Entanglement, fidelity, and quantum phase transition in antiferromagnetic-ferromagnetic alternating Heisenberg chain

The fidelity and entanglement entropy in an antiferromagnetic-ferromagnetic alternating Heisenberg chain are investigated by using the method of density-matrix renormalization-group. The effects of anisotropy on fidelity and entanglement entropy are investigated. The relations between fidelity, entanglement entropy and quantum phase transition are analyzed. It is found that the quantum phase transition point can be well characterized by both the ground-state entropy and fidelity for large system.     

Two-site entropy and quantum phase transitions in low-dimensional models

We propose a new approach to study quantum phase transitions in low-dimensional lattice models. It is based on studying the von Neumann entropy of two neighboring central sites in a long chain. It is demonstrated that the procedure works equally well for fermionic and spin models, and the two-site entropy is a better indicator of quantum phase transition than calculating gaps, order parameters, or the single-site entropy. The method is especially convenient when the density-matrix renormalization-group algorithm is used.     

Quantum phase transition and entanglement in Li atom system

By use of the exact diagonalization method, the quantum phase transition and entanglement in a 6-Li atom system are studied. It is found that entanglement appears before the quantum phase transition and disappears after it in this exactly solvable quantum system. The present results show that the von Neumann entropy, as a measure of entanglement, may reveal the quantum phase transition in this model.     

Entanglement and criticality in quantum impurity systems

We investigate the entanglement between a spin and its environment in impurity systems which exhibit a second-order quantum phase transition separating a delocalized and a localized phase for the spin. As an application, we employ the spin-boson model, describing a two-level system (spin) coupled to a sub-Ohmic bosonic bath with power-law spectral density, J(omega) proportional to omega(s) and 0 < s < 1. Combining Wilson's numerical renormalization group method and hyperscaling relations, we demonstrate that the entanglement between the spin and its environment is always enhanced at the quantum phase transition resulting in a visible cusp (maximum) in the entropy of entanglement. We formulate a correspondence between criticality and impurity entanglement entropy, and the relevance of these ideas to nanosystems is outlined.     

Phase transitions in small systems: Microcanonical vs. canonical ensembles

We compare phase transition(-like) phenomena in small model systems for both microcanonical and canonical ensembles. The model systems correspond to a few classical (non-quantum) point particles confined in a one-dimensional box and interacting via Lennard-Jones-type pair potentials. By means of these simple examples it can be shown already that the microcanonical thermodynamic functions of a small system may exhibit rich oscillatory behavior and, in particular, singularities (non-analyticities) separating different microscopic phases. These microscopic phases may be identified as different microphysical dissociation states of the small system. The microscopic oscillations of microcanonical thermodynamic quantities (e.g., temperature, heat capacity, or pressure) should in principle be observable in suitably designed evaporation/dissociation experiments (which must realize the physical preconditions of the microcanonical ensemble). By contrast, singular phase transitions cannot occur, if a small system is embedded into an infinite heat bath (thermostat), corresponding to the canonical ensemble. For the simple model systems under consideration, it is nevertheless possible to identify a smooth canonical phase transition by studying the distribution of complex zeros of the canonical partition function.     

Quantum phase transition in the one-dimensional quantum Heisenberg XYZ model with Dzyaloshinskii–Moriya interaction

We investigated the quantum phase transition occurred in one-dimensional quantum Heisenberg XYZ model with Dzyaloshinskii–Moriya interaction via the infinite matrix product state representation with the infinite time evolving block decimation method. Entanglement entropy and local order parameter in and near the transition point are given. Scaling relation plays crucial roles on identifying a quantum system with a physically different phase. The scaling relation of the entanglement entropy, local order parameter and finite correlation length with the truncation dimension are also obtained. All the interesting results give a theoretical justification for the high accuracy of infinite time evolved block decimation algorithm which works in the thermodynamical limit.     

Quantum information entropy for one-dimensional system undergoing quantum phase transition

Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic "Landau" potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy S_x and the momentum entropy S_p at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition.     

Diagonal entropy in many-body systems: Volume effect and quantum phase transitions

We investigate the diagonal entropy(DE) of the ground state for quantum many-body systems, including the XY model and the Ising model with next nearest neighbor interactions. We focus on the DE of a subsystem of L continuous spins. We show that the DE in many-body systems, regardless of integrability, can be represented as a volume term plus a logarithmic correction and a constant offset. Quantum phase transition points can be explicitly identified by the three coefficients thereof. Besides, by combining entanglement entropy and the relative entropy of quantum coherence, as two celebrated representatives of quantumness, we simply obtain the DE, which naturally has the potential to reveal the information of quantumness. More importantly, the DE is concerning only the diagonal form of the ground state reduced density matrix, making it feasible to measure in real experiments, and therefore it has immediate applications in demonstrating quantum supremacy on state-of-the-art quantum simulators.     

Quantum entanglement in the Sachdev–Ye–Kitaev model and its generalizations

Entanglement is one of the most important concepts in quantum physics. We review recent progress in understanding the quantum entanglement in many-body systems using large-N solvable models: the Sachdev–Ye–Kitaev (SYK) model and its generalizations. We present the study of entanglement entropy in the original SYK model using three different approaches: the exact diagonalization, the eigenstate thermalization hypothesis, and the pathintegral representation. For coupled SYK models, the entanglement entropy shows linear growth and saturation at the thermal value. The saturation is related to replica wormholes in gravity. Finally, we consider the steady-state entanglement entropy of quantum many-body systems under repeated measurements. The traditional symmetry breaking in the enlarged replica space leads to the measurement-induced entanglement phase transition.     

Multipartite entanglement dynamics and decoherence from a quantum-critical environment

We investigate the entanglement dynamics and decoherence of a multipartite system under an environment which can exhibit a quantum phase transition. Our result implies that the entanglement evolution depends not only on the size of the system and the quantum states of concern but also on the environment. In the sense of the linear entropy to measure decoherence induced by the environment, the decoherence-free subspaces have been identified for our model.