XX Chain Research Articles

PERFECT STATE TRANSFER IN XX CHAINS INDUCED BY BOUNDARY MAGNETIC FIELDS

A recent numerical study of short chains found near-perfect quantum state transfer between the boundary sites of a spin-1/2 XX chain if a sufficiently strong magnetic field acts on these sites. We show that the phenomenon is based on a pair of states strongly localized at the boundaries of the system and provide a simple quantitative analytical explanation.

Entropy of an acoustic black hole in Bose-Einstein condensates

We compute the entanglement entropy associated to the Hawking emission of a $(1+1)$-dimensional acoustic black hole in a Bose-Einstein condensate. We use the brick wall model proposed by 't Hooft, adapted to the momentum space, in order to tackle the case when high frequency dispersion is taken in account. As expected, we find that in the hydrodynamic limit the entropy only depends on the size of the box in the near-horizon region, as for gravitational $(1+1)$-dimensional black holes. When dispersion effects are considered, we find a correction that depends on the square of the size of the near-horizon region measured in units of healing length, very similar to the universal correction to the entropy found in the case of spin-1/2 Heisenberg XX chains.

Generation of non-equilibrium thermal quantum discord and entanglement in a three-spin XX chain by multi-spin interaction and an external magnetic field

The generation of non-equilibrium thermal quantum discord and entanglement is investigated in a three-spin chain whose two end spins are respectively coupled to two thermal reservoirs at different temperatures. We show that the spin chain can be decoupled from the thermal reservoirs by homogeneously applying a magnetic field and including a strong three-spin interaction, and then the maximal steady-state quantum discord and entanglement in the two end spins can always be created. In addition, the present investigation may provide a useful approach to control coupling between a quantum system and its environment.

Entanglement, decoherence and thermal relaxation in exactly solvable models

Exactly solvable models provide an opportunity to study different aspects of reduced quantum dynamics in detail. We consider the reduced dynamics of a single spin in finite XX and XY spin 1/2 chains. First we introduce a general expression describing the evolution of the reduced density matrix. This expression proves to be tractable when the combined closed system (i.e. open system plus environment) is integrable. Then we focus on comparing decoherence and thermalization timescales in the XX chain. We find that for a single spin these timescales are comparable, in contrast to what should be expected for a macroscopic body. This indicates that the process of quantum relaxation of a system with few accessible states can not be separated in two distinct stages - decoherence and thermalization. Finally, we turn to finite-size effects in the time evolution of a single spin in the XY chain. We observe three consecutive stages of the evolution: regular evolution, partial revivals, irregular (apparently chaotic) evolution. The duration of the regular stage is proportional to the number of spins in the chain. We observe a "quiet and cold period" in the end of the regular stage, which breaks up abruptly at some threshold time.

Dynamic Properties of Spin-1/2 XX Chain with Three-Site Interactions of (XZY - YZX)-Type

Dynamic Properties of Spin-1/2 XX Chain with Three-Site Interactions of (XZY - YZX)-Type

Entanglement of Low-Energy Excitations in Conformal Field Theory

In a quantum critical chain, the scaling regime of the energy and momentum of the ground state and low-lying excitations are described by conformal field theory (CFT). The same holds true for the von Neumann and Rényi entropies of the ground state, which display a universal logarithmic behavior depending on the central charge. In this Letter we generalize this result to those excited states of the chain that correspond to primary fields in CFT. It is shown that the nth Rényi entropy is related to a 2n-point correlator of primary fields. We verify this statement for the critical XX and XXZ chains. This result uncovers a new link between quantum information theory and CFT.

Quantum state transfer in a XX chain with impurities

One spin excitation states are involved in the transmission of quantum states and entanglement through a quantum spin chain, the localization properties of these states are crucial to achieve the transfer of information from one extreme of the chain to the other. We investigate the bipartite entanglement and localization of the one excitation states in a quantum XX chain with one impurity. The bipartite entanglement is obtained using the concurrence and the localization is analyzed using the inverse participation ratio (IPR). Changing the strength of the exchange coupling of the impurity allows us to control the number of localized or extended states. The analysis of the IPR allows us to identify scenarios where the transmission of quantum states or entanglement can be achieved with a high degree of fidelity. In particular, we identify a regime where the transmission of quantum states between the extremes of the chain is executed in a short transmission time ∼N/2, where N is the number of spins in the chain, and with a large fidelity.

