Boundary versus bulk behavior of time-dependent correlation functions in one-dimensional quantum systems

Abstract

We study the influence of reflective boundaries on time-dependent responses of one-dimensional quantum fluids at zero temperature beyond the low-energy approximation. Our analysis is based on an extension of effective mobile impurity models for nonlinear Luttinger liquids to the case of open boundary conditions. For integrable models, we show that boundary autocorrelations oscillate as a function of time with the same frequency as the corresponding bulk autocorrelations. This frequency can be identified as the band edge of elementary excitations. The amplitude of the oscillations decays as a power law with distinct exponents at the boundary and in the bulk, but boundary and bulk exponents are determined by the same coupling constant in the mobile impurity model. For nonintegrable models, we argue that the power-law decay of the oscillations is generic for autocorrelations in the bulk, but turns into an exponential decay at the boundary. Moreover, there is in general a nonuniversal shift of the boundary frequency in comparison with the band edge of bulk excitations. The predictions of our effective field theory are compared with numerical results obtained by time-dependent density matrix renormalization group (tDMRG) for both integrable and nonintegrable critical spin-$S$ chains with $S=1/2$, $1$ and $3/2$.

20 pages, 12 figures

References in corpus (27)

• The density-matrix renormalization group in the age of matrix product states
• Real time evolution using the density matrix renormalization group
• Emergence of coherence in a uniform quasi-two-dimensional Bose gas
• Universal theory of nonlinear Luttinger liquids
• Time-step targetting methods for real-time dynamics using DMRG
• Dynamic response of one-dimensional interacting fermions
• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Spectral function of spinless fermions on a one-dimensional lattice
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Coulomb drag by small momentum transfer between quantum wires
• Functional renormalization group for Luttinger liquids with impurities
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas
• Spin-charge separation in one-dimensional fermion systems beyond the Luttinger liquid theory
• Threshold singularities in the dynamic response of gapless integrable models
• Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid
• Relaxation in Luttinger liquids: Bose-Fermi duality
• Real-time dynamics in the one-dimensional Hubbard model
• Local Density of States for Individual Energy Levels in Finite Quantum Wires
• Spin-charge separated quasiparticles in one dimensional quantum fluids
• Low-energy local density of states of the 1D Hubbard model
• The Fine Structure of the Phonon in One Dimension from Quantum Hydrodynamics

Cited by in corpus (6)

• Spinon and bound state excitation "light cones" in Heisenberg XXZ Chains
• Periodic Airy process and equilibrium dynamics of edge fermions in a trap
• Nonreciprocal Quantum Transport at Junctions of Structured Leads
• Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state
• The dynamic structure factor in impurity-doped spin chains
• Exact real time dynamics with free fermions in disguise