We investigate a quantum quench from a critical to an exceptional point. The initial state, prepared in the ground state of a critical hermitian system, is time evolved with a non-hermitian SSH model, tuned to its exceptional point. The single particle density matrix exhibits supersonic modes and multiple light cones, characteristic to non-hermitian time evolution. These propagate with integer multiples of the original Fermi velocity. In the long time limit, the fermionic Green's function decays spatially as $1/x^2$, in sharp contrast to the usual $1/x$ decay of non-interacting fermions. The entanglement entropy is understood as if all these supersonic modes arise from independent quasiparticles (though they do not), traveling with the corresponding supersonic light cone velocity. The entropy production rate decreases with time and develops plateaus during the time evolution, signaling the distinct velocities in the propagation of non-local quantum correlations. At late times, the entanglement entropy saturates to a finite value, satisfying a volume law.
We report on the dynamical formation of exceptional degeneracies in basic correlation functions of non-integrable one- and two-dimensional systems quenched to the vicinity of a critical point. Remarkably, fine-tuned semi-metallic points in the phase diagram of the considered systems are thereby promoted to topologically robust non-Hermitian (NH) nodal phases emerging in the coherent long-time evolution of a dynamically equilibrating system. In the framework of non-equilibrium Green's function methods within the conserving second Born approximation, we predict observable signatures of these nov…
We study how the entanglement spectrum relaxes to its steady state in one-dimensional quadratic systems after a quantum quench. In particular we apply the saddle point expansion to the dimerized chains and 1-D p-wave superconductors. We find that the entanglement spectrum always exhibits a power-law relaxation superimposed with oscillations at certain characteristic angular frequencies. For the dimerized chains, we find that the exponent $ν$ of the power-law decay is always $3/2$. For 1-D p-wave superconductors, however, we find that depending on the initial and final Hamiltonian, the exponent…
Luttinger liquids (LLs) arise by coupling left- and right-moving particles through interactions in one dimension. This most natural partitioning of LLs is investigated by the momentum-space entanglement after a quantum quench using analytical and numerical methods. We show that the momentum-space entanglement spectrum of a LL possesses many universal features both in equilibrium and after a quantum quench. The largest entanglement eigenvalue is identical to the Loschmidt echo, i.e. the overlap of the disentangled and final wavefunctions of the system. The second largest eigenvalue is the overl…
The Quantum Null Energy Condition (QNEC) relates energy to the second variation of entropy in relativistic quantum field theory. We use the QNEC inequality to bound entanglement entropy in quenches. At early times the entanglement entropy grows quadratically in time, and the QNEC provides an upper bound on the prefactor. We demonstrate that the bound is tight, by showing that it is saturated in certain quench protocols: boundary state quenches in conformal field theories in any dimensions. In higher than two dimensions we compute entanglement entropy using AdS/CFT. Our results are the first pu…
We study the growth of entanglement entropy in density matrix renormalization group calculations of the real-time quench dynamics of the Anderson impurity model. We find that with appropriate choice of basis, the entropy growth is logarithmic in both the interacting and noninteracting single-impurity models. The logarithmic entropy growth is understood from a noninteracting chain model as a critical behavior separating regimes of linear growth and saturation of entropy, corresponding respectively to an overlapping and gapped energy spectra of the set of bath states. We find that with an approp…
We discuss the behaviour of holographic entanglement entropy following a local quench in 2+1 dimensional strongly coupled CFTs. The entanglement generated by the quench propagates along an emergent light-cone, reminiscent of the Lieb-Robinson light-cone propagation of correlations in non-relativistic systems. We find the speed of propagation is bounded from below by the entanglement tsunami velocity obtained earlier for global quenches in holographic systems, and from above by the speed of light. The former is realized for sufficiently broad quenches, while the latter pertains for well localiz…
We propose a free falling particle in an AdS space as a holographic model of local quench. Local quenches are triggered by local excitations in a given quantum system. We calculate the time-evolution of holographic entanglement entropy. We confirm a logarithmic time-evolution, which is known to be typical in two dimensional local quenches. To study the structure of quantum entanglement in general quantum systems, we introduce a new quantity which we call entanglement density and apply this analysis to quantum quenches. We show that this quantity is directly related to the energy density in a s…
