79 research outputs found
Thermal transport of the XXZ chain in a magnetic field
We study the heat conduction of the spin-1/2 XXZ chain in finite magnetic
fields where magnetothermal effects arise. Due to the integrability of this
model, all transport coefficients diverge, signaled by finite Drude weights.
Using exact diagonalization and mean-field theory, we analyze the temperature
and field dependence of the thermal Drude weight for various exchange
anisotropies under the condition of zero magnetization-current flow. First, we
find a strong magnetic field dependence of the Drude weight, including a
suppression of its magnitude with increasing field strength and a non-monotonic
field-dependence of the peak position. Second, for small exchange anisotropies
and magnetic fields in the massless as well as in the fully polarized regime
the mean-field approach is in excellent agreement with the exact
diagonalization data. Third, at the field-induced quantum critical line between
the para- and ferromagnetic region we propose a universal low-temperature
behavior of the thermal Drude weight.Comment: 9 pages REVTeX4 including 5 figures, revised version, refs. added,
typos correcte
The anisotropic XY model on the inhomogeneous periodic chain
The static and dynamic properties of the anisotropic XY-model on
the inhomogeneous periodic chain, composed of cells with different
exchange interactions and magnetic moments, in a transverse field are
determined exactly at arbitrary temperatures. The properties are obtained by
introducing the Jordan-Wigner fermionization and by reducing the problem to a
diagonalization of a finite matrix of order. The quantum transitions are
determined exactly by analyzing, as a function of the field, the induced
magnetization 1/n\sum_{m=1}^{n}\mu_{m}\left ( denotes
the cell, the site within the cell, the magnetic moment at site
within the cell) and the spontaneous magnetization which is obtained from the correlations for large spin separations. These results,
which are obtained for infinite chains, correspond to an extension of the ones
obtained by Tong and Zhong(\textit{Physica B} \textbf{304,}91 (2001)). The
dynamic correlations, , and the dynamic
susceptibility, are also obtained at arbitrary
temperatures. Explicit results are presented in the limit T=0, where the
critical behaviour occurs, for the static susceptibility as
a function of the transverse field , and for the frequency dependency of
dynamic susceptibility .Comment: 33 pages, 13 figures, 01 table. Revised version (minor corrections)
accepted for publiction in Phys. Rev.
Dynamical structure factor of the anisotropic Heisenberg chain in a transverse field
We consider the anisotropic Heisenberg spin-1/2 chain in a transverse
magnetic field at zero temperature. We first determine all components of the
dynamical structure factor by combining exact results with a mean-field
approximation recently proposed by Dmitriev {\it et al}., JETP 95, 538 (2002).
We then turn to the small anisotropy limit, in which we use field theory
methods to obtain exact results. We discuss the relevance of our results to
Neutron scattering experiments on the 1D Heisenberg chain compound .Comment: 13 pages, 14 figure
Thermal conductivity of anisotropic and frustrated spin-1/2 chains
We analyze the thermal conductivity of anisotropic and frustrated spin-1/2
chains using analytical and numerical techniques. This includes mean-field
theory based on the Jordan-Wigner transformation, bosonization, and exact
diagonalization of systems with N<=18 sites. We present results for the
temperature dependence of the zero-frequency weight of the conductivity for
several values of the anisotropy \Delta. In the gapless regime, we show that
the mean-field theory compares well to known results and that the
low-temperature limit is correctly described by bosonization. In the
antiferromagnetic and ferromagnetic gapped regime, we analyze the temperature
dependence of the thermal conductivity numerically. The convergence of the
finite-size data is remarkably good in the ferromagnetic case. Finally, we
apply our numerical method and mean-field theory to the frustrated chain where
we find a good agreement of these two approaches on finite systems. Our
numerical data do not yield evidence for a diverging thermal conductivity in
the thermodynamic limit in case of the antiferromagnetic gapped regime of the
frustrated chain.Comment: 4 pages REVTeX4 including 6 figures; published version, main
modification: added emphasis that the data of our Fig. 3 point to a vanishing
of the thermal Drude weight in the thermodynamic limit in this cas
On general relation between quantum ergodicity and fidelity of quantum dynamics
General relation is derived which expresses the fidelity of quantum dynamics,
