spectrum is appropriate. After a half-period of that dynamics any state is transformed into its mirror image with respect to the center of the chain. The absence of fermion interactions preserves these features at arbitrary temperature and allows for the transfer of nontrivially entangled states of several spins or qubits.Comment: Abstract extended, introduction shortened, some clarifications in the text, one new reference. Accepted by Phys. Rev. A (Rapid Communications

Interaction and thermodynamics of spinons in the XX chain

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 -> infinity 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.Comment: 16 pages, 3 figure

Boundaries, Cusps and Caustics in the Multimagnon Continua of 1D Quantum Spin Systems

The multimagnon continua of 1D quantum spin systems possess several interesting singular features that may soon be accessible experimentally through inelastic neutron scattering. These include cusps and composition discontinuities in the boundary envelopes of two-magnon continuum states and discontinuities in the density of states, "caustics", on and within the continuum, which will appear as discontinuities in scattering intensity. In this note we discuss the general origins of these continuum features, and illustrate our results using the alternating Heisenberg antiferromagnetic chain and two-leg ladder as examples.Comment: 18 pages, 10 figure

High Order Coherent Control Sequences of Finite-Width Pulses

The performance of sequences of designed pulses of finite length $\tau$ is analyzed for a bath of spins and it is compared with that of sequences of ideal, instantaneous pulses. The degree of the design of the pulse strongly affects the performance of the sequences. Non-equidistant, adapted sequences of pulses, which equal instantaneous ones up to $\mathcal{O}(\tau^3)$, outperform equidistant or concatenated sequences. Moreover, they do so at low energy cost which grows only logarithmically with the number of pulses, in contrast to standard pulses with linear growth.Comment: 6 pages, 5 figures, new figures, published versio

Dynamics of the spin-half Heisenberg chain at intermediate temperatures

Combining high-temperature expansions with the recursion method and quantum Monte Carlo simulations with the maximum entropy method, we study the dynamics of the spin-1/2 Heisenberg chain at temperatures above and below the coupling J. By comparing the two sets of calculations, their relative strengths are assessed. At high temperatures, we find that there is a low-frequency peak in the momentum integrated dynamic structure factor, due to diffusive long-wavelength modes. This peak is rapidly suppressed as the temperature is lowered below J. Calculation of the complete dynamic structure factor S(k,w) shows how the spectral features associated with the two-spinon continuum develop at low temperatures. We extract the nuclear spin-lattice relaxation rate 1/T1 from the w-->0 limit, and compare with recent experimental results for Sr2CuO3 and CuGeO3. We also discuss the scaling behavior of the dynamic susceptibility, and of the static structure factor S(k) and the static susceptibility X(k). We confirm the asymptotic low-temperature forms S(pi)~[ln(T)]^(3/2) and X(pi)~T^(-1)[ln(T)]^(1/2), expected from previous theoretical studies.Comment: 15 pages, Revtex, 14 PostScript figures. 2 new figures and related discussion of the recursion method at finite temperature adde

Fractional and Integer Excitations in Quantum Antiferromagnetic Spin 1/2 Ladders

Spectral densities are computed in unprecedented detail for quantum antiferromagnetic spin 1/2 two-leg ladders. These results were obtained due to a major methodical advance achieved by optimally chosen unitary transformations. The approach is based on dressed integer excitations. Considerable weight is found at high energies in the two-particle sector. Precursors of fractional spinon physics occur implying that there is no necessity to resort to fractional excitations in order to describe features at higher energies.Comment: 6 pages, 4 figures included, minor text changes, improved figure

Dynamical Structure Factor for the Alternating Heisenberg Chain: A Linked Cluster Calculation

We develop a linked cluster method to calculate the spectral weights of many-particle excitations at zero temperature. The dynamical structure factor is expressed as a sum of exclusive structure factors, each representing contributions from a given set of excited states. A linked cluster technique to obtain high order series expansions for these quantities is discussed. We apply these methods to the alternating Heisenberg chain around the dimerized limit ($\lambda=0$), where complete wavevector and frequency dependent spectral weights for one and two-particle excitations (continuum and bound-states) are obtained. For small to moderate values of the inter-dimer coupling parameter $\lambda$, these lead to extremely accurate calculations of the dynamical structure factors. We also examine the variation of the relative spectral weights of one and two-particle states with bond alternation all the way up to the limit of the uniform chain ($\lambda=1$). In agreement with Schmidt and Uhrig, we find that the spectral weight is dominated by 2-triplet states even at $\lambda=1$, which implies that a description in terms of triplet-pair excitations remains a good quantitative description of the system even for the uniform chain.Comment: 26 pages, 17 figure

Spinons and triplons in spatially anisotropic frustrated antiferromagnets

The search for elementary excitations with fractional quantum numbers is a central challenge in modern condensed matter physics. We explore the possibility in a realistic model for several materials, the spin-1/2 spatially anisotropic frustrated Heisenberg antiferromagnet in two dimensions. By restricting the Hilbert space to that expressed by exact eigenstates of the Heisenberg chain, we derive an effective Schr\"odinger equation valid in the weak interchain-coupling regime. The dynamical spin correlations from this approach agree quantitatively with inelastic neutron measurements on the triangular antiferromagnet Cs_2CuCl_4. The spectral features in such antiferromagnets can be attributed to two types of excitations: descendents of one-dimensional spinons of individual chains, and coherently propagating "triplon" bound states of spinon pairs. We argue that triplons are generic features of spatially anisotropic frustrated antiferromagnets, and arise because the bound spinon pair lowers its kinetic energy by propagating between chains.Comment: 16 pages, 6 figure