Symmetry and Subspace Controllability for Spin Networks With a Single-Node Control

We consider the relation of symmetries and subspace controllability for spin networks with XXZ coupling subject to control of a single node by a local potential (Z-control). Such networks decompose into excitation subspaces. Focusing on the single excitation subspace it is shown that for single-node Z-controls external symmetries are characterized by eigenstates of the system Hamiltonian that have zero overlap with the control node, and there are no internal symmetries. It is further shown that there are symmetries that persist even in the presence of random perturbations. For uniformly coupled XXZ chains a characterization of all possible symmetries is given, which shows a strong dependence on the position of the node we control. Finally, it is shown rigorously for uniform Heisenberg and XX chains subject to single-node Z-control that the lack of symmetry is not only necessary but sufficient for subspace controllability. The latter approach is then generalized to establish controllability results for simple branched networks.

Dynamical Simulation of Integrable and Nonintegrable Models in the Heisenberg Picture

The numerical simulation of quantum many-body dynamics is typically limited by the linear growth of entanglement with time. Recently numerical studies have shown that for 1D Bethe-integrable models the simulation of local operators in the Heisenberg picture can be efficient. Using the spin-1/2 XX chain as generic example of an integrable model that can be mapped to free fermions, we provide a simple explanation for this. We show furthermore that the same reduction of complexity applies to operators that have a high-temperature autocorrelation function which decays slower than exponential, i.e., with a power law. Thus efficient simulability may already be implied by a single conservation law as we will illustrate numerically for the spin-1 XXZ model.

Entanglement in a two-spin (1/2, 3/2) mixed-spin Heisenberg XX chain with an inhomogeneous external magnetic field

By using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XX chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature is higher than the results of the spin-1/2 chain and (1/2,1) mixed-spin chain. And by adjusting the nonuniform parameter b, one is able to obtain more entanglement at a higher temperature.

The ground-state entanglement in the spin-XX chain with a magnetization current

The ground-state entanglement in a transverse spin-1/2 XX chain with a magnetization current is studied. By introducing a magnetization current to the system, a quantum phase transition to current-carrying phase may be presented with the variation of the driving field λ for the magnetic field h > 1; and the ground-state entanglement arises simultaneously at the critical point of quantum phase transition. In our model, the introduction of magnetization current may result in more entanglement between any two nearest-neighbour spins.

Effects of impurity on fidelity of quantum state transfer via spin channels

By adopting the concept of fidelity, we investigated efficiency of quantum state transfer with the XX chain as the quantum channel. Different from the previous works, we concentrated on effects of spin and magnetic impurity on fidelity of quantum state transfer. Our results revealed that the spin impurity cannot prevent one from implementing perfect transfer of an arbitrary one-qubit pure state across the spin channel, however, the presence of magnetic impurity or both spin and magnetic impurities may destroy the otherwise perfect spin channels.

Quantum discord induced by a spin chain with quantum phase transition

We study quantum discord induced by a quantum-critical environment. Two spin halves are independently coupled to the common environment which is modelled by the Ising spin chain in a transverse field. During the time evolution, non-zero discord is induced whereas entanglement cannot be induced due to the special initial state chosen by us. For some cases we analytically obtain quantum discord and its geometric measure. From the numerical results, one can observe that induced quantum discord increases quickly from zero to a steady value when the environment approaches the critical point. Moreover, induced discord may reach its maximum close to the critical point. The special phenomena of induced discord can be used to indicate quantum criticality. We also consider another environment modelled by the spin-1/2 XX chain with three-spin interaction, which also displays second-order quantum phase transition.

A matrix product solution for a nonequilibrium steady state of an XX chain

A one-dimensional XX spin chain of finite length coupled to reservoirs at both ends is solved exactly in terms of a matrix product state ansatz. An explicit representation of matrices of fixed dimension 4 independent of the chain length is found. Expectations of all observables are evaluated, showing that all connected correlations, apart from the nearest neighbor z–z, are zero.