measuring the stability of time evolution to small static variation in the
hamiltonian, in terms of ergodicity of an observable generating the
perturbation as defined by its time correlation function. Fidelity for ergodic
dynamics is predicted to decay exponentially on time-scale proportional to
delta^(-2) where delta is the strength of perturbation, whereas faster,
typically gaussian decay on shorter time scale proportional to delta^(-1) is
predicted for integrable, or generally non-ergodic dynamics. This surprising
result is demonstrated in quantum Ising spin-1/2 chain periodically kicked with
a tilted magnetic field where we find finite parameter-space regions of
non-ergodic and non-integrable motion in thermodynamic limit.Comment: Slightly revised version, 4.5 RevTeX pages, 2 figure
Exact two-spinon dynamical correlation function of the Heisenberg model
We derive the exact contribution of two spinons to the dynamical correlation
function of the spin-1/2 Heisenberg model. For this, we use the isotropic
limits of the exact form factors that have been recently computed through the
quantum affine symmetry of the anisotropic Heisenberg model Comment: 9 pages, Latex, 2 corrections of coefficient
The Oscillatory Behavior of the High-Temperature Expansion of Dyson's Hierarchical Model: A Renormalization Group Analysis
We calculate 800 coefficients of the high-temperature expansion of the
magnetic susceptibility of Dyson's hierarchical model with a Landau-Ginzburg
measure. Log-periodic corrections to the scaling laws appear as in the case of
a Ising measure. The period of oscillation appears to be a universal quantity
given in good approximation by the logarithm of the largest eigenvalue of the
linearized RG transformation, in agreement with a possibility suggested by K.
Wilson and developed by Niemeijer and van Leeuwen. We estimate to be
1.300 (with a systematic error of the order of 0.002) in good agreement with
the results obtained with other methods such as the -expansion. We
briefly discuss the relationship between the oscillations and the zeros of the
partition function near the critical point in the complex temperature plane.Comment: 21 pages, 10 Postcript figures, latex file, uses revte
Critical behavior of interfaces in disordered Potts ferromagnets : statistics of free-energy, energy and interfacial adsorption
A convenient way to study phase transitions of finite spins systems of linear
size is to fix boundary conditions that impose the presence of a
system-size interface. In this paper, we study the statistical properties of
such an interface in a disordered Potts ferromagnet in dimension within
Migdal-Kadanoff real space renormalization. We first focus on the interface
free-energy and energy to measure the singularities of the average and random
contributions, as well as the corresponding histograms, both in the
low-temperature phase and at criticality. We then consider the critical
behavior of the interfacial adsorption of non-boundary states. Our main
conclusion is that all singularities involve the correlation length
appearing in the average free-energy of the interface of dimension , except for
the free-energy width that involves
the droplet exponent and another correlation length
which diverges more rapidly than . We compare with the spin-glass
transition in , where is the 'true' correlation length, and
where the interface energy presents unconventional scaling with a chaos
critical exponent [Nifle and Hilhorst, Phys. Rev. Lett. 68,
2992 (1992)]. The common feature is that in both cases, the characteristic
length scale associated with the chaotic nature of the
low-temperature phase, diverges more slowly than the correlation length.Comment: v2 : thoroughly rewritten paper with new title, new data and new
interpretations (18 pages, 22 figures
Ordering of dipolar Ising crystals
We study Ising systems of spins with dipolar interactions. We find a simple
approximate relation for the interaction energy between pairs of parallel
lattice columns of spins running along the Ising spin direction. This relation
provides insight into the relation between lattice geometry and the nature of
the ordered state. It can be used to calculate ground state energies. We have
also obtained ground state energies and ordering temperatures T_0 from Monte
Carlo simulations. Simple empirical relations, that give T_0 for simple and
body centered tetragonal lattices in terms of lattice parameters are also
established. Finally, the nature of the ordered state and T_0 are determined
for Fe_8 clusters, which crystallize on a triclinic lattice.Comment: 13 pages, 4 eps figures, to be published in PRB. For related work,
see http://pipe.unizar.es/~jf
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