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arXiv:1609.01769 · Physical review. B./Physical review. B

Spinon and bound-state excitation light cones in Heisenberg XXZ chains

A. L. de Paula, Helena Bragança, Rodrigo G. Pereira, Raphael C. Drumond, Maria C. O. Aguiar

Published Jan 17, 2017• 29 citations
arXivHTMLPDF

Abstract

We investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical phase. We analyze the time evolution of the on-site magnetization and bipartite entanglement entropy via adaptive time-dependent density matrix renormalization group. In systems with short-range interactions, such as the one we consider, the velocity of information transfer is expected to be bounded, giving rise to a light-cone effect. Interestingly, our results show that, when the anisotropy parameter of the critical chain is sufficiently close to that of the isotropic ferromagnet, the light cone is determined by the velocity of spin-wave bound states that propagate faster than single-particle (``spinon'') excitations. Furthermore, we investigate how the system approaches equilibrium in the inhomogeneous ground state of the connected system, in which the ferromagnetic chain induces a nonzero magnetization in the critical chain in the vicinity of the interface.

DOI
10.1103/physrevb.95.045125

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We investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical phase. We analyze the time evolution of the on-site magnetization and bipartite entanglement entropy via adaptive time-dependent density matrix renormalization group. In systems with short-range interactions, such as the one we consider, the velocity of information transfer is expected to be bounded, giving rise to a light-cone effect. Interestingly, our results show that, when the anisotropy parameter of the critical chain is sufficiently close to that of the isotropic ferromagnet, the light cone is determined by the velocity of spin-wave bound states that propagate faster than single-particle (``spinon'') excitations. Furthermore, we investigate how the system approaches equilibrium in the inhomogeneous ground state of the connected system, in which the ferromagnetic chain induces a nonzero magnetization in the critical chain in the vicinity of the interface.
The focus of this thesis is to investigate non equilibrium properties of a spin 1/2 chain considered as a closed or an open quantum system. In the first case, the non equilibrium situation is generated by means of a quench (sudden change of the hamiltonian); in the second case, we connect unbalanced magnetic reservoirs at the chain edges. In this thesis, we present two works in the context of closed systems and another one in the case of open systems. To describe the dynamics we use the time-dependent extension of Density MatrixRenormalization Group (DMRG) technique. In the first work, we investigate the non equilibrium dynamics generated by a local quenchin a spin system described by the XXZ Heisenberg model. More specifically, the quench involves connecting two chains, one that is prepared in the ferromagnetic phase and another that is in the paramagnetic phase. After the quench, we observe effective light cones inthe maps of the on-site magnetization and the entanglement entropy as a function of site and time, when these quantities are calculated in the chain that had no magnetic order.We show that these light cones are associated with two kinds of excitation characteristic of the XXZ model, more specifically spinons and bound states. Furthermore, we see that, for long times, the system approaches the equilibrium state of the connected chains. systemwill go to the equilibrium state at infinity time.In the second work, we analyze shielding properties that appear in the transverse Ising model. If the site i=L of the chain has null field and the global state is a Gibbs state, the reduced state of the chain in the right side of the i=L site is shown to have no dependence on the parameters of the left chain. We refer to this effect as a shielding property. Wealso study the chain dynamics after a local quench that changes the magnetic field in the first site. We observe a light cone in the on-site magnetization, however the magnetization pulse is reflected by the site with null field.Finally, in the third work, we connect two magnetic reservoirs at the ends of the XXZ Heisenberg spin chain and calculate the spin and energy currents in the non equilibrium steady state (NESS). We investigate if it is possible to control and manipulate such currents and their respective rectifications by the application of an external magnetic field. Forthat, we introduce a graded asymmetry (gradual change of the parameters) in the field and in the anisotropy parameter of the model. For appropriate choice of the field, we observe that it is possible to force the energy and the spin currents to propagate in opposite directions. This means that we invert not only the currents but also their rectificationsthrough external mechanisms.
