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Register a new userGlobal entanglement and quantum criticality in spin chains
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Entanglement in quantum XY spin chains of arbitrary length is investigated via a recently-developed global measure suitable for generic quantum many-body systems. The entanglement surface is determined over the phase diagram, and found to exhibit structure richer than expected. Near the critical line, the entanglement is peaked (albeit analytically), consistent with the notion that entanglement--the non-factorization of wave functions--reflects quantum correlations. Singularity does, however, accompany the critical line, as revealed by the divergence of the field-derivative of the entanglement along the line. The form of this singularity is dictated by the universality class controlling the quantum phase transition.
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Isotropic XX models of one-dimensional spin-1/2 chains are investigated with the aim to elucidate the formal structure and the physical properties that allow these systems to act as channels for long-distance, high-fidelity quantum teleportation. We introduce two types of models: I) open, dimerized XX chains, and II) open XX chains with small end bonds. For both models we obtain the exact expressions for the end-to-end correlations and the scaling of the energy gap with the length of the chain. We determine the end-to-end concurrence and show that model I) supports true long-distance entanglement at zero temperature, while model II) supports {it ``quasi long-distance} entanglement that slowly falls off with the size of the chain. Due to the different scalings of the gaps, respectively exponential for model I) and algebraic in model II), we demonstrate that the latter allows for efficient qubit teleportation with high fidelity in sufficiently long chains even at moderately low temperatures.
We investigate the performance of superconducting flux qubits for the adiabatic quantum simulation of long distance entanglement (LDE), namely a finite ground-state entanglement between the end spins of a quantum spin chain with open boundary conditions. As such, LDE can be considered an elementary precursor of edge modes and topological order. We discuss two possible implementations which simulate open chains with uniform bulk and weak end bonds, either with Ising or with XX nearest-neighbor interactions. In both cases we discuss a suitable protocol for the adiabatic preparation of the ground state in the physical regimes featuring LDE. In the first case the adiabatic manipulation and the Ising interactions are realized using dc currents, while in the second case microwaves fields are used to control the smoothness of the transformation and to realize the effective XX interactions. We demonstrate the adiabatic preparation of the end-to-end entanglement in chains of four qubits with realistic parameters and on a relatively fast time scale.
Frustration-free (FF) spin chains have a property that their ground state minimizes all individual terms in the chain Hamiltonian. We ask how entangled the ground state of a FF quantum spin-s chain with nearest-neighbor interactions can be for small values of s. While FF spin-1/2 chains are known to have unentangled ground states, the case s=1 remains less explored. We propose the first example of a FF translation-invariant spin-1 chain that has a unique highly entangled ground state and exhibits some signatures of a critical behavior. The ground state can be viewed as the uniform superposition of balanced strings of left and right parentheses separated by empty spaces. Entanglement entropy of one half of the chain scales as log(n)/2 + O(1), where n is the number of spins. We prove that the energy gap above the ground state is polynomial in 1/n. The proof relies on a new result concerning statistics of Dyck paths which might be of independent interest.
Recent theoretical work has shown that the competition between coherent unitary dynamics and stochastic measurements, performed by the environment, along wavefunction trajectories can give rise to transitions in the entanglement scaling. In this work, complementary to these previous studies, we analyze a situation where the role of Hamiltonian and dissipative dynamics is reversed. We consider an engineered dissipation, which stabilizes an entangled phase of a quantum spin$-1/2$ chain, while competing single-particle or interacting Hamiltonian dynamics induce a disentangled phase. Focusing on the single-particle unitary dynamics, we find that the system undergoes an entanglement transition from a logarithmic growth to an area law when the competition ratio between the unitary evolution and the non-unitary dynamics increases. We evidence that the transition manifests itself in state-dependent observables at a finite competition ratio for Hamiltonian and measurement dynamics. On the other hand, it is absent in trajectory-averaged steady-state dynamics, governed by a Lindblad master equation: although purely dissipative dynamics stabilizes an entangled state, for any non-vanishing Hamiltonian contribution the system ends up irremediably in a disordered phase. In addition, a single trajectory analysis reveals that the distribution of the entanglement entropy constitutes an efficient indicator of the transition. Complementarily, we explore the competition of the dissipation with coherent dynamics generated by an interacting Hamiltonian, and demonstrate that the entanglement transition also occurs in this second model. Our results suggest that this type of transition takes place for a broader class of Hamiltonians, underlining its robustness in monitored open quantum many-body systems.
We introduce an experimentally accessible network representation for many-body quantum states based on entanglement between all pairs of its constituents. We illustrate the power of this representation by applying it to a paradigmatic spin chain model, the XX model, and showing that it brings to light new phenomena. The analysis of these entanglement networks reveals that the gradual establishment of quasi-long range order is accompanied by a symmetry regarding single-spin concurrence distributions, as well as by instabilities in the network topology. Moreover, we identify the existence of emergent entanglement structures, spatially localised communities enforced by the global symmetry of the system that can be revealed by model-agnostic community detection algorithms. The network representation further unveils the existence of structural classes and a cyclic self-similarity in the state, which we conjecture to be intimately linked to the community structure. Our results demonstrate that the use of tools and concepts from complex network theory enables the discovery, understanding, and description of new physical phenomena even in models studied for decades.
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