In quantum lattice models, in the large- $N$ limit, boundary conditions have little effect upon local observables for sites in the centers of the lattices. In this paper, we will study the boundary effects upon multipartite nonlocality (a kind of multipartite quantum correlation associated with Bell-type inequalities) in one-dimensional finite-size spin chains, both for zero temperature and for finite temperatures. We define a quantity $\frac{\ensuremath{\delta}\mathcal{S}}{\mathcal{S}}$ to characterize the boundary effects, where $\mathcal{S}$ is a measure of global multipartite nonlocality of the entire lattice, and $\ensuremath{\delta}\mathcal{S}$ is the difference of the measure induced by changing the boundary conditions. We find $\frac{\ensuremath{\delta}\mathcal{S}}{\mathcal{S}}$ does not vanish in the large- $N$ limit. Instead, at zero temperature, with the increase of $N$ , $\frac{\ensuremath{\delta}\mathcal{S}}{\mathcal{S}}$ would increase steadily in the vicinity of the quantum phase transition point of the models, and converge to a nonzero constant in noncritical regions. It shows clearly that boundary effects generally exist, in the form of multipartite correlations, in long chains. The boundary effects are explained by the competition between the two orders of the models. In addition, based on these numerical results, we construct a Bell inequality, which is violated by chains with periodic (closed) boundary conditions and not violated by chains with open boundary conditions. Furthermore, we study $\frac{\ensuremath{\delta}{\mathcal{S}}_{T}}{{\mathcal{S}}_{T}}$ of finite-size chains at finite temperatures, and show that boundary effects survive in finite temperature regions.In quantum lattice models, in the large-$N$ limit, boundary conditions have little effect upon local observables for sites in the centers of the lattices. In this paper, we will study the boundary effects upon multipartite nonlocality (a kind of multipartite quantum correlation associated with Bell-type inequalities) in one-dimensional finite-size spin chains, both for zero temperature and for finite temperatures. We define a quantity $\frac{\ensuremath{\delta}\mathcal{S}}{\mathcal{S}}$ to characterize the boundary effects, where $\mathcal{S}$ is a measure of global multipartite nonlocality of the entire lattice, and $\ensuremath{\delta}\mathcal{S}$ is the difference of the measure induced by changing the boundary conditions. We find $\frac{\ensuremath{\delta}\mathcal{S}}{\mathcal{S}}$ does not vanish in the large-$N$ limit. Instead, at zero temperature, with the increase of $N$, $\frac{\ensuremath{\delta}\mathcal{S}}{\mathcal{S}}$ would increase steadily in the vicinity of the quantum phase transition point of the models, and converge to a nonzero constant in noncritical regions. It shows clearly that boundary effects generally exist, in the form of multipartite correlations, in long chains. The boundary effects are explained by the competition between the two orders of the models. In addition, based on these numerical results, we construct a Bell inequality, which is violated by chains with periodic (closed) boundary conditions and not violated by chains with open boundary conditions. Furthermore, we study $\frac{\ensuremath{\delta}{\mathcal{S}}_{T}}{{\mathcal{S}}_{T}}$ of finite-size chains at finite temperatures, and show that boundary effects survive in finite temperature regions.

