Narrow Results

We apply a meron cluster algorithm to the XY spin chain, which describes a quantum rotor. This is a multi-cluster simulation supplemented by an improved estimator, which deals with objects of half-integer topological charge. This method is powerful enough to provide precise results for the model with a θ-term — it is therefore one of the rare examples, where a system with a complex action can be solved numerically. In particular we measure the correlation length, as well as the topological and magnetic susceptibility. We discuss the algorithmic efficiency in view of the critical slowing down. Due to the excellent performance that we observe, it is strongly motivated to work on new applications of meron cluster algorithms in higher dimensions.

Recently a significant progress in matching the anomalous dimensions of certain class of operators in N = 4 SYM and rotating strings was made. The correspondence was established mainly by use of Bethe ansatz technique applied to the spin s Heisenberg chain model. In a recent paper,¹⁶ the author suggested to solve the Heisenberg model by use of sigma model approach. In this current work we generalize the solutions presented in Ref. 16 and comment on the dual string theory. It turns out that our solution is related to a generalized ansatz for rotating strings which can be reduced to the so-called Neumann–Rosochatius integrable system. We comment on the spin chain sigma model and string solutions and the possibilities for a more precise formulation of the string/gauge theory correspondence.

We use the fermion-current basis in the space of local operators for the computation of the expectation values for the integrable spin chain of spins 1. Our main tool consists in expressing a given local operator in the fermion-current basis. For this, we use the same method as in the spin-1/2 case which is based on the arbitrariness of the Matsubara data.

We consider the two-dimensional O(3) non-linear sigma model with topological term using a lattice regularization introduced by Shankar and Read [Nucl. Phys. B336, 457 (1990)], that is suitable for studying the strong coupling regime. When this lattice model is quantized, the coefficient θ of the topological term is quantized as θ=2πs, with s integer or half-integer. We study in detail the relationship between the low energy behaviour of this theory and the one-dimensional spin-s Heisenberg model. We generalize the analysis to sigma models with other symmetries.

We examine the entanglement of thermal states of n spins interacting through an XYZ type Heisenberg coupling in the presence of a uniform magnetic field, by evaluating the negativities of bipartite partitions of the whole system and subsystems. The corresponding limit temperatures for entanglement are also examined. Results indicate that limit temperatures for global entanglement depend on the type of partition and are higher than those limiting pairwise entanglement, and that their behavior with anisotropy and applied magnetic field may differ significantly from that of the corresponding mean field critical temperature.

We study the zero-temperature critical behavior of dissipative quantum Ising spin chains of finite and infinite length. The spins interact with either constant or random nearest-neighbor ferro-magnetic couplings. They are also subject to a transverse field and coupled to an Ohmic bath of quantum harmonic oscillators. We analyze the coupled system performing Monte Carlo simulations on a classical two-dimensional counterpart model. We find that the coupling to the bath enhances the extent of the ordered phase, as it is known for mean-field spin-glass models. In the case of finite chains we show that a generalization of the Caldeira-Leggett localization transition exists.

We examine the quantum correlations of spin pairs in the ground state of finite XY chains in a transverse field, by evaluating the quantum discord as well as other related entropic measures of quantum correlations. A brief review of the latter, based on generalized entropic forms, is also included. It is shown that parity effects are of crucial importance for describing the behavior of these measures below the critical field. It is also shown that these measures reach full range in the immediate vicinity of the factorizing field, where they become independent of separation and coupling range. Analytical and numerical results for the quantum discord, the geometric discord and other measures in spin chains with nearest neighbor coupling and in fully connected spin arrays are also provided.

Genuine multipartite correlations in finite-size XY chains are studied as a function of the applied external magnetic field. We find that, for low temperatures, multipartite correlations are sensitive to the parity change in the Hamiltonian ground state, given that they exhibit a minimum every time that the ground state becomes degenerate. This implies that they can be used to detect the factorizing point, that is, the value of the external field such that, in the thermodynamical limit, the ground state becomes the tensor product of single-spin states.

The occurrence of fractional revival in quantum spin chains is examined. Analytic models where this phenomenon can be exhibited in exact solutions are provided. It is explained that spin chains with fractional revival can be obtained by isospectral deformations of spin chains with perfect state transfer.

