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Quantum quenches and competing orders: II. quantum non-linear sigma model

Ling-Yan Hung, Wenbo Fu, Subir Sachdev A

Published Feb 4, 2014• 0 citations
OpenAlex

Abstract

We study the non-equilibrium dynamics of a quantum generalization of a O(6) non-linear sigma model of competing orders in the underdoped cuprates (Hayward {\em et al.}, arXiv:1309.6639). We obtain results, in the large $N$ limit of a O($N$) model, on the time-dependence of correlation functions following a pulse disturbance. We find that the oscillatory responses share various qualitative features with recent optical experiments.

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We study the non-equilibrium dynamics of a quantum generalization of a O(6) non-linear sigma model of competing orders in the underdoped cuprates (Hayward {\em et al.}, arXiv:1309.6639). We obtain results, in the large NNN limit of a O(NNN) model, on the time-dependence of correlation functions following a pulse disturbance. We find that the oscillatory responses share various qualitative features with recent optical experiments.
We study the nonequilibrium dynamics of an electronic model of competition between an unconventional charge density wave (a bond density wave) and ddd-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, $(\mathbit{k},\ensuremath{-}\mathbit{k})$, in the Brillouin zone. We also study the nonequilibrium dynamics of a quantum generalization of a O(6) nonlinear $\ensuremath{\sigma}$ model of competing orders in the underdoped cuprates [Hayward et al., Science 343, 1336 (2014)]. We obtain results, in the large NNN limit of a O(N)O(N)O(N) model, on the time dependence of correlation functions following a pulse disturbance. We compare our numerical studies with recent picosecond optical experiments. We find that, generically, the oscillatory responses in our models share various qualitative features with the experiments.
Abstract. We use the semi-classical approach to study the non-equilibrium dynamics of the O(3) non-linear sigma model. For a class of quenches defined in the text, we obtain the order-parameter dynamical correlator in the thermodynamic limit. In particular we predict quench-dependent relaxation times and correlation lengths. The approach developed for the O(3) non-linear sigma model can also be applied to the transverse field Ising chain, where the semi-classical results can be directly compared to both the exact and the numerical ones, revealing the limits of the method. ar X iv
We use the semi-classical approach to study the non-equilibrium dynamics of the O(3) non-linear sigma model. For a class of quenches defined in the text, we obtain the order-parameter dynamical correlator in the thermodynamic limit. In particular we predict quench-dependent relaxation times and correlation lengths. The approach developed for the O(3) non-linear sigma model can also be applied to the transverse field Ising chain, where the semi-classical results can be directly compared to both the exact and the numerical ones, revealing the limits of the method.
We study the non-equlibrium dynamics of an electronic model of competing bond density wave order and ddd-wave superconductivity. In a time-dependent Hartree-Fock+BCS approximation, the dynamics reduces to the equations of motion of operators realizing the generators of SU(4) at each pair of momenta, (k,−k)(\boldsymbol{k}, -\boldsymbol{k})(k,−k), in the Brillouin zone. We compare the results of numerical studies of our model with recent picosecond optical experiments.
Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups, it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties that are usually relevant in solid-state many-body systems. In this paper, we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result, we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states, we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. The comparison reveals which aspects of non-equilibrium dynamics can, as in equilibrium, be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.