Physical Review AApr 15, 201922 citations

Quantum Spin Chains: Phase Behaviour and Dynamic Excitations

Jill C. Bonner, John B. Parkinson

Springer series in solid-state sciencesJan 1, 19840 citations

The Effect of a Long-Range Correlated-Hopping Interaction on Bariev Spin Chains

Tao Yang, Fa-Kai Wen, Kun Hao +2 more

We introduce a long-range particle and spin interaction into the standard Bariev model and show that this interaction is equivalent to a phase shift in the kinetic term of the Hamiltonian. When the particles circle around the chain and across the boundary, the accumulated phase shift acts as a twist boundary condition with respect to the normal periodic boundary condition. This boundary phase term depends on the total number of particles in the system and also the number of particles in different spin states, which relates to the spin fluctuations in the system. The model is solved exactly via a unitary transformation by the coordinate Bethe ansatz. We calculate the Bethe equations and work out the energy spectrum with varying number of particles and spins.We introduce a long-range particle and spin interaction into the standard Bariev model and show that this interaction is equivalent to a phase shift in the kinetic term of the Hamiltonian. When the particles circle around the chain and across the boundary, the accumulated phase shift acts as a twist boundary condition with respect to the normal periodic boundary condition. This boundary phase term depends on the total number of particles in the system and also the number of particles in different spin states, which relates to the spin fluctuations in the system. The model is solved exactly via a unitary transformation by the coordinate Bethe ansatz. We calculate the Bethe equations and work out the energy spectrum with varying number of particles and spins.

EntropyAug 28, 20152 citations

Dynamic properties of quantum spin chains

Joachim Stolze, Taras Verkholyak, Oleg Derzhko +1 more

Oct 15, 20076 citations

Large effects of boundaries on spin amplification in spin chains

Benoit Roubert, Petr A. Braun, Daniel Braun

We investigate the effect of boundary conditions on spin amplification in spin chains. We show that the boundaries play a crucial role for the dynamics: A single additional coupling between the first and last spins can macroscopically modify the physical behavior compared to the open chain, even in the limit of infinitely long chains. We show that this effect can be understood in terms of a bifurcation in Hilbert space that can give access to different parts of Hilbert space with macroscopically different physical properties of the basis functions, depending on the boundary conditions. On the technical side, we introduce semiclassical methods whose precision increases with increasing chain length and allow us to analytically demonstrate the effects of the boundaries in the thermodynamic limit.We investigate the effect of boundary conditions on spin amplification in spin chains. We show that the boundaries play a crucial role for the dynamics: A single additional coupling between the first and last spins can macroscopically modify the physical behavior compared to the open chain, even in the limit of infinitely long chains. We show that this effect can be understood in terms of a bifurcation in Hilbert space that can give access to different parts of Hilbert space with macroscopically different physical properties of the basis functions, depending on the boundary conditions. On the technical side, we introduce semiclassical methods whose precision increases with increasing chain length and allow us to analytically demonstrate the effects of the boundaries in the thermodynamic limit.

arXiv:1003.5863Physical Review AAug 3, 20101 citation

In quantum lattice models, in the large-

N

limit, boundary conditions have little effect upon local observables for sites in the centers of the lattices. In this paper, we will study the boundary effects upon multipartite nonlocality (a kind of multipartite quantum correlation associated with Bell-type inequalities) in one-dimensional finite-size spin chains, both for zero temperature and for finite temperatures. We define a quantity $\frac{\ensuremath{\delta}\mathcal{S}}{\mathcal{S}}$ to characterize the boundary effects, where

\mathcal{S}

is a measure of global multipartite nonlocality of the entire lattice, and $\ensuremath{\delta}\mathcal{S}$ is the difference of the measure induced by changing the boundary conditions. We find $\frac{\ensuremath{\delta}\mathcal{S}}{\mathcal{S}}$ does not vanish in the large-

N

limit. Instead, at zero temperature, with the increase of

N

, $\frac{\ensuremath{\delta}\mathcal{S}}{\mathcal{S}}$ would increase steadily in the vicinity of the quantum phase transition point of the models, and converge to a nonzero constant in noncritical regions. It shows clearly that boundary effects generally exist, in the form of multipartite correlations, in long chains. The boundary effects are explained by the competition between the two orders of the models. In addition, based on these numerical results, we construct a Bell inequality, which is violated by chains with periodic (closed) boundary conditions and not violated by chains with open boundary conditions. Furthermore, we study $\frac{\ensuremath{\delta}{\mathcal{S}}_{T}}{{\mathcal{S}}_{T}}$ of finite-size chains at finite temperatures, and show that boundary effects survive in finite temperature regions.