Understanding phase transitions in quantum matters constitutes a significant part of present day condensed matter physics. Quantum phase transitions concern ground state properties of many-body systems, and hence their signatures are expected to be pronounced in low-energy states. Here we report signature of a quantum critical point manifested in strongly out-of-equilibrium states with finite energy density with respect to the ground state and extensive (subsystem) entanglement entropy, generated by an external pulse. These non-equilibrium states are evidently completely disordered (e.g., paramagnetic in case of a magnetic ordering transition). The pulse is applied by switching a coupling of the Hamiltonian from an initial value (λI) to a final value (λF) for sufficiently long time and back again. The signature appears as non-analyticities (kinks) in the energy absorbed by the system from the pulse as a function of λF at critical-points (i.e., at values of λF corresponding to static critical-points of the system). As one excites higher and higher eigenstates of the final Hamiltonian H(λF) by increasing the pulse height (|λF - λI|), the non-analyticity grows stronger monotonically with it. This implies adding contributions from higher eigenstates help magnifying the non-analyticity, indicating strong imprint of the critical-point on them. Our findings are grounded on exact analytical results derived for Ising and XY chains in transverse field.
Summary form only given. Understanding and probing phase transitions in non-equilibrium systems is an ongoing challenge in physics. A particular instance are phase transitions that occur between a non-fluctuating absorbing phase [1], e.g., an extinct population, and one in which the relevant order parameter, such as the population density, assumes a finite value. Here we report the observation of signatures of such a non-equilibrium phase transition in an open driven quantum system. In our experiment rubidium atoms in a quasi one-dimensional cold disordered gas are laser-excited to Rydberg states under so-called facilitation conditions [2]. This conditional excitation process competes with spontaneous decay (see Fig. 1a) and leads to a crossover between a stationary state with no excitations and one with a finite number of Rydberg excitations (see Fig. 1b, where the phase diagram is plotted as a function of the driving strength and detuning from resonance) [3]. We relate the underlying physics to that of an absorbing state phase transition in the presence of a field which slightly offsets the system from criticality. We observe a characteristic power-law scaling of the Rydberg excitation density as well as increased fluctuations close to the transition point. Furthermore, we argue that the observed transition relies on the presence of atomic motion which introduces annealed disorder into the system and enables the formation of long-ranged correlations. Our study paves the road for future investigations into the largely unexplored physics of non-equilibrium phase transitions in open many-body quantum systems.
A critical point is associated with a diverging relaxation time which always makes the dynamics across a critical point fascinating. For example, when the temperature of a classical system undergoing a classical phase transition (CPT) at a finite temperature T c is suddenly changed from a value higher than the critical temperature to a lower value across the critical point, the system does not equilibrate instantaneously. Domains of ordered regions are formed which grow following a phase ordering dynamics which leads to a dynamical scaling [104]. In this section, we will discuss the recent studies of non-equilibrium dynamics of quantum systems driven across QCPs where the dynamics is unitary unlike the dynamics across a finite temperature critical point. The non-equilibrium dynamics of a transverse XY spin chain was first investigated in a series of papers [48, 46, 47] where the time evolution of the model was studied in the presence of various time-dependent magnetic fields and the nonergodic behavior of the magnetization was pointed out. A similar result was also obtained in [505]. There is a recent upsurge in studies of non-equilibrium dynamics of a quantum system swept across a QCP. These studies are important for exploring the universality associated with quantum critical dynamics. Moreover, recent experiments with ultracold atomic gases [343, 663, 478, 87] have stimulated numerous theoretical studies. The main properties of these atomic gases are low dissipation rates and phase coherence over a long time so that the dynamics is well described by the usual quantum evolution of a closed system. In the subsequent sections, we shall discuss that when a quantum system initially prepared in its ground state is driven across a QCP, the dynamics fails to be adiabatic however slow the rate of change in the parameters of the Hamiltonian may be. This is due to the divergence of the characteristic time scale of the quantum system, namely, the relaxation time close to the QCP. This non-adiabaticity results in the occurrence of defects in the final state of the quantum Hamiltonian.
Abstract Dynamical phase transition in quantum many body systems is usually studied by taking it in the ground state and then quenching a parameter to a new value. We investigate here the dynamics when one performs the time evolution of a generic state and observe that the rate function related to the Loschmidt echo shows non-analytic behavior of two types, one related, and the other unrelated, to the appearance of a quantum phase transition. Specifically, we consider a quantum Ising chain in an initial configuration which is a generic superposition of the eigenstates, and follow its dynamics under the transverse Ising Hamiltonian with a constant field. Depending on the the configuration of the initial state, some singularities appear in the rate function which do not correspond to the equilibrium phase transition of the Hamiltonian. However another class of singularity is found having a connection with the quantum critical point. Some features of the singularities of the rate function have been derived analytically and it is observed that the occupancy of quasiparticle eigenstates plays the key role in triggering the non-analyticities.
