Physics Faculty PublicationsCopyright (c) 2014 University of Rhode Island All rights reserved.
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Recent documents in Physics Faculty Publicationsen-usWed, 22 Oct 2014 01:36:52 PDT3600Integrable and Nonintegrable Classical Spin Clusters: Trajectories and Geometric Structure of Invariants
http://digitalcommons.uri.edu/phys_facpubs/79
http://digitalcommons.uri.edu/phys_facpubs/79Mon, 20 Oct 2014 10:34:53 PDT
This study investigates the nonlinear dynamics of a pair of exchange-coupled spins with biaxial exchange and single-site anisotropy. It represents a Hamiltonian system with 2 degrees of freedom for which we have already established the (nontrivial) integrability criteria and constructed the integrals of the motion provided they exist. Here we present a comparative study of the phase-space trajectories for two specific models with the same symmetry properties, one of which (the XY model with exchange anisotropy) is integrable, and the other (the XY model with single-site anisotropy) nonintegrable. In the integrable model, the integrals of the motion (analytic invariants) can be reconstructed numerically by means of time averages of dynamical variables over all trajectories. In the nonintegrable model, such time averages over trajectories define nonanalytic invariants, where the nonanalyticities are associated with the presence of chaotic trajectories. A prominent feature in the nonintegrable model is the occurrence of very long time scales caused by the presence of low- ux cantori, which form "sticky" coats on the boundary between chaotic regions and regular islands or "leaky" walls between dierent chaotic regions. These cantori dominate the convergence properties of time averages and presumably determine the long-time asymptotic properties of dynamic correlation functions. Finally, we present a special class of integrable systems containing arbitrarily many spins coupled by general biaxial exchange anisotropy.
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Niraj Srivastava et al.Quantum and Classical Spin Clusters: Disappearance of Quantum Numbers and Hamiltonian Chaos
http://digitalcommons.uri.edu/phys_facpubs/78
http://digitalcommons.uri.edu/phys_facpubs/78Wed, 01 Oct 2014 13:10:11 PDT
We present a direct link between manifestations of classical Hamiltonian chaos and quantum nonintegrability effects as they occur in quantum invariants. In integrable classical Hamiltonian systems, analytic invariants (integrals of the motion) can be constructed numerically by means of time averages of dynamical variables over phase-space trajectories, whereas in near-integrable models such time averages yield nonanalytic invariants with qualitatively different properties. Translated into quantum mechanics, the invariants obtained from time averages of dynamical variables in energy eigenstates provide a topographical map of the plane of quantized actions (quantum numbers) with properties which again depend sensitively on whether or not the classical integrability condition is satisfied. The most conspicuous indicator of quantum chaos is the disappearance of quantum numbers, a phenomenon directly related to the breakdown of invariant tori in the classical phase flow. All results are for a system consisting of two exchange-coupled spins with biaxial exchange and single-site anisotropy, a system with a nontrivial integrability condition.
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Niraj Srivastava et al.Dynamics of Semi-infinite Quantam Spin Chains at T = ∞
http://digitalcommons.uri.edu/phys_facpubs/77
http://digitalcommons.uri.edu/phys_facpubs/77Tue, 16 Sep 2014 06:24:58 PDT
Time-dependent spin autocorrelation functions and their spectral densities for the semi-infinite one-dimensionals=1/2 XY and XXZ models atT=∞ are determined in part by rigorous calculations in the fermion representation and in part by the recursion method in the spin representation. Boundary effects yield valuable new insight into the different dynamical processes which govern the transport of spin fluctuations in the two models. The results obtained for theXXX model bear the unmistakable signature of spin diffusion in the form of a squareroot infrared divergence in the spectral density.
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Joachim Stolze et al.InfInfinite-temperature Dynamics of the Equivalent-neighbor XYZ Model
http://digitalcommons.uri.edu/phys_facpubs/76
http://digitalcommons.uri.edu/phys_facpubs/76Tue, 09 Sep 2014 06:48:14 PDT
The dynamics of the classical XYZ model with uniform interaction is investigated by the recursion method and, in part, by exact analysis. The time evolution is anharmonic for arbitrary N (number of spins); only the cases N=2 and ∞ are completely integrable. For the special (uniaxially symmetric) equivalent-neighbor XXZ model, the nonlinearities in the equations of motion disappear in the limit N-->∞, and the spin autocorrelation functions are determined exactly for infinite temperature: The function exhibits a Gaussian decay to a nonzero constant, and the function decays to zero, algebraically or like a Gaussian, depending on the amount of uniaxial anisotropy. For the general XYZ case, the T=∞ dynamical behavior includes four different universality classes, categorized according to the decay law of the spectral densities at high frequencies. That decay law governs the growth rate of the sequence of recurrents that determine the relaxation function in the continued-fraction representation. The four universality classes may serve as prototypes for a classification of the dynamics of classical and quantum many-body systems in general.
