Quantum spin models with variable-range interactions can exhibit certain quantum characteristics that a short-ranged model cannot possess. By considering the quantum XYZ model whose interaction strength between different sites varies either exponentially or polynomially, we report the creation of long-range entanglement in dynamics both in the absence and presence of system-bath interactions. Specifically, during closed dynamics, we determine a parameter regime from which the system should start its evolution so that the resulting state after quench can produce a high time-averaged entanglement having low fluctuations. Both in the exponential and power-law decays, it occurs when the magnetic field is weak and the interactions in the z-direction are nonvanishing. When part of the system interacts with the bath repeatedly or is attached to a collection of harmonic oscillators along with dephasing noise in the z-direction, we observe that long-range entanglement of the subparts which are not attached with the environment remains constant with time in the beginning of the evolution, known as freezing of entanglement, thereby demonstrating a method to protect long-range entanglement. We find that the frozen entanglement content in any length and the time up to which freezing occurs called the freezing terminal to follow a complementary relation for all ranges of interactions. However, we find that for a fixed range of entanglement, there exists a critical value of interaction length which leads to the maximum freezing terminal.
Quantum spin models with variable-range interactions can exhibit certain quantum characteristics that a short-ranged model cannot possess. By considering the quantum XYZ model whose interaction strength between different sites varies either exponentially or polynomially, we report the creation of long-range entanglement in dynamics both in the absence and presence of system-bath interactions. Specifically, during closed dynamics, we determine a parameter regime from which the system should start its evolution so that the resulting state after quench can produce a high time-averaged entanglement having low fluctuations. Both in the exponential and power-law decays, it occurs when the magnetic field is weak and the interactions in the z-direction are nonvanishing. When part of the system interacts with the bath repeatedly or is attached to a collection of harmonic oscillators along with dephasing noise in the z-direction, we observe that long-range entanglement of the subparts which are not attached with the environment remains constant with time in the beginning of the evolution, known as freezing of entanglement, thereby demonstrating a method to protect long-range entanglement. We find that the frozen entanglement content in any length and the time up to which freezing occurs called the freezing terminal to follow a complementary relation for all ranges of interactions. However, we find that for a fixed range of entanglement, there exists a critical value of interaction length which leads to the maximum freezing terminal.
We show that bipartite entanglement in an one-dimensional quantum spin model undergoing time evolution due to local Markovian environments can be frozen over time. We demonstrate this by using a number of paradigmatic quantum spin models including the anisotropic XY model in the presence of a uniform and an alternating transverse magnetic field (ATXY), the XXZ model, the XYZ model, and the ${J}_{1}\ensuremath{-}{J}_{2}$ model involving the next-nearest-neighbor interactions. We show that the length of the freezing interval, for a chosen pair of nearest-neighbor spins, may remain independent of the length of the spin chain, for example, in paramagnetic phases of the ATXY model, indicating a scale invariance. Freezing of entanglement is found to be robust against a change in the environment temperature, the presence of disorder in the system, and whether the noise is dissipative or not dissipative. Moreover, we connect the freezing of entanglement with the propagation of information through a quantum many-body system, as considered in the Lieb-Robinson theorem. We demonstrate that the variation of the freezing duration exhibits a quadratic behavior against the distance of the nearest-neighbor spin pair from the noise source, obtained from exact numerical simulations, in contrast to the linear one as predicted by the Lieb-Robinson theorem.
An exactly solvable model for the decoherence of one and two-qubit states interacting with a spin bath, in the presence of a time-dependent magnetic field is studied. The magnetic field is static along $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{z}$ direction and oscillatory in the transverse plane. The transition probability and Rabi oscillations between the spin states of a single qubit is shown to depend on the size of bath, the distribution of qubit-bath couplings, and the initial bath polarization. In contrast to the fast Gaussian decay for short times, the polarization of the qubit shows an oscillatory power-law decay for long times. The loss of entanglement for the maximally entangled two-qubit states can be controlled by tuning the frequency of the rotating field. The decay rates of entanglement and purity for all the Bell states are the same when the qubits are noninteracting, and different when they are interacting.
