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.

Periodic Airy process and equilibrium dynamics of edge fermions in a trap

“…Let us note that the matrix elements in (36) are the N fermion quantum propagator and can be written as determinants of the quantum propagator of the single particle problem…”

“…It is natural to ask how these systems of fermions at equilibrium evolve in imaginary time τ (which can be seen as the analytic continuation of the real time equilibrium quantum dynamics of the fermions τ = it). Similar questions have been studied in the condensed matter literature [33][34][35][36][37][38] but mostly in the bulk of the Fermi gas, or in the absence of a confining potential. Our main focus here is on the dynamics at the edge, for which it is useful to exploit connections to random matrices [39] and determinantal processes [40].…”

Dynamic structure factor in impurity-doped spin chains

“…The relative change from doping near the dispersion |vq| → ω is infinitely large, so that the first order impurity contribution diverges near the dispersion |vq| → ω with a stronger powerlaw than the bulk and a 1/L expansion from the thermodynamic limit always breaks down. Previous studies also found that the divergence in the thermodynamic limit is not universal, but instead strongly dependent on either the cut-off procedure [48,49] or higher order terms and non-linear effects [10][11][12][13][14][15][16][17][18]. Naively, it could have been expected that bosonization works particularly well in the thermodynamic limit, but instead it turns out that the finite-size theory is much better controlled and quantitatively accurate even for |vq| → ω as shown in Fig.…”

“…Spin chains have been the center of attention as prototypical quantum many body systems ever since the early days of quantum mechanics [1] and up to this day significant advances are made, e.g. in describing exact form factors [2][3][4][5][6], exact correlations [7], nonequilibrium states [8,9], and dynamic correlations in the regime of a non-linear spectrum [10][11][12][13][14][15][16][17][18]. Recently, there has been renewed experimental interest in intentionally doped spin chain systems [19,20] with new results on the Knight shift [21,22], magnetic ordering [23], and the dynamic structure factor [24][25][26][27].…”

Nonreciprocal quantum transport at junctions of structured leads

“…Interestingly, we show that the Born weak-coupling master equation is in excellent agreement with matrix product state (MPS) simulations. The Born equation is determined by the first order correlations of the leads, which decay as power-laws in XXZ spin chains [40,41]. Since such slow decay is a rather generic feature of manybody systems [42], the effects reported here could be observed in a number of different architectures such as optical lattices [1], cold atoms [2,3], trapped ions [4,5], and superconducting leads coupled to quantum dots [6,7,43].…”