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We study the dynamical response of a system to a sudden change of the tuning parameter $lambda$ starting (or ending) at the quantum critical point. In particular we analyze the scaling of the excitation probability, number of excited quasiparticles, heat and entropy with the quench amplitude and the system size. We extend the analysis to quenches with arbitrary power law dependence on time of the tuning parameter, showing a close connection between the scaling behavior of these quantities with the singularities of the adiabatic susceptibilities of order $m$ at the quantum critical point, where $m$ is related to the power of the quench. Precisely for sudden quenches the relevant susceptibility of the second order coincides with the fidelity susceptibility. We discuss the generalization of the scaling laws to the finite temperature quenches and show that the statistics of the low-energy excitations becomes important. We illustrate the relevance of those results for cold atoms experiments.
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We discuss the quench dynamics near a quantum critical point focusing on the sine-Gordon model as a primary example. We suggest a unified approach to sudden and slow quenches, where the tuning parameter $lambda(t)$ changes in time as $lambda(t)sim upsilon t^r$, based on the adiabatic expansion of the excitation probability in powers of $upsilon$. We show that the universal scaling of the excitation probability can be understood through the singularity of the generalized adiabatic susceptibility $chi_{2r+2}(lambda)$, which for sudden quenches ($r=0$) reduces to the fidelity susceptibility. In turn this class of susceptibilities is expressed through the moments of the connected correlation function of the quench operator. We analyze the excitations created after a sudden quench of the cosine potential using a combined approach of form-factors expansion and conformal perturbation theory for the low-energy and high-energy sector respectively. We find the general scaling laws for the probability of exciting the system, the density of excited quasiparticles, the entropy and the heat generated after the quench. In the two limits where the sine-Gordon model maps to hard core bosons and free massive fermions we provide the exact solutions for the quench dynamics and discuss the finite temperature generalizations.
Landau theory is used to investigate the behaviour of a metallic magnet driven towards a quantum critical point by the application of pressure. The observed dependence of the transition temperature with pressure is used to show that the coupling of the magnetic order to the lattice diverges as the quantum critical point is approached. This means that a first order transition will occur in magnets (both ferromagnets and antiferromagnets) because of the coupling to the lattice. The Landau equations are solved numerically without further approximations. There are other mechanisms that can cause a first order transition so the significance of this work is that it will enable us to determine the extent to which any particular first order transition is driven by coupling to the lattice or if other causes are responsible.
We show that the change of the fluctuation spectrum near the quantum critical point (QCP) may result in the continuous change of critical exponents with temperature due to the increase in the effective dimensionality upon approach to QCP. The latter reflects the crossover from thermal fluctuations white noise mode to the quantum fluctuations regime. We investigate the critical dynamics of an exemplary system obeying the Bose-Einstein employing the Keldysh-Schwinger approach and develop the renormalization group technique that enables us to obtain analytical expressions for temperature dependencies of critical exponents.
Fluctuation-induced forces occur generically when long-ranged correlations (e.g., in fluids) are confined by external bodies. In classical systems, such correlations require specific conditions, e.g., a medium close to a critical point. On the other hand, long-ranged correlations appear more commonly in certain non-equilibrium systems with conservation laws. Consequently, a variety of non-equilibrium fluctuation phenomena, including fluctuation-induced forces, have been discovered and explored recently. Here, we address a long-standing problem of non-equilibrium critical Casimir forces emerging after a quench to the critical point in a confined fluid with order-parameter-conserving dynamics and non-symmetry-breaking boundary conditions. The interplay of inherent (critical) fluctuations and dynamical non-local effects (due to density conservation) gives rise to striking features, including correlation functions and forces exhibiting oscillatory time-dependences. Complex transient regimes arise, depending on initial conditions and the geometry of the confinement. Our findings pave the way for exploring a wealth of non-equilibrium processes in critical fluids (e.g., fluctuation-mediated self-assembly or aggregation). In certain regimes, our results are applicable to active matter.
The standard phase-ordering process is obtained by quenching a system, like the Ising model, to below the critical point. This is usually done with periodic boundary conditions to insure ergodicity breaking in the low temperature phase. With this arrangement the infinite system is known to remain permanently out of equilibrium, i.e. there exists a well defined asymptotic state which is time-invariant but different from the ordered ferromagnetic state. In this paper we establish the critical nature of this invariant state, by demonstrating numerically that the quench dynamics with periodic and antiperiodic boundary conditions are indistinguishable one from the other. However while the asymptotic state does not coincide with the equilibrium state for the periodic case, it coincides instead with the equilibrium state of the antiperiodic case, which in fact is critical. The specific example of the Ising model is shown to be one instance of a more general phenomenon, since an analogous picture emerges in the spherical model, where boundary conditions are kept fixed to periodic, while the breaking or preserving of ergodicity is managed by imposing the spherical constraint either sharply or smoothly.
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