We study the sudden quench of a one-dimensional p-wave superconductor through its topological signature in the entanglement spectrum. The long-time evolution of the system and its topological characterization depend on a pseudomagnetic field ${\bs R}_{\mbox{\text eff}}(k)$, which connects both the initial and the final Hamiltonians, hence exhibiting a memory effect. In particular, we explore the robustness of the Majorana zero-mode associated with the entanglement cut in the topologically nontrivial phase and identify the parameter space in which the mode can survive in the infinite-time limit…
We study the quench dynamics of entanglement spectra in the Kitaev chain with variable-range pairing quantified by power-law decay rate $α$. Considering the post-quench Hamiltonians with flat bands, we demonstrate that the presence of entanglement-spectrum crossings during its dynamics is able to characterize the topological phase transitions (TPTs) in both short-range ($α$ > 1) or long-range ($α$ < 1) sector. Properties of entanglement-spectrum dynamics are revealed for the quench protocols in the long-range sector or with $α$ as the quench parameter. In particular, when the lowest upper-half…
Quantum entanglement may have various origins ranging from solely interaction-driven quantum correlations to single-particle effects. Here, we explore the dependence of entanglement on time-dependent single-particle basis transformations in fermionic quantum many-body systems, thus aiming at isolating single-particle sources of entanglement growth in quench dynamics. Using exact diagonalization methods, for paradigmatic non-integrable models we compare to the standard real space cut various physically motivated bipartitions. Moreover, we search for a minimal entanglement basis using local opti…
We study the dynamics of the quenched Anderson model at finite temperature using matrix product states. Exploiting a chain mapping for the electron bath, we investigate the entanglement structure in the MPS for various orderings of the two chains, which emerge from the thermofield transformation employed to deal with nonzero temperature. We show that merging both chains can significantly lower the entanglement at finite temperatures as compared to an intuitive nearest-neighbor implementation of the Hamiltonian. Analyzing the population of the free bath modes -- possible when simulating the ful…
We numerically investigate the momentum-space entanglement entropy and entanglement spectrum of the random-dimer model and its generalizations, which circumvent Anderson localization, after a quench in the Hamiltonian parameters. The type of dynamics that occurs depends on whether or not the Fermi level of the initial state is near the energy of the delocalized states present in these models. If the Fermi level of the initial state is near the energy of the delocalized states, we observe an interesting slow logarithmic-like growth of the momentum-space entanglement entropy followed by an event…
We compute concurrence and negativity as measures of two-site entanglement generated by a power-law quench (characterized by a rate 1/tau and an exponent alpha) which takes an anisotropic XY chain in a transverse field through a quantum critical point (QCP). We show that only the even-neighbor pairs of sites get entangled in such a process. Moreover, there is a critical rate of quench, 1/tau_c, above which no two-site entanglement is generated; the entire entanglement is multipartite. The ratio of the two-site entanglements between consecutive even neighbors can be tuned by changing the quench…
We formulate dynamical phase transitions in subsystems embedded in larger quantum systems. Introducing the entanglement echo as an overlap of the initial and instantaneous entanglement ground states, we show its analytic structure after a quench provides natural definition of dynamical phase transitions in the subsystem. These transitions come in two varieties, the entanglement-type transitions and the bulk-type Loschmidt transitions. The entanglement-type transitions arise from periodic reorganization of quantum correlations between the subsystem and its environment, manifesting in instantane…
Multipartite entanglement, such as witnessed through the quantum Fisher information (QFI), is a crucial resource for quantum technologies, but its experimental certification is highly challenging. Here, we propose an experimentally friendly protocol to measure the QFI. It relies on recording the short-time dynamics of simple observables after a quench from a thermal state, works for spins, bosons, and fermions, and can be implemented in standard cold-atom experiments and other platforms with temporal control over the system Hamiltonian. To showcase the protocol, we simulate it for the one-dime…