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Jian-Min Liu et al.Dynamics of an Integrable Two-sublattice Spin Model with Long-range Interaction
http://digitalcommons.uri.edu/phys_facpubs/75
http://digitalcommons.uri.edu/phys_facpubs/75Tue, 09 Sep 2014 06:43:24 PDT
The dynamics of the classical two-sublattice XYZ model with uniform intersublattice interaction and zero intrasublattice interaction is completely integrable for arbitrary system sizes. This makes the system amenable to an exact analysis of dynamic correlation functions. Here we present some exact results for the case with isotropic interaction (XXX model). The dynamical properties of the two-sublattice XYZ model are compared with those of the equivalent-neighbor XYZ model and categorized into universality classes of dynamical behavior.
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Jian-Min Liu et al.Computation of Dominant Eigenvalues and Eigenvectors: A Comparative Study of Algorithms
http://digitalcommons.uri.edu/phys_facpubs/74
http://digitalcommons.uri.edu/phys_facpubs/74Tue, 09 Sep 2014 06:34:39 PDT
We investigate two widely used recursive algorithms for the computation of eigenvectors with extreme eigenvalues of large symmetric matrices -- the modified Lanczös method and the conjugate-gradient method. The goal is to establish a connection between their underlying principles and to evaluate their performance in applications to Hamiltonian and transfer matrices of selected model systems of interest in condensed matter physics and statistical mechanics. The conjugate-gradient method is found to converge more rapidly for understandable reasons, while storage requirements are the same for both methods.
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M. P. Nightingale et al.Spin diffusion in the one-dimensional s = 1/2 XXZ model at infinite temperature
http://digitalcommons.uri.edu/phys_facpubs/73
http://digitalcommons.uri.edu/phys_facpubs/73Thu, 24 Jul 2014 07:49:44 PDT
Time-dependent spin-autocorrelation functions at T = ∞ and (in particular) their spectral densities for the bulk spin and the boundary spin of the semi-infinite spin-1/2 XXZ model (with exchange parameters Jx = Jy = J, Jz) are investigated on the basis of (i) rigorous bounds in the time domain and (ii) a continued-fraction analysis in the frequency domain. We have found strong numerical evidence for spin diffusion in quantum spin models. For Jz/J increasing from zero, the results of the short-time expansion indicate a change of the bulk-spin xx-autocorrelation function from Gaussian decay to exponential decay. The continued-fraction analysis of the same dynamic quantity signals a change from exponential decay to power-law decay as Jz/J pproaches unity and back to a more rapid decay upon further increase of that parameter. By contrast, the change in symmetry at Jz/J = 1 has virtually no impact on the bulk-spin zz-autocorrelation function (as expected). Similar contrasting properties are observable in the boundary-spin autocorrelation functions.
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Markus Böhm et al.Ordering and fluctuations in the ground state of the one-dimensional and two-dimensional S = 1/2 X X Z antiferromagnets: A study of dynamical properties based on the recursion method
http://digitalcommons.uri.edu/phys_facpubs/72
http://digitalcommons.uri.edu/phys_facpubs/72Wed, 23 Jul 2014 13:31:43 PDT
The recursion method is applied to the T = 0 dynamics of the S = 1/2 X X Z model on a linear chain and a square lattice. By means of new calculational techniques for the analysis of the continued-fraction coefficients pertaining to specific dynamical quantities, we obtain reliable information on the type of ordering in the ground state, on the size of gaps in the dynamically relevant excitation spectrum, on the bandwidths of dominant structures in spectral densities, on the exponents of infrared singularities, and on the detailed shape of spectral-weight distributions. We investigate some characteristic properties of the dynamic structure factors S (q, w) and the spin autocorrelation functions S(w) = N-1 Eq S{q, w), specifically their dependence on the uniaxial anisotropy, i.e., on the parameter which controls the type of ordering and the amount of quantum fluctuations in the ground state. We find, for example, that the different degrees of ordering in the planar regime of the one-dimensional and two-dimensional systems (criticality versus antiferromagnetic long-range order) have characteristic signatures in the dynamical properties which are conspicuously displayed in our results.
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V. S. Viswanath et al.Spectral signature of quantum spin diffusion in dimensions d = 1, 2, and 3
http://digitalcommons.uri.edu/phys_facpubs/71
http://digitalcommons.uri.edu/phys_facpubs/71Wed, 23 Jul 2014 13:15:58 PDT
The spectral densities of dynamical spin autocorrelation functions at infinite temperature are studied for the S = 1/2 XXZ model (with exchange couplings Jx = Jy = J, Jz) on the linear chain, the square lattice, and the simple cubic lattice. The low-frequency behavior of a given spectral density is inferred from certain characteristic properties of its continued-fraction coefficients as determined from computed frequency moments. The analysis yields estimates for the Jz/J dependence of the infrared-singularity exponent. In the d = 1 case, the exponent for spin fluctuations perpendicular to the O(2) symmetry axis responds sensitively as the anisotropy parameter sweeps across the O(3) symmetry point Jz/J = 1, while the exponent for the parallel fluctuations shows little variation. In the cases d = 2 and d = 3 the same observations are made for autocorrelation functions of aggregate spins in chains and lattice planes, respectively.