Universal corrections to scaling for block entanglement in spin-1/2 XX chains

We consider the Rényi entropies in the one-dimensional spin-1/2 Heisenberg XX chain in amagnetic field. The case n = 1 corresponds to the von Neumann ‘entanglement’ entropy. Using a combination of methodsbased on the generalized Fisher–Hartwig conjecture and a recurrence relation connected tothe Painlevé VI differential equation we obtain the asymptotic behaviour, accurate to order, of the Rényi entropies for large block lengths . For n = 1, 2, 3, 10 this constitutesthe 3, 6, 10, 48 leading termsrespectively. The o(1) contributions are found to exhibit a rich structure of oscillatorybehaviour, which we analyse in some detail both for finiten and in the limit .

Casimir effect in the nonequilibrium steady state of a quantum spin chain

We present a fully microscopics-based calculation of the Casimir effect in a nonequilibrium system, namely an energy flux driven quantum XX chain. The force between the walls (transverse-field impurities) is calculated in a nonequilibrium steady state which is prepared by letting the system evolve from an initial state with the two halves of the chain prepared at equilibrium at different temperatures. The steady state emerging in the large-time limit is homogeneous but carries an energy flux. The Casimir force in this nonequilibrium state is calculated analytically in the limit when the transverse fields are small. We find that the the Casimir force range is reduced compared to the equilibrium case, and suggest that the reason for this is the reduction of fluctuations in the flux carrying steady state.

Quantum phase transition and entanglement in Heisenberg XX spin chain with impurity

In this paper, we study the quantum phase transition and the effect of impurity on the thermal entanglement between any two lattices in three-qubit Heisenberg XX chain in a uniform magnetic field. We show that the quantum phase transition always appears when impurity parameter is an arbitrary constant and unequal to zero, the external magnetic field and impurity parameters have a great effect on it. Also, there exists a relation between the quantum phase transition and the entanglement. By modulating the temperature, magnetic field and the impurity parameters, the entanglement between any two lattices can exhibit platform-like behaviour, which can be used to realize entanglement switch.

Multipartite entanglement in the Heisenberg XX chain with impurity

We studied the entanglements of the Heisenberg XX chain with impurity in the presence of a uniform magnetic field along the z axes by means of negativity. Through analyzing NL-A and N1-A, we show that the critical temperatures for nonzero negativities depend on the impurity parameter J1 and the magnetic field B. It is also shown that as qubit L increases, the entanglements increase when L is odd but decrease when L is even. And the entanglements of the even-qubit chains are larger than those of the odd-qubit chains. The condition is similar with L=3 for NL-A when qubit L is odd, but the entanglements increase with the increase of even qubit L.

Operator fidelity approach to the quantum phase transition of the spin-1/2 XX chain with three-spin interaction and the (1/2,1) XXZ mixed-spin chain

We make use of the operator fidelity and its susceptibility to study the quantum phase transition (QPT) of the spin-1/2 XX spin chain with three-spin interaction. The analytical results of operator fidelity and the susceptibility are obtained. From the numerical results one can see that the operator fidelity and its susceptibility present nontrivial behaviors at the critical point. We also consider the (1/2, 1) XXZ mixed-spin chain in which the ground states are degenerate. The operator fidelity approach is still effective to indicate the QPT in this system. We also generally analyze the relation between operator fidelity and QPT.

Entanglement in a periodic XX model with long-range interactions

The nearest-neighbor concurrence and block–block entanglement of a period-two XX chain with a transverse field h and a uniform long-range interaction I in the z-direction are studied numerically. It is found that when I > 0, the nearest-neighbor concurrence and block–block entanglement are both discontinuous at the critical points, where the system undergoes first-order quantum phase transitions. When the long-range interaction is weak , there are two critical points and . Between these two points there is a critical region, where the block–block entanglement . In one noncritical region is equal to a non-zero constant while in the other noncritical region is always zero. Furthermore, the effect of periodicity on the concurrence and block–block entanglement is discussed.