We present a new class of local quenches described by mixed states, parameterized universally by two parameters. We compute the evolutions of entanglement entropy for both a holographic and Dirac fermion CFT in two dimensions. This turns out to be equivalent to calculations of two point functions on a torus. We find that in holographic CFTs, the results coincide with the known results of pure state local operator quenches. On the other hand, we obtain new behaviors in the Dirac fermion CFT, which are missing in the pure state counterpart. By combining our results with the inequalities known fo…
We investigate bipartite entanglement in random quantum $XY$ models at equilibrium. Depending on the intrinsic time scales associated with equilibration of the random parameters and measurements associated with observation of the system, we consider two distinct kinds of disorder, namely annealed and quenched disorders. We conduct a comparative study of the effects of disorder on nearest-neighbor entanglement, when the nature of randomness changes from being annealed to quenched. We find that entanglement properties of the annealed and quenched disordered systems are drastically different from…
We show that, in the gapless Kondo Regime, a single local quench at one end of a Kondo spin chain induces a fast and long lived oscillatory dynamics. This quickly establishes a high quality entanglement between the spins at the opposite ends of the chain. This entanglement is mediated by the Kondo Cloud, attains a constant high value independent of the length for large chains, and shows thermal robustness. In contrast, when the Kondo cloud is absent, e.g. in the gapped dimer regime, only finite size end to end effects can create some entanglement on a much longer time-scale for rather short ch…
We consider the time evolution of the gaps of the entanglement spectrum for a block of consecutive sites in finite transverse field Ising chains after sudden quenches of the magnetic field. We provide numerical evidence that, whenever we quench at or across the quantum critical point, the time evolution of the ratios of these gaps allows to obtain universal information. They encode the low-lying gaps of the conformal spectrum of the Ising boundary conformal field theory describing the spatial bipartition within the imaginary time path integral approach to global quenches at the quantum critica…
We investigate the time evolution towards the asymptotic steady state of a one dimensional interacting system after a quantum quench. We show that at finite time the latter induces entanglement between right- and left- moving density excitations, encoded in their cross-correlators, which vanishes in the long-time limit. This behavior results in a universal time-decay in system spectral properties $ \propto t^{-2} $, in addition to non-universal power-law contributions typical of Luttinger liquids. Importantly, we argue that the presence of quench-induced entanglement clearly emerges in transpo…
We consider the entanglement entropy in 2d conformal field theory in a class of excited states produced by the insertion of a heavy local operator. These include both high-energy eigenstates of the Hamiltonian and time-dependent local quenches. We compute the universal contribution from the stress tensor to the single interval Renyi entropies and entanglement entropy, and conjecture that this dominates the answer in theories with a large central charge and a sparse spectrum of low-dimension operators. The resulting entanglement entropies agree precisely with holographic calculations in three-d…
In a recent work by Gong and Ueda (arXiv:1710.05289), the classification of (1+1)-dimensional quench dynamics for the ten Altland-Zirnbauer classes is achieved, and entanglement-spectrum crossings of the time-dependent states for the topological classes (AIII, DIII, CII, BDI, and D) are discovered as a consequence of the bulk-edge correspondence. We note that, their classification scheme relies on the limit that the energy spectrum of the post-quench Hamiltonian is flat, because any finite band dispersion leads to the break down of time-reversal and chiral symmetries for the parent Hamiltonian…
We investigate the evolution of complexity and entanglement following a quench in a one-dimensional topological system, namely the Su-Schrieffer-Heeger model. We demonstrate that complexity can detect quantum phase transitions and shows signatures of revivals; this observation provides a practical advantage in information processing. We also show that the complexity saturates much faster than the entanglement entropy in this system, and we provide a physical argument for this. Finally, we demonstrate that complexity is a less sensitive probe of topological order, compared with measures of enta…
We study the time evolution of the entanglement negativity after a local quantum quench in (1+1)-dimensional conformal field theories (CFTs), which we introduce by suddenly joining two initially decoupled CFTs at their endpoints. We calculate the negativity evolution for both adjacent intervals and disjoint intervals explicitly. For two adjacent intervals, the entanglement negativity grows logarithmically in time right after the quench. After developing a plateau-like feature, the entanglement negativity drops to the ground-state value. For the case of two spatially separated intervals, a ligh…
