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Register a new userSemiclassical dynamics of domain walls in the one-dimensional Ising ferromagnet in a transverse field
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Added by
Hans-J\\\"urgen Mikeska
Publication date
2004
fields
Physics
and research's language is
English
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We investigate analytically and numerically the dynamics of domain walls in a spin chain with ferromagnetic Ising interaction and subject to an external magnetic field perpendicular to the easy magnetization axis (transverse field Ising model). The analytical results obtained within the continuum approximation and numerical simulations performed for discrete classical model are used to analyze the quantum properties of domain walls using the semiclassical approximation. We show that the domain wall spectrum shows a band structure consisting of 2$S$ non-intersecting zones.
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We study the out-of-equilibrium dynamics of one-dimensional quantum Ising-like systems, arising from sudden quenches of the Hamiltonian parameter $g$ driving quantum transitions between disordered and ordered phases. In particular, we consider quenches to values of $g$ around the critical value $g_c$, and mainly address the question whether, and how, the quantum transition leaves traces in the evolution of the transverse and longitudinal magnetizations during such a deep out-of-equilibrium dynamics. We shed light on the emergence of singularities in the thermodynamic infinite-size limit, likely related to the integrability of the model. Finite systems in periodic and open boundary conditions develop peculiar power-law finite-size scaling laws related to revival phenomena, but apparently unrelated to the quantum transition, because their main features are generally observed in quenches to generic values of $g$. We also investigate the effects of dissipative interactions with an environment, modeled by a Lindblad equation with local decay and pumping dissipation operators within the quadratic fermionic model obtainable by a Jordan-Wigner mapping. Dissipation tends to suppress the main features of the unitary dynamics of closed systems. We finally address the effects of integrability breaking, due to further lattice interactions, such as in anisotropic next-to-nearest neighbor Ising (ANNNI) models. We show that some qualitative features of the post-quench dynamics persist, in particular the different behaviors when quenching to quantum ferromagnetic and paramagnetic phases, and the revival phenomena due to the finite size of the system.
Recent analytical and numerical work on field driven domain wall propagation in nanowires has shown that for large transverse anisotropy and sufficiently large applied fields the Walker profile becomes unstable before the breakdown field, giving way to a slower stationary domain wall. We perform an asymptotic expansion of the Landau Lifshitz Gilbert equation for large transverse magnetic anisotropy and show that the asymptotic dynamics reproduces this behavior. At low applied field the speed increases linearly with the field and the profile is the classic Landau profile. Beyond a critical value of the applied field the domain wall slows down. The appearance of a slower domain wall profile in the asymptotic dynamics is due to a transition from a pushed to a pulled front of a reaction diffusion equation.
We derive an effective low-energy theory for a ferromagnetic $(2N+1)$-leg spin-$frac{1}{2}$ ladder with strong $XXZ$ anisotropy $left|J_{parallel}^zright|ll left|J_{parallel}^{xy}right|$, subject to a kink-like non-uniform magnetic field $B_z(X)$ which induces a domain wall (DW). Using Bosonization of the quantum spin operators, we show that the quantum dynamics is dominated by a single one-dimensional mode, and is described by a sine-Gordon model. The parameters of the effective model are explored as functions of $N$, the easy-plane anisotropy $Delta=-J_{parallel}^z/J_{parallel}^{xy}$, and the strength and profile of the transverse field $B_z(X)$. We find that at sufficiently strong and asymmetric field, this mode may exhibit a quantum phase transition from a Luttinger liquid to a spin-density-wave (SDW) ordered phase. As the effective Luttinger parameter grows with the number of legs in the ladder ($N$), the SDW phase progressively shrinks in size, recovering the gapless dynamics expected in the two-dimensional limit $Nrightarrowinfty$.
The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior in the vicinity of quantum phase transitions (QPTs). It is now well understood for one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by fundamental differences of the associated QPTs and their underlying conformal field theories. In this work, we take the first steps towards exploring the QKZM in two dimensions. We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods. As a central result, we quantify universal QKZM behavior close to the QPT. However, upon traversing further into the ferromagnetic regime, we observe deviations from the QKZM prediction. We explain the observed behavior by proposing an {it extended QKZM} taking into account spectral information as well as phase ordering. Our work provides a starting point towards the exploration of dynamical universality in higher-dimensional quantum matter.
Luttinger liquid theory of one-dimensional quantum systems ignores exponentially weak backscattering of particles. This endows Luttinger liquids with superfluid properties. The corresponding two-fluid hydrodynamic description available at present applies only to Galilean-invariant systems, whereas most experimental realizations of one-dimensional quantum liquids lack Galilean invariance. Here we develop the two-fluid theory of such quantum liquids. In the low-frequency limit the theory reduces to single-fluid hydrodynamics. However, the absence of Galilean invariance brings about three new transport coefficients. We obtain expressions for these coefficients in terms of the backscattering rate.
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