Entanglement exhibits universal behavior near the ground-state critical point where correlations are long ranged and the thermodynamic entropy is vanishing. On the other hand, a quantum quench imparts extensive energy and results in a build up of entropy, hence no critical behavior is expected at long times. In this work, we present a new paradigm in the quench dynamics of integrable spin chains which exhibit a ground-state order-disorder phase transition at a critical line. Specifically, we consider a quench along the critical line which displays a volume-law behavior of the entropy and exponentially decaying correlations; however, we show that quantum criticality is hidden in higher-order correlations and becomes manifest via measures such as the mutual information and logarithmic negativity. Furthermore, we showcase the scale invariance of the Rényi mutual information between disjoint regions as further evidence for genuine critical behavior. We attribute the emergent quantum criticality to the soft mode not getting excited in spite of the quench. Moreover, the results presented here are universal to models whose low-energy or long-wavelength dynamics are well described by a free-fermionic field theory. Our results are amenable to an experimental realization on different quantum simulator platforms, particularly the Rydberg simulators. Published by the American Physical Society 2024
Entanglement exhibits universal behavior near the ground-state critical point where correlations are long ranged and the thermodynamic entropy is vanishing. On the other hand, a quantum quench imparts extensive energy and results in a build up of entropy, hence no critical behavior is expected at long times. In this work, we present a new paradigm in the quench dynamics of integrable spin chains which exhibit a ground-state order-disorder phase transition at a critical line. Specifically, we consider a quench along the critical line which displays a volume-law behavior of the entropy and exponentially decaying correlations; however, we show that quantum criticality is hidden in higher-order correlations and becomes manifest via measures such as the mutual information and logarithmic negativity. Furthermore, we showcase the scale invariance of the Rényi mutual information between disjoint regions as further evidence for genuine critical behavior. We attribute the emergent quantum criticality to the soft mode not getting excited in spite of the quench. Moreover, the results presented here are universal to models whose low-energy or long-wavelength dynamics are well described by a free-fermionic field theory. Our results are amenable to an experimental realization on different quantum simulator platforms, particularly the Rydberg simulators. Published by the American Physical Society 2024
Long-range interacting spin systems are ubiquitous in physics and exhibit a variety of ground-state disorder-to-order phase transitions. We consider a prototype of infinite-range interacting models known as the Lipkin-Meshkov-Glick model describing the collective interaction of N spins and investigate the dynamical properties of fluctuations and correlations after a sudden quench of the Hamiltonian. Specifically, we focus on critical quenches, where the initial state and/or the postquench Hamiltonian are critical. Depending on the type of quench, we identify three distinct behaviors where both the short-time dynamics and the stationary state at long times are effectively thermal, quantum, and genuinely nonequilibrium, characterized by distinct universality classes and static and dynamical critical exponents. These behaviors can be identified by an infrared effective temperature that is finite, zero, and infinite (the latter scaling with the system size as N^{1/3}), respectively. The quench dynamics is studied through a combination of exact numerics and analytical calculations utilizing the nonequilibrium Keldysh field theory. Our results are amenable to realization in experiments with trapped-ion experiments where long-range interactions naturally arise.
We study the entanglement between disjoint subregions in quantum critical systems through the lens of the logarithmic negativity. We work with systems in arbitrary dimensions, including conformal field theories and their corresponding lattice Hamiltonians, as well as resonating valence-bond states. At small separations, the logarithmic negativity is big and displays universal behavior, but we show nonperturbatively that it decays faster than any power at large separations. This can already be seen in the minimal setting of single-spin subregions. The corresponding absence of distillable entanglement at large separations generalizes the one-dimensional result, and indicates that quantum critical ground states do not possess long-range bipartite entanglement, at least for bosons. For systems with fermions, a more suitable definition of the logarithmic negativity exists that takes into account fermion parity, and we show that it decays algebraically. Along the way we obtain general results for the moments of the partially transposed density matrix. Published by the American Physical Society 2024
The study of quantum phase transitions requires the preparation of a many-body system near its ground state, a challenging task for many experimental systems. The measurement of quench dynamics, on the other hand, is now a routine practice in most cold atom platforms. Here we show that quintessential ingredients of quantum phase transitions can be probed directly with quench dynamics in integrable and nearly integrable systems. As a paradigmatic example, we study global quench dynamics in a transverse-field Ising model with either short-range or long-range interactions. When the model is integrable, we discover a new dynamical critical point with a nonanalytic signature in the short-range correlators. The location of the dynamical critical point matches that of the quantum critical point and can be identified using a finite-time scaling method. We extend this scaling picture to systems near integrability and demonstrate the continued existence of a dynamical critical point detectable at prethermal timescales. We quantify the difference in the locations of the dynamical and quantum critical points away from (but near) integrability. Thus, we demonstrate that this method can be used to approximately locate the quantum critical point near integrability. The scaling method is also relevant to experiments with finite time and system size, and our predictions are testable in near-term experiments with trapped ions and Rydberg atoms.
We investigate the signature of quantum criticality in the long-time stationary state of the long-range Kitaev chain by performing various quench protocols. In this model, the pairing interaction decays with distance according to a power law with exponent α. Using quantum information-theoretic measures, such as mutual information and logarithmic negativity, we show that, irrespective of the values of α, critical-to-critical quench displays quantum criticality even in the stationary state. Remarkably, in the presence of long-range pairing interactions, where fermionic correlators decay algebraically even at non-critical points, signature of quantum criticality persists in the stationary state. Furthermore, the effective central charge, calculated from both mutual information and logarithmic negativity of stationary state following a critical-to-critical quench, agrees with the central charge of the corresponding ground states for both α=0 and α=2. Therefore, information of the universality class can be inferred from the stationary state.
We investigate the signature of quantum criticality in the long-time stationary state of the long-range Kitaev chain by performing various quench protocols. In this model, the pairing interaction decays with distance according to a power law with exponent $\ensuremath{\alpha}$. Using quantum information-theoretic measures, such as mutual information and logarithmic negativity, we show that irrespective of the values of $\ensuremath{\alpha}$, critical-to-critical quench displays quantum criticality even in the stationary state. Remarkably, in the presence of long-range pairing interactions, where fermionic correlators decay algebraically even at noncritical points, the signature of quantum criticality persists in the stationary state. Furthermore, the effective central charge, calculated from both mutual information and logarithmic negativity of the stationary state following a critical-to-critical quench, agrees with the central charge of the corresponding ground states for both $\ensuremath{\alpha}=0$ and $\ensuremath{\alpha}=2$. Therefore, information of the universality class can be inferred from the stationary state.
We study the universal real-time relaxation behaviors of a long-range quantum XY chain following a quench. Our research includes both the noncritical and critical quench. In the case of noncritical quench, i.e., neither the initial state nor the postquench Hamiltonian is at a critical point of equilibrium phase transition, a quench to the commensurate phase or incommensurate phase gives a scaling of t−3/2 or t−1/2, respectively, which is the same as the counterpart of the short-range XY model. However, for a quench to the boundary line between the commensurate and incommensurate phases, the scaling law t−μ may be different from the t−3/4 law of the counterpart of the short-range model. More interestingly, the decaying exponent μ may depend on the choice of the parameters of the postquench Hamiltonian because of the different asymptotic behaviors of the energy spectrum. Furthermore, in certain cases, the scaling behavior may be outside the range of predictions made by the stationary phase approximation, because an inflection point emerges in the energy spectrum. For the critical quench, i.e., the initial state or the postquench Hamiltonian is at a critical point of equilibrium phase transition, the aforementioned scaling law t−μ may be changed because of the gap-closing property of the energy spectrum of the critical point.