The dynamics of a particle influenced by strongly coupled quantum critical theories is studied by the holographic approach. Based upon the bottom-up approach a real-time prescription for the AdS/CFT correspondence in the context of nonequilibrium physics is developed in accordance with the field theoretic requirements, by which the associated holographic influence functional is obtained. We then study the decoherence dynamics of a particle induced by the quantum critical theories with a dynamical exponent
z. We find that as
z increases, the decoherence effect becomes less significant. Similar behavior is found as we heat up the environment. However, in this case the decoherence effect is enhanced not only by its strong coupling constant but also from the finite temperature effect. Finally a comparison is made with the result of a particle influenced by the free field.
Phase transitions occur when a macroscopic number of local degrees of freedom coherently change their behavior. In ground states of quantum many-body systems, phase transitions due to quantum fluctuations are observed as non-analytic behaviors of order parameters, such as magnetization, as functions of a conjugate parameter, such as the magnetic field. However, as soon as thermal fluctuations are present, these effects are believed to disappear for local observables. We show that this is not necessarily the case: order parameters may still show non-analytic behaviors within their dynamics. With the example of the Ising model and using methods based on hydrodynamic fluctuations, we evaluate the exact order-parameter correlation time, in space-time directions of all velocities, in equilibrium states at nonzero temperature. We reveal non-analytic behaviors of spin correlation times as functions of the magnetic field, velocity, and temperature. As a function of the magnetic field, they occur at values that continuously approach that of the zero-temperature equilibrium transition point as the velocity is decreased and reach it within the light cone, where we obtain a new, temperature-independent logarithmic divergence characterizing the collective dynamics. Thus, collective effects induced by quantum fluctuations persist within the dynamics of local observables.
We study high-frequency response functions, notably the optical conductivity, in the vicinity of quantum critical points (QCPs) by allowing for both detuning from the critical coupling and finite temperature. We consider general dimensions and dynamical exponents. This leads to a unified understanding of sum rules. In systems with emergent Lorentz invariance, powerful methods from quantum field theory allow us to fix the high-frequency response in terms of universal coefficients. We test our predictions analytically in the large-N O(N) model and using the gauge-gravity duality and numerically via quantum Monte Carlo simulations on a lattice model hosting the interacting superfluid-insulator QCP. In superfluid phases, interacting Goldstone bosons qualitatively change the high-frequency optical conductivity and the corresponding sum rule.
We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schrödinger model. We derive the long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle–hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on a microscopic analysis of the model, without invoking, at any stage, any correspondence with a continuous field theory. Furthermore, our approach only makes use of certain general properties of the model, so that it should be applicable, possibly with minor modifications, to a wide class of (not necessarily integrable) gapless one-dimensional Hamiltonians.
We develop a holographic model for thermalization following a quench near a quantum critical point with nontrivial dynamical critical exponent. The anti-de Sitter Vaidya null collapse geometry is generalized to asymptotically Lifshitz spacetime. Nonlocal observables such as two-point functions and entanglement entropy in this background then provide information about the length and time scales relevant to thermalization. The propagation of thermalization exhibits similar ``horizon'' behavior as has been seen previously in the conformal case and we give a heuristic argument for why it also appears here. Finally, analytic upper bounds are obtained for the thermalization rates of the nonlocal observables.
We present an argument to support the existence of dissipative modes in relativistic field theories. For an |
O(N)||
φ4| theory in spatial dimension |
1≤d≤3|, the two-point function of |
φ| is shown to develop a pole of the form |
p0∼iΓ−1(p2+m2)| at small energy |
p0| and momentum |
p|, with a nonzero finite coefficient or relaxation constant, |
Γ|, when evaluated in the two-particle irreducible (2PI) framework at the next-leading order (NLO) of |
1/N| expansion. In contrast, an NLO calculation in the one-particle irreducible (1PI) framework fails to give a nonzero |
Γ|. The dissipative mode emerges from multiple scattering of a particle with other particles, which is appropriately treated in the 2PI–NLO calculation through the resummation of secular terms to improve the long-time behavior of the two-point function. Assuming that this slow dissipative mode survives at the critical point, one can identify the dynamic critical exponent |
z| for the two-point function as |
z=2−η|. We also discuss possible improvement of the result.