This article reviews and extends recent results concerning entanglement and frustration in multipartite systems which have some symmetry with respect to the ordering of the particles. Starting point of the discussion are Bell inequalities: their relation to frustration in classical systems and their satisfaction for quantum states which have a symmetric extension. We then discussed how more general global symmetries of multipartite systems constrain the entanglement between two neighboring particles. We prove that maximal entanglement (measured in terms of the entanglement of formation) is always attained for the ground state of a certain nearest neighbor interaction Hamiltonian having the considered symmetry with the achievable amount of entanglement being a function of the ground state energy. Systems of Gaussian states, i.e. quantum harmonic oscillators, are investigated in more detail and the results are compared to what is known about ordered qubit systems.

We study translationally invariant rings of qubits with a finite number of sites N, and determine the maximal nearest-neighbor entanglement for a fixed z-component of the total spin. For small numbers of sites we present analytical results. We establish a relation between the maximal nearest-neighbor concurrence and the ground state energy of an XXZ spin model. This connection allows us to calculate the concurrence numerically for N≤24. We point out some interesting finite-size effects. Finally, we generalize our results beyond nearest neighbors.

We study the entanglement of a two-qubit one-dimensional XYZ Heisenberg chain in thermal equilibrium at temperature T. We obtain an analytical expression for the concurrence of this system in terms of the parameters of the Hamiltonian and T. We show that depending on the relation among the coupling constants, it is possible to increase the amount of entanglement of the system by increasing its anisotropy. We also show numerically that for all sets of the coupling constants entanglement is a monotonically decreasing function of the temperature T, proving that we must have at least an external magnetic field in the z-direction to obtain a behavior where entanglement increases with T.

We present a communication protocol for chains of permanently coupled qubits which achieves perfect quantum state transfer and which is efficient with respect to the number of chains employed in the scheme. The system consists of M uncoupled identical quantum chains. Local control (gates, measurements) is only allowed at the sending/receiving end of the chains. Under a quite general hypothesis on the interaction Hamiltonian of the qubits, a theorem can be proved which shows that the receiver is able to asymptotically recover the messages by repetitive monitoring of his qubits. We show how two parallel Heisenberg spin chains can be used as quantum wires. Perfect state transfer with a probability of failure lower than P in a Heisenberg chain of N spin-1/2 particles can be achieved in a time scale of the order of .

We show how defects in a spin chain described by the XXZ model may be used to generate entangled states, such as Bell and W states, and how to maintain them with high fidelity. We also discuss, in the presence of several excitations, how the anisotropy of the system may be combined with defects to effectively assist in the creation of the desired states.

Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. Until now, however, it was not clear whether this entanglement can be used as a resource in quantum information theory. Here we show that this entanglement is physical, demonstrating the principles of its extraction from a typical spin chain by scattering two particles off the system. Moreover, we show how to simulate this process using present-day optical lattice technology.

We analyze the communication efficiency of quantum information transfer along unmodulated spin chains by computing the communication rates of various protocols. The effects of temporal correlations are discussed, showing that they can be exploited to boost the transmission efficiency.

We explicitate the relation between Hamiltonians for networks of interacting qubits in the XYZ model and graph Laplacians. We then study evolution in networks in which all sites can communicate with each other. These are modeled by the complete graphK_n and called all-to-all networks. It turns out that K_n does not exhibit perfect state transfer (PST). However, we prove that deleting an edge in K_n allows PST between the two non-adjacent sites, when n is a multiple of four. An application is routing a qubit over n different sites, by switching off the link between the sites that we wish to put in communication. Additionally, we observe that, in certain cases, the unitary inducing evolution in K_n is equivalent to the Grover operator.

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.

Many proposals for quantum devices are based on qubits that are physically realized by the spin magnetic moment of some quantum object. In this case, one of the most often adopted strategies for manipulating qubits is that of using external magnetic fields. However, selectively applying a field just to one qubit may be a practically unattainable goal, as it is, for instance, in most solid-state based setups. In this work, we present a proposal for using nonlinear excitations of solitonic type to accomplish the above task. Our scheme entails the generation of a dynamical soliton in a classical spin-chain which is locally coupled with one qubit: as the soliton runs through, the qubit behaves, due to its interaction with the chain, as if it were subject to a magnetic field with a time dependence that follows from the soliton's features. We here present results for the time evolution of the qubit density-matrix induced by the overall dynamics of the above scheme.

We review some recent advances in understanding the correspondence between anomalous dimensions of gauge-invariant operators of planar N=4 SYM theory and string energies in AdS₅ × S⁵.