Signal propagation in the nonequilibrium evolution after quantum quenches has recently attracted much experimental and theoretical interest. A key question arising in this context is what principles, and which of the properties of the quench, determine the characteristic propagation velocity. Here we investigate such issues for a class of quench protocols in one of the central paradigms of interacting many-particle quantum systems, the spin-1/2 Heisenberg XXZ chain. We consider quenches from a variety of initial thermal density matrices to the same final Hamiltonian using matrix product state methods. The spreading velocities are observed to vary substantially with the initial density matrix. However, we achieve a striking data collapse when the spreading velocity is considered to be a function of the excess energy. Using the fact that the XXZ chain is integrable, we present an explanation of the observed velocities in terms of "excitations" in an appropriately defined generalized Gibbs ensemble.
Abstract. We study the out-of-equilibrium time evolution after a local quench connecting two anisotropic spin-1/2 XXZ Heisenberg open chains via an impurity bond. The dynamics is obtained by means of the adaptive time-dependent density-matrix renormalization group. We show that the entanglement entropies (Von Neumann and Rényi), in the presence of a weakened bond depend on the sign of the bulk interaction. For attractive interaction ( ∆ < 0), the defect turns out to be irrelevant and the evolution is asymptotically equivalent to the one without defect obtained by conformal field theory. For repulsive interaction ( ∆> 0), the defect is relevant and the entanglement saturates to a finite value. This out-of-equilibrium behavior generalizes the well known results for the ground-state entanglement entropy of the model. 1.
The excitations of the Heisenberg antiferromagnetic spin chain in zero field are known as spinons. As pairwise-created fractionalized excitations, spinons are important in the understanding of inelastic neutron scattering experiments in (quasi-)one-dimensional materials. In the present paper, we consider the real space-time dynamics of spinons originating from a local spin flip on the antiferromagnetic ground state of the (an)isotropic Heisenberg spin-1/2 model and the Babujan-Takhtajan spin-1 model. By utilizing algebraic Bethe ansatz methods at finite system size to compute the expectation value of the local magnetization and spin-spin correlations, spinons are visualized as propagating domain walls in the antiferromagnetic spin ordering with anisotropy dependent behavior. The spin-spin correlation after the spin flip displays a light cone, satisfying the Lieb-Robinson bound for the propagation of correlations at the spinon velocity.
We propose and explore the physics of a toy multiferroic model by coupling two distinct dipolar XXZ models in transverse fields. We determine first the rich ground-state phase diagram of the model using density matrix renormalization group techniques. Then, we explore the dynamics of the system after global and local quenches, using the time-evolving block decimation algorithm. After a global quench, the system displays decaying coupled oscillations of the electric and magnetic spins, in agreement with the Eigenstate Thermalization Hypothesis (ETH) for many-body interacting quantum systems. Notably, the spin-spin interactions lead to a sizeable quadratic shift in the oscillation frequency as the inter-chain coupling is increased. Local quenches lead to a light-cone-like propagation of excitations. In this case, the inter-chain coupling drives a transfer of energy between the chains that generates a novel fast spin-wave mode along the 'magnetic' chain at the speed of the 'electric' spin-wave. This suggests a limited control mechanism for faster information transfer in magnetic spin chains using electric fields that harnesses the electric dipoles as intermediaries.
We study a quantum quench in which a magnetic impurity is suddenly coupled to Hubbard chains, whose low-energy physics is described by Tomonaga-Luttinger liquid theory. Using the time-dependent density-matrix renormalization-group (tDMRG) technique, we analyze the propagation of charge, spin, and entanglement in the chains after the quench and relate the light-cone velocities to the dispersion of holons and spinons. We find that the local magnetization at the impurity site decays faster if we increase the interaction in the chains, even though the spin velocity decreases. We derive an analytical expression for the relaxation of the impurity magnetization which is in good agreement with the tDMRG results at intermediate timescales, providing valuable insight into the time evolution of the Kondo screening cloud in interacting systems.