On entanglement evolution across defects in critical chains

We consider a local quench where two free-fermion half-chains are coupled via a defect. We show that the logarithmic increase of the entanglement entropy is governed by the same effective central charge which appears in the ground-state properties and which is known exactly. For unequal initial filling of the half-chains, we determine the linear increase of the entanglement entropy.Comment: 11 pages, 5 figures, minor changes, reference adde

On reduced density matrices for disjoint subsystems

We show that spin and fermion representations for solvable quantum chains lead in general to different reduced density matrices if the subsystem is not singly connected. We study the effect for two sites in XX and XY chains as well as for sublattices in XX and transverse Ising chains.Comment: 10 pages, 4 figure

On the relation between entanglement and subsystem Hamiltonians

We show that a proportionality between the entanglement Hamiltonian and the Hamiltonian of a subsystem exists near the limit of maximal entanglement under certain conditions. Away from that limit, solvable models show that the coupling range differs in both quantities and allow to investigate the effect.Comment: 7 pages, 2 figures version2: minor changes, typos correcte

Entanglement spectra of critical and near-critical systems in one dimension

The entanglement spectrum of a pure state of a bipartite system is the full set of eigenvalues of the reduced density matrix obtained from tracing out one part. Such spectra are known in several cases to contain important information beyond that in the entanglement entropy. This paper studies the entanglement spectrum for a variety of critical and near-critical quantum lattice models in one dimension, chiefly by the iTEBD numerical method, which enables both integrable and non-integrable models to be studied. We find that the distribution of eigenvalues in the entanglement spectra agrees with an approximate result derived by Calabrese and Lefevre to an accuracy of a few percent for all models studied. This result applies whether the correlation length is intrinsic or generated by the finite matrix size accessible in iTEBD. For the transverse Ising model, the known exact results for the entanglement spectrum are used to confirm the validity of the iTEBD approach. For more general models, no exact result is available but the iTEBD results directly test the hypothesis that all moments of the reduced density matrix are determined by a single parameter.Comment: 6 pages, 5 figure

Exact relationship between the entanglement entropies of XY and quantum Ising chains

We consider two prototypical quantum models, the spin-1/2 XY chain and the quantum Ising chain and study their entanglement entropy, S(l,L), of blocks of l spins in homogeneous or inhomogeneous systems of length L. By using two different approaches, free-fermion techniques and perturbational expansion, an exact relationship between the entropies is revealed. Using this relation we translate known results between the two models and obtain, among others, the additive constant of the entropy of the critical homogeneous quantum Ising chain and the effective central charge of the random XY chain.Comment: 6 page

Entanglement evolution after connecting finite to infinite quantum chains

We study zero-temperature XX chains and transverse Ising chains and join an initially separate finite piece on one or on both sides to an infinite remainder. In both critical and non-critical systems we find a typical increase of the entanglement entropy after the quench, followed by a slow decay towards the value of the homogeneous chain. In the critical case, the predictions of conformal field theory are verified for the first phase of the evolution, while at late times a step structure can be observed.Comment: 15 pages, 11 figure

Half the entanglement in critical systems is distillable from a single specimen

We establish that the leading critical scaling of the single-copy entanglement is exactly one half of the entropy of entanglement of a block in critical infinite spin chains in a general setting, using methods of conformal field theory. Conformal symmetry imposes that the single-copy entanglement for critical many-body systems scales as E_1(\rho_L)=(c/6) \log L- (c/6) (\pi^2/\log L) + O(1/L), where L is the number of constituents in a block of an infinite chain and c corresponds to the central charge. This proves that from a single specimen of a critical chain, already half the entanglement can be distilled compared to the rate that is asymptotically available. The result is substantiated by a quantitative analysis for all translationally invariant quantum spin chains corresponding to general isotropic quasi-free fermionic models. An analytic example of the XY model shows that away from criticality the above simple relation is only maintained near the quantum phase transition point.Comment: 4 pages RevTeX, 1 figure, final versio

Spin Transport Properties in Heisenberg Antiferromagnetic Spin Chains: Spin Current induced by Twisted Boundary Magnetic Fields

Spin transport properties of the one-dimensional Heisenberg antiferromagnetic spin systems for both $S=1/2$ and S=1 are studied by applying twisted boundary magnetic field. The spin current displays significantly different behavior of the spin transport properties between $S=1/2$ and S=1 cases. For the spin-half case, a London equation for the current and the detection of an alternating electric field are proposed for the linear response regime. The correlation functions reveal the spiral nature of spin configuration for both ground state and the spinon excitations. For the spin-one chain otherwise, a kink is generated in the ground state for the size is larger than the correlation length, leading to an exponential dependence of spin current with respect to the chains length. The midgap state emerges from the degenerate ground state even for small boundary fields.Comment: 4 pages, 5 figure

Critical behaviour in parabolic geometries

We study two-dimensional systems with boundary curves described by power laws. Using conformal mappings we obtain the correlations at the bulk critical point. Three different classes of behaviour are found and explained by scaling arguments which also apply to higher dimensions. For an Ising system of parabolic shape the behaviour of the order at the tip is also found.Comment: Old paper, for archiving. 6 pages, 1 figure, epsf, IOP macr