In quantum field theory, entanglement entropy under spatial bipartitioning serves as a powerful information-theoretic probe of quantum correlations. In this work, we present the first comprehensive numerical study of the dynamical evolution and geometric scaling of entanglement entropy in a nonperturbative, strong-field QED setting -- specifically, in the context of the Sauter-Schwinger effect. While the weak-field regime is dominated by area-law states, we show that the entanglement entropy undergoes a transition from area-law to a volume-law scaling for certain strong-field regimes in the pulse-profile parameter space -- signaling a fundamental shift in the underlying correlation structure induced by nonperturbative pair production. For intermediate regimes, the scaling is a power-law that interpolates between area- and volume-law behavior. Finally, we provide interpretations based on the behavior of the low-energy pair-creation spectrum and discuss how these insights could inform future investigations of related phenomena.
In quantum field theory, entanglement entropy under spatial bipartitioning serves as a powerful information-theoretic probe of quantum correlations. In this work, we present the first comprehensive numerical study of the dynamical evolution and geometric scaling of entanglement entropy in a nonperturbative, strong-field QED setting -- specifically, in the context of the Sauter-Schwinger effect. While the weak-field regime is dominated by area-law states, we show that the entanglement entropy undergoes a transition from area-law to a volume-law scaling for certain strong-field regimes in the pulse-profile parameter space -- signaling a fundamental shift in the underlying correlation structure induced by nonperturbative pair production. For intermediate regimes, the scaling is a power-law that interpolates between area- and volume-law behavior. Finally, we provide interpretations based on the behavior of the low-energy pair-creation spectrum and discuss how these insights could inform future investigations of related phenomena.
Entanglement entropy in the vacuum state of local field theories exhibits an area law. However, nonlocal theories at large N and strong coupling violate this area law. In these theories, the leading divergence in the entanglement entropy is extensive for regions smaller than the effective nonlocality scale and proportional to this effective nonlocality scale for regions larger than it. This raises the question: is a volume law a generic feature of nonlocal theories, or is it only present at strong coupling and large N ? This paper investigates entanglement entropy of large regions in weakly coupled non-local theories, to leading order in the coupling. The two theories studied are ϕ 4 theory on the noncommutative plane and ϕ 4 theory with a dipole type nonlocal modification using a fixed nonlocality scale. Both theories are found to follow an area law to first order in the coupling, hence no evidence is found for a volume law. This indicates that, perturbatively the nonlocal interactions considered are not generating sufficient entanglement at distances of the nonlocality scale to change the leading divergence, at least to first order in the coupling. An argument against volume laws at higher orders is also presented.
We study different aspects of quantum entanglement and its measures, including entanglement entropy in the vacuum state of a certain Lifshitz free scalar theory. We present simple intuitive arguments based on “non-local” effects of this theory that the scaling of entanglement entropy depends on the dynamical exponent as a characteristic parameter of the theory. The scaling is such that in the massless theory for small entangling regions it leads to area law in the Lorentzian limit and volume law in the z → ∞ limit. We present strong numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior. In (2 + 1)-dimensions we also study some shape dependent aspects of entanglement. We argue that in the massless limit corner contributions are no more additive for large enough dynamical exponent due to non-local effects of Lifshitz theories. We also comment on possible holographic duals of such theories based on the sign of tripartite information.
Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay of correlation functions, but also reflected by scaling laws of a quite profound quantity: the entanglement entropy of ground states. This entropy of the reduced state of a subregion often merely grows like the boundary area of the subregion, and not like its volume, in sharp contrast with an expected extensive behavior. Such ``area laws'' for the entanglement entropy and related quantities have received considerable attention in recent years. They emerge in several seemingly unrelated fields, in the context of black hole physics, quantum information science, and quantum many-body physics where they have important implications on the numerical simulation of lattice models. In this Colloquium the current status of area laws in these fields is reviewed. Center stage is taken by rigorous results on lattice models in one and higher spatial dimensions. The differences and similarities between bosonic and fermionic models are stressed, area laws are related to the velocity of information propagation in quantum lattice models, and disordered systems, nonequilibrium situations, and topological entanglement entropies are discussed. These questions are considered in classical and quantum systems, in their ground and thermal states, for a variety of correlation measures. A significant proportion is devoted to the clear and quantitative connection between the entanglement content of states and the possibility of their efficient numerical simulation. Matrix-product states, higher-dimensional analogs, and variational sets from entanglement renormalization are also discussed and the paper is concluded by highlighting the implications of area laws on quantifying the effective degrees of freedom that need to be considered in simulations of quantum states.
