We examine dynamic structure factors of spin- $1∕2$ chains with nearest-neighbor interactions of $XX$ and Dzyaloshinskii-Moriya type and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can be eliminated from the Hamiltonian by suitable transformation of the spin variables. As a result, the dynamic structure factors of periodic or random chains can be computed from those of the uniform chains. Using the exact analytical and precise numerical results available for the uniform systems, we illustrate the effects of regular alternation or random disorder on dynamic structure factors of quantum spin chains.We examine dynamic structure factors of spin-$1∕2$ chains with nearest-neighbor interactions of $XX$ and Dzyaloshinskii-Moriya type and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can be eliminated from the Hamiltonian by suitable transformation of the spin variables. As a result, the dynamic structure factors of periodic or random chains can be computed from those of the uniform chains. Using the exact analytical and precise numerical results available for the uniform systems, we illustrate the effects of regular alternation or random disorder on dynamic structure factors of quantum spin chains.

arXiv:0802.0389Physical Review BOct 15, 200715 citations

Quantum Spin Chains: Phase Behaviour and Dynamic Excitations

Jill C. Bonner, John B. Parkinson

Springer series in solid-state sciencesJan 1, 19840 citations

Dynamical Entropy

Robert Alicki, M. Fannes

A non-zero Kolmogrov–Sinai entropy for a classical dynamical system is a signature of dynamical instability. This chapter presents an approach to quantifying randomizing dynamical behaviour in deterministic quantum systems based on a spin chain model. The starting point is an operational partition that is refined in the course of time. To each partition corresponds a correlation matrix and the dynamics lead eventually to a shift-invariant state on a quantum spin chain with its associated entropy. General properties and bounds are proved, which allow for the computation of the entropy in a number of simple model systems such as finite systems, shift dynamics on a quantum spin chain, free shifts, and Powers–Price shifts.A non-zero Kolmogrov–Sinai entropy for a classical dynamical system is a signature of dynamical instability. This chapter presents an approach to quantifying randomizing dynamical behaviour in deterministic quantum systems based on a spin chain model. The starting point is an operational partition that is refined in the course of time. To each partition corresponds a correlation matrix and the dynamics lead eventually to a shift-invariant state on a quantum spin chain with its associated entropy. General properties and bounds are proved, which allow for the computation of the entropy in a number of simple model systems such as finite systems, shift dynamics on a quantum spin chain, free shifts, and Powers–Price shifts.

Oxford University Press eBooksJul 12, 20010 citations

Quantum Spin Chains

Jill C. Bonner, Henk W. J. Blöte, Hans Beck +1 more

Springer series in solid-state sciencesJan 1, 198146 citations

Quench dynamics and relaxation in isolated integrable quantum spin chains

Fabian H. L. Eßler, Maurizio Fagotti

Abstract We review the dynamics after quantum quenches in integrable quantum spin chains. We give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the description of the steady state by (generalized) Gibbs ensembles. We then turn to general features in the time evolution of local observables after the quench, using a simple model of free fermions as an example. In the second part we present an overview of recent progress in describing quench dynamics in two key paradigms for quantum integrable models, the transverse field Ising chain and the anisotropic spin-1/2 Heisenberg chain.Abstract We review the dynamics after quantum quenches in integrable quantum spin chains. We give a pedagogical introduction to relaxation in isolated quantum systems, and discuss the description of the steady state by (generalized) Gibbs ensembles. We then turn to general features in the time evolution of local observables after the quench, using a simple model of free fermions as an example. In the second part we present an overview of recent progress in describing quench dynamics in two key paradigms for quantum integrable models, the transverse field Ising chain and the anisotropic spin-1/2 Heisenberg chain.

arXiv:1603.06452Journal of Statistical Mechanics Theory and ExperimentJun 1, 2016753 citations

We examine dynamic structure factors of spin-

1∕2

chains with nearest-neighbor interactions of

XX

and Dzyaloshinskii-Moriya type and with periodic and random changes in the sign of these interactions. This special kind of inhomogeneity can be eliminated from the Hamiltonian by suitable transformation of the spin variables. As a result, the dynamic structure factors of periodic or random chains can be computed from those of the uniform chains. Using the exact analytical and precise numerical results available for the uniform systems, we illustrate the effects of regular alternation or random disorder on dynamic structure factors of quantum spin chains.