Quantum entanglement and its main quantitative measures, the entanglement entropy and entanglement negativity, play a central role in many body physics. An interesting twist arises when the system considered has symmetries leading to conserved quantities: Recent studies introduced a way to define, represent in field theory, calculate for 1+1D conformal systems, and measure, the contribution of individual charge sectors to the entanglement measures between different parts of a system in its ground state. In this paper, we apply these ideas to the time evolution of the charge-resolved contributi…
We investigate the entanglement spreading in the anisotropic spin-1/2 Heisenberg (XXZ) chain after a geometric quench. This corresponds to a sudden change of the geometry of the chain or, in the equivalent language of interacting fermions confined in a box trap, to a sudden increase of the trap size. The entanglement dynamics after the quench is associated with the ballistic propagation of a magnetization wavefront. At the free fermion point (XX chain), the von-Neumann entropy S_A exhibits several intriguing dynamical regimes. Specifically, at short times a logarithmic increase is observed, si…
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 …
Sachdev-Ye-Kitaev (SYK) is a concrete solvable model with non-Fermi liquid behavior and maximal chaos. In this work, we study the entanglement Rényi entropy for the subsystems of the SYK model in the Kourkoulou-Maldacena states. We use the path-integral approach and take the saddle point approximation in the large-$N$ limit. We find a first-order transition exist when tuning the subsystem size for the $q=4$ case, while it is absent for the $q=2$ case. We further study the entanglement dynamics for such states under the real-time evolution for noninteracting, weakly interacting and strongly int…
We use tensor network simulations to calculate the time evolution of the lower part of the entanglement spectrum and return rate functions after global quantum quenches in the Ising model. We consider ground state quenches towards mesonic parameter ranges with confined fermion pairs as nonperturbative bound states in a semiclassical regime and the relativistic E$_8$ theory. We find that in both cases only the dominant eigenvalue of the modular Hamiltonian fully encodes the meson content of the quantum many-body system or quantum field theory, giving rise to nearly identical entanglement oscill…
Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics, respectively. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure initial state maintains the system globally at zero entropy, at long time after the quench local properties are captured by an appropriate statistical ensemble with non zero thermodynamic entropy, which can be interpreted as the entanglement accumulated during the dynamics. Therefore, understanding the post-qu…
We numerically investigate the growth of the entanglement entropy S_{ent}(t) in time t---after a global quench from a product state---in quantum chains with various kinds of disorder. The main focus is, in particular, on fermionic chains with bond disorder. In the noninteracting case at criticality we numerically test recent predictions by the real space renormalization group for the entanglement growth in time, the maximal entanglement as a function of block size, and the decay of a density wave order parameter. We show that multiprecision calculations are required to reach the scaling regime…
We study thermalization in the holographic (1+1)-dimensional CFT after simultaneous generation of two high-energy excitations in the antipodal points on the circle. The holographic picture of such quantum quench is the creation of BTZ black hole from a collision of two massless particles. We perform holographic computation of entanglement entropy and mutual information in the boundary theory and analyze their evolution with time. We show that equilibration of the entanglement in the regions which contained one of the initial excitations is generally similar to that in other holographic quench …
We give a pedagogical introduction to the Generalized Hydrodynamic approach to inhomogeneous quenches in integrable many-body quantum systems. We review recent applications of the theory, focusing in particular on two classes of problems: bipartitioning protocols and trap quenches, which represent two prototypical examples of broken translational symmetry in either the system initial state or post-quench Hamiltonian. We report on exact results that have been obtained for generic time-dependent correlation functions and entanglement evolution, and discuss in detail the range of applicability of…
The non-equilibrium evolution of the block entanglement entropy is investigated in the XY chain in a transverse magnetic field after the Hamiltonian parameters are suddenly changed from and to arbitrary values. Using Toeplitz matrix representation and multidimensional phase methods, we provide analytic results for large blocks and for all times, showing explicitly the linear growth in time followed by saturation. The consequences of these analytic results are discussed and the effects of a finite block length is taken into account numerically.
