Abstract We present a framework for investigating the response of conformally invariant confined 1 + 1-dimensional systems to a quantum quench. While conformal invariance is generally destroyed in a global quantum quench, systems that can be described as or mapped to integrable deformations of a CFT may present special instances where a conformal field theory-based analysis could provide useful insight into the non-equilibrium dynamics. We investigate this possibility by considering a quench analogous to that of the quantum Newton’s Cradle experiment (Kinoshita et al 2006 Nature 440 900 ) and demonstrating qualitative agreement between observables derived in the CFT framework and those of the experimental system. We propose that this agreement may be a feature of the proximity of the experimental system to an integrable deformation of a c = 1 CFT.
Abstract We present a framework for investigating the response of conformally invariant confined 1 + 1-dimensional systems to a quantum quench. While conformal invariance is generally destroyed in a global quantum quench, systems that can be described as or mapped to integrable deformations of a CFT may present special instances where a conformal field theory-based analysis could provide useful insight into the non-equilibrium dynamics. We investigate this possibility by considering a quench analogous to that of the quantum Newton’s Cradle experiment (Kinoshita et al 2006 Nature 440 900 ) and demonstrating qualitative agreement between observables derived in the CFT framework and those of the experimental system. We propose that this agreement may be a feature of the proximity of the experimental system to an integrable deformation of a c = 1 CFT.
Entanglement evolutions after a global quantum quench and a local quantum quench in 1+1 dimensional conformal field theories (CFTs) show qualitatively different behaviors, and are studied within two different setups. In this work, we bridge global and local quantum quenches in (1+1)-d CFTs in the same setup, by studying the entanglement evolution from a specific inhomogeneous initial state. By utilizing conformal mappings, this inhomogeneous quantum quench is analytically solvable. It is found that the entanglement evolution shows a global quantum quench feature in the short time limit, and a local quantum quench feature in the long time limit. The same features are observed in single-point correlation functions of primary fields. We provide a clear physical picture for the underlying reason.
Abstract. We describe several results concerning global quantum quenches from states with short-range correlations to quantum critical points whose low-energy properties are described by a 1 + 1-dimensional conformal field theory (CFT), extending the work of Calabrese and Cardy (2006 Phys. Rev. Lett . 96 136801 ): (a) for the special class of initial states discussed in that paper we show that, once a finite region falls inside the horizon, its reduced density matrix is exponentially close in L 2 norm to that of a thermal Gibbs state; (b) small deformations of this initial state in general lead to a (non-Abelian) generalized Gibbs distribution with, however, the possibility of parafermionic conserved charges; (c) small deformations of the CFT, corresponding to curvature of the dispersion relation and (non-integrable) left-right scattering, lead to a dependence of the speed of propagation on the initial state, as well as diffusive broadening of the horizon.
We develop a method to calculate generic time-dependent correlation functions for inhomogeneous quantum quenches in (1+1)-dimensional conformal field theory (CFT) induced by sudden Hamiltonian deformations that modulate the energy density inhomogeneously. Our Letter particularly focuses on the effects of spatial boundaries, which have remained unresolved by previous analytical methods. For generic postquench Hamiltonian, we develop a generic method to calculate the correlations by mirroring the system, which otherwise are Euclidean path integrals in complicated spacetime geometries difficult to calculate. On the other hand, for a special class of inhomogeneous postquench Hamiltonians, including the Möbius and sine-square-deformation Hamiltonians, we show that the quantum quenches exhibit simple boundary effects calculable from Euclidean path integrals in a straightforward strip spacetime geometry. Applying our method to the time evolution of entanglement entropy, we find that, for generic cases, the entanglement entropy shows discontinuities (shockwave fronts) propagating from the boundaries. In contrast, such discontinuities are absent in cases with simple boundary effects. We verify that our generic CFT formula matches well with numerical calculations from free-fermion tight-binding models for various quench scenarios.
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 paper, we consider the energy and momentum transport in (1+1)-dimension conformal field theories (CFTs) that are deformed by an irrelevant operator TT, using the integrability based generalized hydrodynamics, and holography. The two complementary methods allow us to study the energy and momentum transport after the in-homogeneous quench, derive the exact nonequilibrium steady states, and calculate the Drude weights. Our analysis reveals that all of these quantities satisfy universal formulae regardless of the underlying CFT, thereby generalizing the universal formulas for these quantities in pure CFTs. We also compute the exact momentum diffusion constant using the integrability-based method and confirm that it agrees with the conformal perturbation. These fundamental physical insights have important consequences for our understanding of the TT-deformed CFTs. First of all, they provide the first check of the TT-deformed AdS3/CFT2 correspondence from the dynamical standpoint. And second, we are able to identify a remarkable connection between the TT-deformed CFTs and reversible cellular automata.