This thesis reports the results obtained during my PhD research in the field of out of equilibrium quantum many-body systems. Chapter 1 consists in a brief introduction of the field and the introduction of concept that are useful for the following chapters. In Chapter 2 the statistics of the work as a tool for characterizing the dynamics of many-body quantum systems is introduced its general features discussed. Then, such a statistics is computed for generic time-dependent protocols (both global and local) in the quantum Ising chain and in the Gaussian field theory, showing, in particular, that in its low-energy part there are features that are independent of the details of the specific chosen protocol. Chapter 3 is devoted to the study of the dynamical phase transition in the
O(N) quantum vector model in the
N→∞ limit, whose critical properties in generic dimensions are characterized. Moreover, a strong connection between such a transition and the statistics of excitations produced in a double quench as a function of the waiting time is showed. The chapter ends by studying the fate of the dynamical transition and the its critical properties when a ramp of finite duration
τ is applied to the system instead of a sudden quench. In particular, we will show that when
τ→∞ the critical point tends to the equilibrium critical point (at zero temperature) in a power-law fashion and that for every finite
τ the critical properties are always the same (and different from the equilibrium critical properties). Finally in Chapter 4 we will discuss the emergence of a non adiabatic behavior in the dynamics of the order parameter for a low dimensional quantum system driven within a gapped phase by considering in detail the case of a quantum Ising chain subject to a linear variation in time of the transverse field, showing that, no matter how slowly the ramp is performed, such a change leads eventually to the disruption of the order.
Quantum phase transitions occur strictly at zero temperature and are accessed by varying a physical parameter such as a magnetic field or chemical potential. While these transitions themselves are experimentally inaccessible, the existence of a zero temperature quantum critical point has remarkable effects on the dynamical properties of interacting quantum many-body systems at finite temperatures. In this thesis, we study dynamics in four strongly interacting many-body systems near quantum critical points in the context of NMR relaxation, quantum quenches, many-body quantum chaos, and charge diffusion. In chapter 1, we begin by revisiting the issue of NMR relaxation in the quantum disordered phase of Ising spin chains. We find that the imaginary part of the spin susceptibility at low frequences is dominated by rare quantum processes which leads to an NMR relaxation rate that scales as
1/T1∼exp(−T2Δ) near the quantum critical point rather than the previously conjectured
1/T1∼exp(−TΔ). These results resolve certain discrepancies between the energy scales measured with different experimental probes in the quantum disordered paramagnetic phase of the Ising chain system
CoNb2O6. In chapter 2, we study the non-equilibrium dynamics of Sachdev-Ye-Kitaev (SYK) models with
q body interactions after a quantum quench, considering a quench protocol which drives the system from an initial state with long-lived quasiparticle excitations to a final state lacking any long-lived quasiparticle excitations. For
q=4, we find that the timescale for the system to locally thermalize
τeq∼kBTℏ and for
q→∞ we find that the system thermalizes instantaneously. In chapter 3, we study the real time dynamics of quantum electrodynamics in 2+1 dimensions with
Nf flavors of fermions. We focus on thermalization and the onset of many-body quantum chaos and compute the quantum Lyapunov exponent in a
Nf1 expansion. We briefly comment on chaos, locality, and gauge invariance. Finally, in Chapter 4 we consider whether the butterfly velocity - a speed at which quantum information propagates - may provide a fundamental bound on diffusion constants in dirty incoherent metals by computing the charge diffusion constant and the butterfly velocity in charge-neutral holographic matter with long wavelength ``hydrodynamic" disorder. In this limit, we find that the butterfly velocity does not set a sharp lower bound for the charge diffusion constant.
The task of exploring and understanding various aspects of far-from-equilibrium dynamics of closed and generic quantum many-body systems has received a thrust of attention in recent years, driven partly by remarkable advances in ultracold experimental technologies. In this work, for the paradigmatic Ising spin chain with transverse and longitudinal fields and partly motivated by the practice of site-resolved control in contemporary ultracold experiments, we present numerical observations of several
fine-grained (small-subsystem level) features of far-from-equilibrium dynamics from a quantum informational point of view, induced by quantum quenches far across the Ising critical point between states deep inside the para- and ferro-magnetic regimes. Rather featureless dynamics is seen for ferromagnetic to paramagnetic quenches, but paramagnetic to ferromagnetic quenches exhibit rich behaviour, including recurrences of an approximately Page-like dynamics of entanglement entropies of one- and two-spin subsystems, periodic but short-lived occurrences of approximately
1−uniform states, a series of sudden deaths and revivals of entanglement between two spins in the system's bulk, non-analytic cusps in single-copy entanglement entropy for three-spin and bigger subsystems, insufficient mixedness and a series of scrambling-
unscrambling of local mutual information between neighboring spins. Moreover, essentially indistinguishable dynamics is seen at very early times between the integrable limit (zero longitudinal field) and non-integrable cases, with the former eventually showing signatures of better mixing and faster approach to equilibration than the latter. These features are expected to hold for quench dynamics across Ising quantum critical points in more complicated systems.