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arXiv:1710.07811 · Physical review. B./Physical review. B

Finite-temperature dynamical correlations for the dimerized spin- 12 chain

Emanuele Coira, Peter Barmettler, Thierry Giamarchi, Corinna Kollath

Published Sep 28, 2018• 9 citations
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Abstract

We use the density matrix renormalization group method to compute the frequency and momentum-resolved spin-spin correlation functions of a dimerized spin-1/2 chain under a magnetic field at finite temperature. The spectral features strongly depend on the regime of the magnetic field. For increasing magnetic fields, the transitions from a gapped spin liquid phase to a Tomonaga-Luttinger liquid, and then to a totally polarized phase, can be identified in the spectra. Compared to the zero-temperature case, the finite-temperature excitations give rise to additional spectral features that we compute numerically and identify analytically as transitions from thermally excited states. We compute quantitatively the broadening of the dispersion of a single spin-flip excitation due to the temperature and find a strong asymmetric broadening. We discuss the consequences of these findings for neutron experiments on dimerized one-dimensional quantum chains.

DOI
10.1103/physrevb.98.104435

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We study the correlation functions of quantum spin-1/21/21/2 two-leg ladders at finite temperature, under a magnetic field, in the gapless phase at various relevant temperatures $T\ensuremath{\ne}0$, momenta qqq, and frequencies $\ensuremath{\omega}$. We compute those quantities using the time-dependent density-matrix renormalization group (T-DMRG) in an optimal numerical scheme. We compare these correlations with the ones of dimerized quantum spin chains and simple spin chains, that we compute by a similar technique. We analyze the intermediate energy modes and show that the effect of temperature leads to the formation of an essentially dispersive mode corresponding to the propagation of a triplet mode in an incoherent background, with a dispersion quite different from the one occurring at very low temperatures. We compare the low-energy part of the spectrum with the predictions of the Tomonaga-Luttinger liquid field theory at finite temperature. We show that the field theory describes in a remarkably robust way the low-energy correlations for frequencies or temperatures up to the natural cutoff (the effective dispersion) of the system. We discuss how our results could be tested in, e.g., neutron-scattering experiments.
We study the dynamical response of the half-filled one-dimensional Hubbard model for a range of interaction strengths UUU and temperatures TTT by a combination of numerical and analytical techniques. Using time-dependent density matrix renormalization group computations we find that the single-particle spectral function undergoes a crossover to a spin-incoherent Luttinger liquid regime at temperatures $T\ensuremath{\sim}J=4{t}^{2}/U$ for sufficiently large U>4tU>4tU>4t. At smaller values of UUU and elevated temperatures the spectral function is found to exhibit two thermally broadened bands of excitations, reminiscent of what is found in the Hubbard-I approximation. The dynamical density-density response function is shown to exhibit a finite-temperature resonance at low frequencies inside the Mott gap, with a physical origin similar to the Villain mode in gapped quantum spin chains. We complement our numerical computations by developing an analytic strong-coupling approach to the low-temperature dynamics in the spin-incoherent regime.
Inelastic neutron-scattering and finite-temperature density matrix renormalization group (DMRG) calculations are used to investigate the spin excitation spectrum of the S=1/2S=1/2S=1/2 Heisenberg spin chain compound K2CuSO4Cl2{\mathrm{K}}_{2}{\mathrm{CuSO}}_{4}{\mathrm{Cl}}_{2}K2​CuSO4​Cl2​ at several temperatures in a magnetic field near saturation. Critical correlations characteristic of the predicted z=2,d=1z=2,\phantom{\rule{0.16em}{0ex}}d=1z=2,d=1 quantum phase transition occurring at saturation are shown to be consistent with the observed neutron spectra. The data is well described with a scaling function computed using a free fermion description of the spins, valid close to saturation, and the corresponding scaling limits. One of the most prominent nonuniversal spectral features of the data is a novel thermally activated longitudinal mode that remains underdamped across most of the Brillouin zone.
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The physics of the strongly interacting Hubbard chain (with $t/U\ensuremath{\ll}1$) at finite temperatures undergoes a crossover to a spin-incoherent regime when the temperature is very small relative to the Fermi energy, but larger than the characteristic spin energy scale. This crossover can be understood by means of Ogata and Shiba's factorized wave function, where charge and spin are totally decoupled, and assuming that the charge remains in the ground state, while the spin is thermally excited and at an effective ``spin temperature.'' We use the time-dependent density matrix renormalization group method to calculate the dynamical contributions of the spin, to reconstruct the single-particle spectral function of the electrons. The crossover is characterized by a redistribution of spectral weight both in frequency and momentum, with an apparent shift by kF{k}_{F}kF​ of the minimum of the dispersion.