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Markus Böhm et al.Charge and spin dynamics in the one-dimensional t-Jz and t-J models
http://digitalcommons.uri.edu/phys_facpubs/70
http://digitalcommons.uri.edu/phys_facpubs/70Fri, 18 Jul 2014 13:45:48 PDT
The impact of the spin-flip terms on the (static and dynamic) charge and spin correlations in the Luttingerliquid ground state of the one-dimensional (1D) t-J model is assessed by comparison with the same quantities in the 1D t-Jz model, where spin-flip terms are absent. We employ the recursion method combined with a weak-coupling or a strong-coupling continued-fraction analysis. At Jz /t=0+ we use the Pfaffian representation of dynamic spin correlations. The changing nature of the dynamically relevant charge and spin excitations on approach of the transition to phase separation is investigated in detail. At the transition point, the t-Jz ground state has zero (static) charge correlations and very short-ranged (static) spin correlations, whereas the t-J ground state is critical. The t-Jz charge excitations (but not the spin excitations) at the transition have a single-mode nature, whereas charge and spin excitations have a complicated structure in the t-J model. A major transformation of the t-J spin excitations takes place between two distinct regimes within the Luttingerliquid phase, while the t-Jz spin excitations are found to change much more gradually. In the t-Jz model, phase separation is accompanied by Néel long-range order, caused by the condensation of electron clusters with an already existing alternating up-down spin configuration (topological long-range order). In the t-J model, by contrast, the spin-flip processes in the exchange coupling are responsible for continued strong spin fluctuations (dominated by two-spinon excitations) in the phase-separated state.
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Shu Zhang et al.Dimer and Néel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first- and second-neighbor couplings
http://digitalcommons.uri.edu/phys_facpubs/69
http://digitalcommons.uri.edu/phys_facpubs/69Fri, 18 Jul 2014 13:36:27 PDT
The dynamical properties at T = 0 of the one-dimensional (1D) s = 1/2 nearest-neighbor (NN) XXZ model with an additional isotropic next-nearest-neighbor (NNN) coupling are investigated by means of the recursion method in combination with a weak-coupling continued-fraction analysis. The focus is on the dynamic structure factors Szz(q,v) and SDD(q,v), which describe (for q = π) the fluctuations of the Néel and dimer order parameters, respectively. We calculate the dependence on the exchange constants of the infrared exponent, the renormalized bandwidth of spinon excitations, and the spectral-weight distribution in Szz(p,v) and SDD(π,v), all in the spin-fluid phase, which is realized for planar NN anisotropy and sufficiently weak NNN coupling. For some parameter values we find a discrete branch of excitations above the spinon continuum. They contribute to Szz(q,v) but not to SDD(q,v).
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Yongmin Yu et al.Gaussian, exponential, and power-law decay of time-dependent correlation functions in quantum spin chains
http://digitalcommons.uri.edu/phys_facpubs/68
http://digitalcommons.uri.edu/phys_facpubs/68Fri, 18 Jul 2014 13:18:17 PDT
Dynamic spin correlation functions (Sf(t)Sj) for the one-dimensional S = ~ XX model H = -JI:,{SfSf+l + SfSf+1 } are calculated exactly for finite open chains with uptoN= 10000 spins. Over a certain time range the results are free of finite-size effects and thus represent correlation functions of an infinite chain (bulk regime) or a semi-infinite chain (boundary regime). In the bulk regime, the long-time asymptotic decay as inferred by extrapolation is Gaussian at T = oo, exponential at 0 < T < oo, and power-law (~ t-112 ) at T = 0, in agreement with exact results. In the boundary regime, a power-law decay is obtained at all temperatures; the characteristic exponent is universal at T = 0 (~ r 1 ) and at 0 < T < oo (~ r 3 12 ), but is site dependent at T = oo. In the high-temperature regime (T I J ~ 1) and in the low-temperature regime (T I J « 1 ), crossovers between different decay laws can be observed in (Sf(t)Sj). Additional crossovers are found between bulk-type and boundary-type decay for i = j near the boundary, and between spacelike and timelike behavior for i -:f. j.
