Linear quantum quench in the Heisenberg XXZ chain: time dependent Luttinger model description of a lattice system

Abstract

We study variable-rate linear quenches in the anisotropic Heisenberg (XXZ) chain, starting at the XX point. This is equivalent to switching on a nearest neighbour interaction for hard-core bosons or an interaction quench for free fermions. The physical observables we investigate are: the energy pumped into the system during the quench, the spin-flip correlation function, and the bipartite fluctuations of the z component of the spin in a box. We find excellent agreement between exact numerics (infinite system time-evolving block decimation, iTEBD) and analytical results from bosonization, as a function of the quench time, spatial coordinate and interaction strength. This provides a stringent and much-needed test of Luttinger liquid theory in a non-equilibrium situation.

6 pages, 3 figures, minor changes, new references

References in corpus (15)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• The Luttinger model following a sudden interaction switch-on
• Scaling of entanglement support for Matrix Product States
• Quantum quench dynamics of the Luttinger model
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Many-body Landau-Zener dynamics in coupled 1D Bose liquids
• Universal properties of hard-core bosons confined on one-dimensional lattices
• Luttinger liquid universality in the time evolution after an interaction quench
• Crossover from adiabatic to sudden interaction quench in a Luttinger liquid
• Adiabatic quenches through an extended quantum critical region
• Slow quench dynamics of a trapped one-dimensional Bose gas confined to an optical lattice
• Quench dynamics of the Tomonaga-Luttinger model with momentum dependent interaction

Cited by in corpus (11)

• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Time evolution during and after finite-time quantum quenches in the transverse-field Ising chain
• Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach
• Marginal quenches and drives in Tomonaga-Luttinger liquids
• Escort distribution function of work done and diagonal entropies in quenched Luttinger liquids
• Orthogonality catastrophe beyond bosonization from post-selection
• Operator correlations in a quenched non-Hermitian Luttinger liquid
• Optimal protocols for finite-duration quantum quenches in the Luttinger model
• Exact Dynamics and Shortcuts to Adiabaticity in the Tomonaga-Luttinger Liquid
• Transitionless Quantum Driving of the Tomonaga-Luttinger Liquid
• Electrostatic solution of massless quenches in Luttinger liquids