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Taras Krokhmalskii

Publications and source records attributed to Taras Krokhmalskii.

45 records · Page 3Linked to original sources
arXiv2004

Regularly alternating spin-1/2 anisotropic XY chains: The ground-state and thermodynamic properties

Using the Jordan-Wigner transformation and continued fractions we calculate rigorously the thermodynamic quantities for the spin-1/2 transverse Ising chain with periodically varying intersite interactions and/or on-site fields. We consider in detail the properties of the chains having a period of the transverse field modulation equal to 3. The regularly alternating transverse Ising chain exhibits several quantum phase transition points, where the number of transition points for a given period of alternation strongly depends on the specific set of the Hamiltonian parameters. The critical behavior in most cases is the same as for the uniform chain. However, for certain sets of the Hamiltonian parameters the critical behavior may be changed and weak singularities in the ground-state quantities appear. Due to the regular alternation of the Hamiltonian parameters the transverse Ising chain may exhibit plateau-like steps in the zero-temperature dependence of the transverse magnetization vs. transverse field and many-peak temperature profiles of the specific heat. We compare the ground-state properties of regularly alternating transverse Ising and transverse XX chains and of regularly alternating quantum and classical chains. Making use of the corresponding unitary transformations we extend the elaborated approach to the study of thermodynamics of regularly alternating spin-1/2 anisotropic XY chains without field. We use the exact expression for the ground-state energy of such a chain of period 2 to discuss how the exchange interaction anisotropy destroys the spin-Peierls dimerized phase.

cond-mat.stat-mech↗
arXiv2004

Exact results for spatial decay of the one-body density matrix in low-dimensional insulators

We provide a tight-binding model of insulator, for which we derive an exact analytic form of the one-body density matrix and its large-distance asymptotics in dimensions $D=1,2$. The system is built out of a band of single-particle orbitals in a periodic potential. Breaking of the translational symmetry of the system results in two bands, separated by a direct gap whose width is proportional to the unique energy parameter of the model. The form of the decay is a power law times an exponential. We determine the power in the power law and the correlation length in the exponential, versus the lattice direction, the direct-gap width, and the lattice dimension. In particular, the obtained exact formulae imply that in the diagonal direction of the square lattice the inverse correlation length vanishes linearly with the vanishing gap, while in non-diagonal directions, the linear scaling is replaced by the square root one. Independently of direction, for sufficiently large gaps the inverse correlation length grows logarithmically with the gap width.

cond-mat.stat-mech↗
arXiv2003

Spatial decay of the one-body density matrix in insulators revised

In the framework of the band theory, we consider two tight-binding models of insulators. The first one, proposed recently by Taraskin et al, is a translationally invariant system, built out of two independent non-overlapping bands of single-particle orbitals that are coupled by a weak inter-band hybridization. This kind of insulator exhibits unphysical properties: we show, in particular, that the one-body density matrix does not depend on the width of the gap between the bands. Consequently, there is no delocalization effect with increasing metallicity. In the second model there are also two bands. However, they are not imposed by construction but are created from a band of single-particle orbitals due to the breaking of the translational symmetry by a periodic potential. These bands are separated by a gap for all nonzero values of the unique energy parameter of the model. We demonstrate that the one-body density matrix has the same structure as in the first model. As a result, the large distance asymptotic formulae derived by Taraskin et al in dimensions $D=1,2,3$, apply as well, but only for very large gap widths. In D=1 and in the diagonal direction of D=2 cases, we derive a stronger asymptotic formula, valid for all gap widths. The both kinds of asymptotic formulae are composed of a dimension-dependent power-law factor and a gap-dependent exponentially decaying factor. The latter asymptotics implies that the exponential decay rate vanishes linearly with the vanishing gap. In non-diagonal directions, we have found numerically that the linear scaling is replaced by the square root one. Independently of the direction, the exponential decay rate grows logarithmically with the gap width, for sufficiently large gaps.

cond-mat.stat-mech↗
arXiv2003

Dynamics of zz spin correlations in the square-lattice spin-1/2 isotropic XY model

Using the Jordan-Wigner fermionization in two dimensions we obtain the zz wave vector- and frequency-dependent structure factor for the spin-1/2 isotropic XY model on a spatially anisotropic square lattice. We use the obtained results to discuss a role of the interchain interaction for the dynamic properties of quasi-one-dimensional systems.

cond-mat↗
arXiv2002

Quantum phase transitions in alternating transverse Ising chains: Rigorous analytical and exact numerical results

We examine the ground state properties of the s=1/2 transverse Ising chain with regularly alternating bonds and fields using exact analytical results and exact numerical data for long (up to N=900) and short (N=20) chains. For a given period of alternation the system may exhibit a series of quantum phase transitions, where the number of transitions depends on the concrete set of the parameters of the Hamiltonian. The critical behaviour for the nonuniform and the uniform chain is the same.

cond-mat↗
arXiv1998

Dynamics of transverse correlations in the spin-1/2 isotropic XY chain with a correlated Lorentzian disorder

Using a numerical approach we examine the dynamics of $zz$ correlations for the spin-$1\over2$ isotropic XY chain with random Lorentzian intersite coupling and transverse field at sites that depends linearly on the neighbouring couplings. We study in detail the wave vector- and frequency-dependent $zz$ structure factor at different values of Hamiltonian parameters and temperature. We discuss the changes in the frequency profiles of the $zz$ dynamic structure factor caused by the introduced correlated disorder.

cond-mat↗
arXiv1998

Dynamic properties of spin-1/2 XY chains

We have considered a numerical scheme for the calculation of the equilibrium properties of spin-1/2 XY chains. Within its frames it is necessary to solve in the last resort only the 2N\times 2N eigenvalue and eigenvector problem but not the 2^N\times 2^N one as for an arbitrary system consisting of N spins 1/2. To illustrate the approach we have presented some new results. Namely, the xx dynamic structure factor for the Ising model in transverse field, the density of states for the isotropic chain with random intersite couplings and transverse fields that linearly depend on the surrounding couplings, and the zz dynamic structure factor for the Ising model in random transverse field. The results obtained are hopped to be useful for an interpretation of observable data for one-dimensional spin-1/2 XY substances.

cond-mat.stat-mech↗