We theoretically study the response of a many-body localized system to a local quench from a quantum information perspective. We find that the local quench triggers entanglement growth throughout the whole system, giving rise to a logarithmic lightcone. This saturates the modified Lieb-Robinson bound for quantum information propagation in many-body localized systems previously conjectured based on the existence of local integrals of motion. In addition, near the localization-delocalization transition, we find that the final states after the local quench exhibit volume-law entanglement. We also…
The time evolution of the entanglement entropy in non-equilibrium quantum systems provides crucial information about the structure of the time-dependent state. For quantum quench protocols, by combining a quasiparticle picture for the entanglement spreading with the exact knowledge of the stationary state provided by Bethe ansatz, it is possible to obtain an exact and analytic description of the evolution of the entanglement entropy. Here we discuss the application of these ideas to several integrable models. First we show that for non-interacting systems, both bosonic and fermionic, the exact…
A formidable perspective in understanding quantum criticality of a given many-body system is through its entanglement contents. Until now, most progress are only limited to the disorder-free case. Here, we develop an efficient scheme to compute the entanglement entropy of $(2+1)$-dimensional quantum critical points with randomness, from a conceptually novel angle where the quenched disorder can be considered as dimensionally reducible interactions. As a concrete example, we reveal novel entanglement signatures of $(2+1)$-dimensional Dirac fermion exposed to a random magnetic field, which hosts…
We study the time evolution after a quantum quench in a family of models whose degrees of freedom are fermions coupled to spins, where quenched disorder appears neither in the Hamiltonian parameters nor in the initial state. Focussing on the behaviour of entanglement, both spatial and between subsystems, we show that the model supports a state exhibiting combined area/volume law entanglement, being characteristic of the quantum disentangled liquid. This behaviour appears for one set of variables, which is related via a duality mapping to another set, where this structure is absent. Upon adding…
We derive dynamics of the entanglement wedge cross section from the reflected entropy for local operator quench states in the holographic CFT. By comparing between the reflected entropy and the mutual information in this dynamical setup, we argue that (1) the reflected entropy can diagnose a new perspective of the chaotic nature for given mixed states and (2) it can also characterize classical correlations in the subregion/subregion duality. Moreover, we point out that we must improve the bulk interpretation of a heavy state even in the case of well-studied entanglement entropy. Finally, we sh…
We study the growth of entanglement in quantum systems with a conserved quantity exhibiting diffusive transport, focusing on how initial inhomogeneities are imprinted on the entropy. We propose a simple effective model, which generalizes the minimal cut picture of \textit{Jonay et al.} in such a way that the `line tension' of the cut depends on the local entropy density. In the case of noisy dynamics, this is described by a Kardar-Parisi-Zhang (KPZ) equation coupled to a diffusing field. We investigate the resulting dynamics and find that initial inhomogeneities of the conserved charge give ri…
We show that the dynamics resulting from preparing a one-dimensional quantum system in the ground state of two decoupled parts, then joined together and left to evolve unitarily with a translational invariant Hamiltonian (a local quench), can be described by means of quantum field theory. In the case when the corresponding theory is conformal, we study the evolution of the entanglement entropy for different bi-partitions of the line. We also consider the behavior of one- and two-point correlation functions. All our findings may be explained in terms of a picture, that we believe to be valid mo…
Classical correlations of ground states typically decay exponentially and polynomially, respectively for gapped and gapless short-ranged quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither …
