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Register a new userAvalanche of entanglement and correlations at quantum phase transitions
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Added by
Konstantin Krutitsky
Publication date
2016
fields
Physics
and research's language is
English
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We study the ground-state entanglement in the quantum Ising model with nearest neighbor ferromagnetic coupling $J$ and find a sequential increase of entanglement depth with growing $J$. This entanglement avalanche starts with two-point entanglement, as measured by the concurrence, and continues via the three-tangle and four-tangle, until finally, deep in the ferromagnetic phase for $J=infty$, arriving at pure $ell$-partite (GHZ type) entanglement of all $ell$ spins. Comparison with the two, three, and four-point correlations reveals a similar sequence and shows strong ties to the above entanglement measures for small $J$. However, we also find a partial inversion of the hierarchy, where the four-point correlation exceeds the three- and two-point correlations, well before the critical point is reached. Qualitatively similar behavior is also found for the Bose-Hubbard model, suggesting that this is a general feature of a quantum phase transition. This should have far reaching consequences for approximations starting from a mean-field limit.
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In this work, we establish a general theory of phase transitions and quantum entanglement in the equilibrium state at arbitrary temperatures. First, we derived a set of universal functional relations between the matrix elements of two-body reduced density matrix of the canonical density matrix and the Helmholtz free energy of the equilibrium state, which implies that the Helmholtz free energy and its derivatives are directly related to entanglement measures because any entanglement measures are defined as a function of the reduced density matrix. Then we show that the first order phase transitions are signaled by the matrix elements of reduced density matrix while the second order phase transitions are witnessed by the first derivatives of the reduced density matrix elements. Near second order phase transition point, we show that the first derivative of the reduced density matrix elements present universal scaling behaviors. Finally we establish a theorem which connects the phase transitions and entanglement at arbitrary temperatures. Our general results are demonstrated in an experimentally relevant many-body spin model.
We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of modes (electrons coupled through the eta-pairing mechanism). We first detect the two/multi-partite nature of each quantum phase transition by a comparative study of the singularities of Von Neumann entropy and quantum mutual information. We establish the existing relations between the correlations in the momentum representation and those exhibited in the complementary picture: the direct lattice representation. The presence of multipartite entanglement is then investigated in detail through the Q-measure, namely a generalization of the Meyer-Wallach measure of entanglement. Such a measure becomes increasingly sensitive to correlations of a multipartite nature increasing the size of the reduced density matrix. In momentum space, we succeed in obtaining the latter for our system at arbitrary size and we relate its behaviour to the nature of the various QPTs.
We show that entanglement monotones can characterize the pronounced enhancement of entanglement at a quantum phase transition if they are sensitive to long-range high order correlations. These monotones are found to develop a sharp peak at the critical point and to exhibit universal scaling. We demonstrate that similar features are shared by noise correlations and verify that these experimentally accessible quantities indeed encode entanglement information and probe separability.
We study the behavior of bipartite entanglement at fixed von Neumann entropy. We look at the distribution of the entanglement spectrum, that is the eigenvalues of the reduced density matrix of a quantum system in a pure state. We report the presence of two continuous phase transitions, characterized by different entanglement spectra, which are deformations of classical eigenvalue distributions.
Dissimilar notions of quantum correlations have been established, each being motivated through particular applications in quantum information science and each competing for being recognized as the most relevant measure of quantumness. In this contribution, we experimentally realize a form of quantum correlation that exists even in the absence of entanglement and discord. We certify the presence of such quantum correlations via negativities in the regularized two-mode Glauber-Sudarshan function. Our data show compatibility with an incoherent mixture of orthonormal photon-number states, ruling out quantum coherence and other kinds of quantum resources. By construction, the quantumness of our state is robust against dephasing, thus requiring fewer experimental resources to ensure stability. In addition, we theoretically show how multimode entanglement can be activated based on the generated, nonentangled state. Therefore, we implement a robust kind of nonclassical photon-photon correlated state with useful applications in quantum information processing.
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