A bstract Understanding the mechanisms by which complex correlations emerge through the dynamics of quantum many-body systems remains a fundamental challenge in modern physics. To address this, quench dynamics starting from nonthermal states have been extensively studied, leading to significant progress. In this paper, we propose a novel quench protocol, termed the “crosscap quench”, to investigate how highly structured thermal pure states relax into typical ones. We begin by analyzing conformal field theories (CFTs) and derive universal features in the time evolution of the entanglement entropy. Furthermore, leveraging the AdS/CFT correspondence, we study holographic CFTs, providing an analytically tractable example in chaotic CFTs. Finally, we validate these findings through numerical simulations in both nonintegrable and integrable quantum spin systems.
A bstract Understanding the mechanisms by which complex correlations emerge through the dynamics of quantum many-body systems remains a fundamental challenge in modern physics. To address this, quench dynamics starting from nonthermal states have been extensively studied, leading to significant progress. In this paper, we propose a novel quench protocol, termed the “crosscap quench”, to investigate how highly structured thermal pure states relax into typical ones. We begin by analyzing conformal field theories (CFTs) and derive universal features in the time evolution of the entanglement entropy. Furthermore, leveraging the AdS/CFT correspondence, we study holographic CFTs, providing an analytically tractable example in chaotic CFTs. Finally, we validate these findings through numerical simulations in both nonintegrable and integrable quantum spin systems.
We study quantum quench dynamics in (1+1)-dimensional critical systems, starting from thermal pure states called crosscap states, and evolving them under spatially inhomogeneous Hamiltonians. The spatial inhomogeneity is introduced through a deformation of the Hamiltonian, expressed as linear combinations of the generators of the SL(q)(2,R) subalgebra of the Virasoro algebra. We analyze the free massless Dirac fermion theory and holographic conformal field theory as prototypical examples of integrable and non-integrable dynamics. Consistent with general expectations, "Möbius-type" deformations lead to thermalization in the non-integrable case, and to periodic revivals in the integrable one. In contrast, "sine-square-type" and "displacement-type" deformations prevent both thermalization and scrambling, instead producing late-time, graph-like entanglement patterns. These patterns emerge from the interplay between the deformed Hamiltonian and the crosscap initial state and appear to be universal: they are determined solely by the deformation profile while remaining largely insensitive to microscopic details. Finally, we perform a holographic calculation in three-dimensional gravity using AdS3/CFT2, which reproduces the main features of our (1+1)-dimensional study.
The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics. It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments. The entanglement dynamics emerging from long-range correlated states is far less studied, although no less viable using modern quantum simulation experiments. In this work, we investigate the dynamics of the bipartite entanglement entropy and mutual information from initial states which have long-range entanglement with correlation between antipodal points of a finite and periodic system. Starting from these crosscap states, we study both brickwork quantum circuits and Hamiltonian dynamics and find distinct patterns of behaviour depending on the type of dynamics and whether the system is integrable or chaotic. Specifically, we study both dual unitary and random unitary quantum circuits as well as free and interacting fermion Hamiltonians. For integrable systems, we find that after a time delay the entanglement experiences a linear in time decrease followed by a series of revivals, while, in contrast, chaotic systems exhibit constant entanglement entropy. On the other hand, both types of systems experience an immediate linear decrease of the mutual information in time. In chaotic systems this then vanishes, whereas integrable systems instead experience a series of revivals. We show how the quasiparticle and membrane pictures of entanglement dynamics can be modified to describe this behaviour, and derive explicitly the quasiparticle picture in the case of free fermion models which we then extend to all integrable systems.
Abstract The notion of a crosscap state, a special conformal boundary state first defined in 2d CFT, was recently generalized to 2d massive integrable quantum field theories and integrable spin chains. It has been shown that the crosscap states preserve integrability. In this work, we first generalize this notion to the Lieb-Liniger model, which is a prototype of integrable non-relativistic many-body systems. We then show that the defined crosscap state preserves integrability. We derive the exact overlap formula of the crosscap state and the on-shell Bethe states. As a byproduct, we prove the conjectured overlap formula for integrable spin chains rigorously by coordinate Bethe ansatz. It turns out that the overlap formula for both models take the same form as a ratio of Gaudin-like determinants with a trivial prefactor. Finally we study quench dynamics of the crosscap state, which turns out to be surprisingly simple. The stationary density distribution is simply a constant. We also derive the analytic formula for dynamical correlation functions in the Tonks-Girardeau limit.