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Joachim Stolze et al.Quantum integrability and action operators in spin dynamics
http://digitalcommons.uri.edu/phys_facpubs/67
http://digitalcommons.uri.edu/phys_facpubs/67Wed, 16 Jul 2014 10:09:17 PDT
A new formulation of the quantum integrability condition for spin systems is proposed. It eliminates the ambiguities inherent in formulations derived from a direct transcription of the classical integrability criterion. In the new formulation, quantum integrability of an N-spin system depends on the existence of a unitary transformation which expresses the Hamiltonian as a function of N action operators. All operators are understood to be algebraic expressions of the spin-components with no restriction to any nite-dimensional matrix representation. The consequences of quantum (non-)integrability on the structure of quantum invariants are discussed in comparison with the consequences of classical (non-)integrability on the corresponding classical invariants. Our results indicate that quantum integrability is universal for systems with N = 1 and contingent for systems with N ≥ 2.
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Stefan Weigert et al.Incipience of quantum chaos in the spin-boson model
http://digitalcommons.uri.edu/phys_facpubs/66
http://digitalcommons.uri.edu/phys_facpubs/66Fri, 11 Jul 2014 13:45:49 PDT
The peculiar spectral properties of the spin-boson model make it suitable for an investigation of quantum nonintegrability effects and level statistics from a new perspective. For fixed spin quantum number s, its energy spectrum consists of 2s + 1 sequences of levels with no upper bound. These sequences are identified and labelled consecutively by means of a quantum invariant calculated from the time average of a non-stationary operator. For integrable cases, level repulsion (on the energy axis) is limited to states within each sequence. From the observed spectral properties, we infer a series of s-dependent level-spacing distributions. They converge towards a Poisson distribution for s —> ∞. For nonintegrable cases, level repulsion becomes a universal phenomenon, but the amount of repulsion between two states decreases with increasing separation (in label) of the two sequences to which they belong. For small s, the quantum nonintegrability effects are compelling but not at all chaotic. Nevertheless, they contain all the ingredients necessary to produce the symptoms commonly described as indicators of quantum chaos. In this model, we can observe quantum chaos in the making under very controllable conditions.
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Michel Cibils et al.Hamiltonian Chaos IV
http://digitalcommons.uri.edu/phys_facpubs/65
http://digitalcommons.uri.edu/phys_facpubs/65Mon, 16 Jun 2014 13:02:07 PDTNicolas Regez et al.Hamiltonian Chaos III
http://digitalcommons.uri.edu/phys_facpubs/64
http://digitalcommons.uri.edu/phys_facpubs/64Mon, 16 Jun 2014 12:49:48 PDTNiraj Srivastava et al.Hamiltonian Chaos II
http://digitalcommons.uri.edu/phys_facpubs/63
http://digitalcommons.uri.edu/phys_facpubs/63Mon, 16 Jun 2014 12:42:46 PDTNiraj Srivastava et al.Hamiltonian Chaos
http://digitalcommons.uri.edu/phys_facpubs/62
http://digitalcommons.uri.edu/phys_facpubs/62Mon, 16 Jun 2014 12:38:49 PDTNiraj Srivastava et al.COMPUTATIONAL PROBES OF COLLECTIVE EXCITATIONS IN LOW-DIMENSIONAL MAGNETISM
http://digitalcommons.uri.edu/phys_facpubs/61
http://digitalcommons.uri.edu/phys_facpubs/61Fri, 13 Jun 2014 09:22:23 PDT
The investigation of the dynamics of quantum many-body systems is a concerted effort involving computational studies of mathematical models and experimental studies of material samples. Some commonalities of the two tracks of investiga- tion are discussed in the context of the quantum spin dynamics of low-dimensional magnetic systems, in particular spin chains. The study of quantum fluctuations in such systems at equilibrium amounts to exploring the spectrum of collective exci- tations and the rate at which they are excited from the ground state by dynamical variables of interest. The exact results obtained via Bethe ansatz or algebraic analysis (quantum groups) for a select class of completely integrable models can be used as benchmarks for numerical studies of nonintegrable models, for which computational access to the spectrum of collective excitations is limited.
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Gerhard Müller et al.Spin Flip Loss in Magnetic Storage of Ultracold Neutrons
http://digitalcommons.uri.edu/phys_facpubs/60
http://digitalcommons.uri.edu/phys_facpubs/60Wed, 11 Jun 2014 12:07:24 PDT
We analyze the depolarization of ultracold neutrons confined in a magnetic field configuration similar to those used in existing or proposed magnetogravitational storage experiments aiming at a precise measurement of the neutron lifetime. We use an approximate quantum mechanical analysis such as pioneered by Walstrom et al [Nucl. Instrum. Methods Phys. Res. A 599, 82 (2009)]. Our analysis is not restricted to purely vertical modes of neutron motion. The lateral motion is shown to cause the predominant depolarization loss in a magnetic storage trap.
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A. Steyerl et al.