We use a simple holographic toy model to study global quantum quenches in strongly-coupled, hyperscaling-violating-Lifshitz quantum field theories using entanglement entropy as a probe. Generalizing our results in arxiv:1705.10324 , we show that the holographic entanglement entropy of small subsystems can be written as a simple linear response relation. We use this relation to derive a time-dependent first law of entanglement entropy. In general, this law has a time-dependent term resembling relative entropy which we propose as a good order parameter to characterize out-of-equilibrium-states i…
Quenched randomness can have a dramatic effect on the dynamics of isolated 1D quantum many-body systems, even for systems that thermalize. This is because transport, entanglement, and operator spreading can be hindered by `Griffiths' rare regions which locally resemble the many-body-localized phase and thus act as weak links. We propose coarse-grained models for entanglement growth and for the spreading of quantum operators in the presence of such weak links. We also examine entanglement growth across a single weak link numerically. We show that these weak links have a stronger effect on entan…
We study the time dependence of the entanglement between two quantum wires after suddenly connecting them via tunneling through an impurity. The result at large times is given by the well known formula $S(t) \approx {1\over 3}\ln {t}$. We show that the intermediate time regime can be described by a universal cross-over formula $S=F(tT_K)$, where $T_K$ is the crossover (Kondo) temperature: the function $F$ describes the dynamical "healing" of the system at large times. We discuss how to obtain analytic information about $F$ in the case of an integrable quantum impurity problem using the massles…
We study a particular type of local quench in a generic quantum critical one-dimensional system, using conformal field theory (CFT) techniques, and providing numerical checks of the results in free fermion systems. The system is initially cut into two subsystems $A$ and $B$ which are glued together at time $t=0$. We study the entanglement entropy (EE) between the two parts $A$ and $B$, using previous results by Calabrese and Cardy, and further extending them. We also study in detail the (logarithmic) Loschmidt echo (LLE). For finite-size systems both quantities turn out to be (almost) periodic…
Entanglement Suppression Due to Black Hole Scattering
Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）；Inamori Research Institute for Science（稻盛理工研究院）
We consider a molecular dynamics method, the so-called flea gas for computing the evolution of entanglement after inhomogeneous quantum quenches in an integrable quantum system. In such systems the evolution of local observables is described at large space-time scales by the Generalized Hydrodynamics approach, which is based on the presence of stable, ballistically propagating quasiparticles. Recently it was shown that the GHD approach can be joined with the quasiparticle picture of entanglement evolution, providing results for entanglement growth after inhomogeneous quenches. Here we apply th…
We propose a charged falling particle in an AdS space as a holographic model of local charged quench generalizing model of arXiv:1302.5703. The quench is followed by evolving currents and inhomogeneous distribution of chemical potential. We derive the analytical formula describing the evolution of the entanglement entropy. At some characteristic time after the quench, we find that the entanglement shows a sharp dip. This effect is universal and independent of the dimension of the system. At finite temperature generalization of this model, we find that multiple dips and ramps appear.
We report dynamical quantum phase transition portrait in the alternating field transverse XY spin chain with Dzyaloshinskii-Moriya interaction by investigating singularities in the Loschmidt echo and the corresponding rate function after a sudden quench of system parameters. Unlike the Ising model, the analysis of Loschmidt echo yields non-uniformly spaced transition times in this model. Comparative study between the equilibrium and the dynamical quantum phase transitions in this case reveals that there are quenches where one occurs without the other, and the regimes where they co-exist. Howev…