Quantum systems display counterintuitive features, escaping our everyday-life intuition, whose origin is related to entanglement. This phenomenon arises when different parts of the same systems display correlations, which cannot be understood via classical mechanics, and they are dubbed as quantum. To characterize the correlations above, it is necessary to find good entanglement measures which are able to capture quantitatively the quantum features of a given system. This motivates the investigation and the computation of quantities such as the von Neumann entropy of regions, which provides information about how a system is entangled. Our focus is quantum one-dimensional systems close to their critical point, where quantum correlations are enhanced, and a characterization via Quantum Field Theory (QFT) can be provided. In particular, we aim to understand the role of symmetries and localized defects on the entanglement properties. Those aspects display an intimate connection. First, via replica trick, the entropy is expressed via a replica permutation symmetry. Then, single defects break symmetries that are present in the corresponding homogeneous systems. Due to these reasons, the characterization of symmetry actions on subsystems can be viewed as a unifying framework for quantifying entanglement. We split this thesis into two parts. The first part is devoted to the symmetry-resolved entanglement. We first compute it in massive integrable field theories, giving analytical predictions for free fermions/bosons and the 3-state Potts model. For instance, we characterize the universal corrections to area law via form factor bootstrap. We also study excited states of field theories, and we characterize both low-energy states of Conformal Field Theory (CFT) and quasi-particle states. The second part deals with quantum correlations across defects. We provide a CFT framework to compute Rényi entropy and negativity in the ground state of conformal junctions, giving analytical predictions for free fermions and bosons. We find logarithmic growth of the entanglement measures above, and we relate the universal prefactor to the boundary conditions, encoded in a boundary scattering matrix. Then, we focus on the entanglement dynamics, and we study the time evolution of correlations for two paradigmatic classes of quench protocols. For a global quench, we find a linear growth of entropy across the defect whose slope is computed both in CFT, for thermal states, and for free fermions, via a modification of the quasi-particle picture. For a domain wall melting protocol, also known as inhomogeneous quench, we find that, while local observables are easily understood via hydrodynamics and local generalized Gibbs ensembles, the same is not true for the entropy. In contrast, by employing the quasi-particle picture, we provide precise predictions for the dynamics of entanglement, revealing the influence of long-range correlations between points that are specular with respect to the defect.
In this thesis we study the time dependence of correlators such as Green function, entanglement (Renyi) entropy and mutual information following quantum quench in Conformal Field Theories (CFTs) and their holographic duals (AdS).
We develop a new recursive method to analytically study the thermalization of retarded Green function in CFTs holographically dual to thin shell AdS Vaidya space times. Using this method, analytic results for short time thermalization of the Green function are obtained; its long time behaviour is obtained by implementing this method numerically. This method is also used to study the late time behaviour of the minimally coupled scalar in AdS3 Vaidya and the shear vector mode in AdS5 Vaidya. Studying the latter, we obtain the universal ratio of the shear viscosity to entropy density from a time dependent process.
We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in CFTs at finite temperature for which the locally excited states have a finite temporal width. We show that the time dependence of Renyi and entanglement entropies, at second order in width, is universal and is determined by the expectation value of the stress tensor in the replica geometry.
We study local quenches in two dimensional CFT at large central charge by operators carrying higher spin charge. The holographic description is used to obtain the single interval entanglement entropy, mutual information and scrambling time following the quench. We find that the change in entanglement entropy is finite (and real) only if the spin-three charge, q, is bounded by the energy of the perturbation, E, as |q|/c < E^2/c^2. For larger values of the spin-three charge, the scrambling time is shorter than for pure gravity and controlled by the spin-three Lyapunov exponent.
We study the time evolution of the entanglement structure of holographic conformal field theories after a local quench. Using the mutual information between two spatial intervals as a probe, we find that 1+1-dimensional conformal field theories exhibit a rich pattern of dynamical phase transitions. In the large-central-charge limit, mutual information develops sharp non-analyticities at critical times, providing a concrete entanglement-based realization of dynamical quantum phase transitions. We find that the dynamics organize into six distinct phases of mutual information, each controlled by the dominance of a different conformal block, or equivalently, a different holographic geodesic configuration. This phase structure goes beyond the standard quasi-particle picture, explaining non-analytic features that are not captured by simple light-cone propagation from the quench points. We further identify a dynamical D4 symmetry acting on the interval endpoints that controls the presence or absence of mutual information. The onset of mutual information is governed by the breaking of this symmetry to a Z2×Z2 subgroup, suggesting a symmetry-based characterization of non-equilibrium entanglement dynamics analogous to the role of symmetry in equilibrium critical phenomena. Finally, numerical studies of critical spin chains indicate that finite-c effects smooth out the sharp large-c transitions between different mutual-information phases, while the transitions between phases with and without mutual information appear to remain non-analytic. These results offer a unifying perspective on real-time entanglement dynamics and their critical features in conformal many-body systems.