Quantum entanglement, a defining feature of quantum theory, is generated dynamically by the Schwinger effect—the production of particle-antiparticle pairs from a strong electric field. In this work, we go beyond traditional particle-number analyses to study the quantum entanglement gen- erated in this process. We partition the system into momentum modes and calculate entanglement entropy and logarithmic negativity as functions of time. For a single Sauter pulse, entanglement exhibits a monotonic growth that closely tracks the pair creation process. Strikingly, a train of alternating pulses induces coherent interference, leading to a cumulative enhancement of entan- glement and revealing a clear interplay between successive creation events. Most significantly, we show that the temporal delay (𝑇) between pulses acts as a tunable parameter, controlling the level of entanglement via constructive or destructive interference. This tunability provides a distinct sig- nature of vacuum memory, establishing pair production as a platform for entanglement-controlled strong-field physics.
Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many-body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study the interplay of these competing tendencies by considering time evolution combining both unitary and projective dynamics. We begin by constructing a toy model of Bell pair dynamics which demonstrates that measurements can keep a system in a state of low, i.e., area-law, entanglement, in contrast with the volume-law entanglement produced by generic pure unitary time evolution. While the simplest Bell pair model has area-law entanglement for any measurement rate, as seen in certain noninteracting systems, we show that more generic models of entanglement can feature an area-to-volume law transition at a critical value of the measurement rate, in agreement with recent numerical investigations. As a concrete example of these ideas, we analytically investigate Clifford evolution in qubit systems which can exhibit an entanglement transition. We are able to identify stabilizer size distributions characterizing the area law, volume law, and critical ``fixed points.'' We also discuss a Floquet random unitary circuit, where the answers depend on the order of limits---one order of limits yields area-law entanglement for any nonzero measurement rate, whereas a different order of limits allows for an arealaw--volumelaw transition. Finally, we provide a rigorous argument that a system subjected to projective measurements can only exhibit a volume-law entanglement entropy if it also features a subleading correction term, which provides a universal signature of projective dynamics in the high-entanglement phase.
Entanglement is a fundamental feature of quantum mechanics and plays an important role in characterizing many-body systems and quantum phase transitions. A quantitative measure of quantum correlations between subsystems is entanglement entropy. In this thesis, we study the entanglement entropy of an interacting quantum field theory, the O(N) model. In local quantum field theories, the leading-order contribution in the scaling of entanglement entropy obeys an area law. This dominant term is governed by short-distance physics near the entangling surface and depends on the ultraviolet regularization, making it non-universal. Beyond this lead- ing scaling behavior, entanglement entropy can contain subleading universal contributions, which encode intrinsic information about the underlying quantum field theory. In this thesis, we calculate one such universal term: the correlation length coefficient r, which appears as a correction to the entanglement entropy evaluated slightly away from the quantum critical point. The analysis is carried out in D = 2 + 1 spacetime dimensions for an infinite cylindrical geometry. We study the model in the vicinity of criticality using the large-N expansion, which enables controlled analytical calculations. Our main result is that the coefficient r scales linearly with the number of field components N . This behavior is consistent with the interpretation of r as a universal quantity associated with the degrees of freedom of the theory. The calculation is based on the replica method and renormalization group arguments, which are presented in detail. Finally, we discuss the physical meaning of the result and possible methods for verifying it, and we review related results for the O(N) model in different geometries.