In distributed quantum networks, interacting spin systems can mediate the generation of highly entangled links between distant nodes. We investigate the role of effective parity-time (PT)-symmetric non-Hermitian spin-1/2 bulks weakly coupled to two quantum links, obtained due to the environmental interactions affecting both the bulk and the links. Focusing on effective non-Hermitian nearest-neighbor (NN) Su-Schrieffer-Heeger (SSH) models, we analyze how non-Hermiticity influences the dynamical formation of long-distance entanglement (LDE). For a paradigmatic model consisting of a quantum XX bulk subjected to imaginary staggered magnetic fields, we analytically determine the exceptional points arising from the resulting bulk-mediated interactions between the links. Combining analytical and numerical methods, we demonstrate that an initially fully separable state can dynamically evolve into highly entangled link states near these exceptional points in the broken regime. Further, after optimizing over time and system parameters, near-unit time-averaged entanglement between the links emerges under weak imaginary magnetic fields and bulk-link couplings, which cannot be attained in the corresponding Hermitian systems. Moreover, the non-Hermitian dynamics exhibit a freezing of high entanglement in the vicinity of exceptional points, a feature absent in Hermitian counterparts. We also identify regimes of long-range interaction strengths that yield a higher time-averaged entanglement than the corresponding NN models. Furthermore, we establish that LDE persists in the stationary regime, highlighting the promise of engineered non-Hermitian dynamics for realizing robust and frozen entangled links in quantum networks.
The study of coherence dynamics in open quantum systems, specifically addressing various physical realizations of quantum systems and environments, is a long-standing and central pillar of quantum science and technology. As such, a large body of work establishes a firm theoretical understanding of these processes. Nevertheless, a fundamental aspect of decoherence dynamics, namely the central limit theorem of qubit dephasing in the central spin model, which leads to a Gaussian approximation, lacks formal proof in realistically relevant scenarios. Here we prove this approximation for a bath depicted by an Ising spin system, in the presence of disorder and several (most relevant) functional forms of qubit-bath coupling. Importantly, we show that in certain cases, namely for short-range (exponentially decaying) coupling, this approximation breaks. These results provide a theoretical framework for studying decoherence dynamics in various systems and lead to insights into dephasing behavior with implications for applications in quantum information, quantum computing, and other quantum technologies.
CoNb2O6 is a rare realization of the transverse-field Ising model, making it a useful tool for studying both equilibrium and nonequilibrium many-body quantum physics. Despite a large body of work dedicated to characterizing this material, details of the ordered states in the presence of relatively weak transverse fields have not been discussed in detail. Here, we present a detailed study of CoNb2O6 via ac susceptibility measurements in order to further characterize its low-temperature behavior in the presence of a transverse field. Specifically, we call attention to an unconventional freezing transition in zero field below TF=1.2 K, occurring within the well-known commensurate antiferromagnetic (CAFM) state that onsets at TN2=1.9 K. We performed a series of transverse-field quenches into this frozen state, which resulted in a slowly relaxing susceptibility, ${\ensuremath{\chi}}^{\ensuremath{'}}(t)$, that followed a logarithmic decay within the time range measured. We discuss the frozen state in the context of the freezing of previously discussed ``free'' chains arising from domain walls between the four degenerate sublattices of the CAFM state. We also attempted to observe Kibble-Zurek scaling by quenching the transverse field into the frozen state at different rates. This produced a null result; the behavior can be fully explained by coarsening of domains over the time scale of the quenches. The absence of a clear Kibble-Zurek scaling is itself surprising, given the proposed ubiquity of the phenomenon for general second-order phase transitions.
The entanglement of two qubits, each defined as an effective two-level, spin 1/2 system, is investigated for the case that the qubits interact via a Heisenberg XY interaction and are subject to decoherence due to population relaxation and thermal effects. For zero temperature, the time-dependent concurrence is studied analytically and numerically for some typical initial states, including a separable (unentangled) initial state. An analytical formula for non-zero steady state concurrence is found for any initial state, and optimal parameter values for maximizing steady state concurrence are given. The steady state concurrence is found analytically to remain non-zero for low, finite temperatures. We also identify the contributions of global and local coherence to the steady state entanglement.