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
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.
Understanding the transport properties of quantum many-body systems is a central challenge in condensed matter and statistical physics. Theoretical studies usually rely on two main approaches: Dynamics of linear-response functions in closed systems and boundary-driven dynamics governed by Markovian master equations for open systems. While the equivalence of their dynamical behavior has been explored in recent studies, a systematic comparison of the transport coefficients obtained from these two classes of approaches remains a largely open question. Here, we address this gap by comparing and contrasting the dc diffusion constant
Ddc according to the two approaches, focusing on the specific example of magnetization transport in the spin-
1/2 XXZ chain. Using exact numerical simulations for finite system sizes, we find (i) a clear mismatch between the two
Ddc and (ii) a strong dependence of
Ddc on the system-bath coupling strength for the open system, where neither (i) nor (ii) tend to vanish in the thermodynamic limit. These findings suggest limitations of the open-system approach to transport coefficients. To gain insight into the origin of (i) and (ii), we go beyond
Ddc and analyze the full time dependence of the diffusion coefficient
D(t) in the open system. In this way, we find that both (i) and (ii) vanish up to a finite time scale. While this time scale gradually increases with system size and tends to be macroscopic in the thermodynamic limit, this increase is still slow compared to the increase of the time to reach the steady state, where (i) and (ii) do not vanish. This observation can be seen as a wrong, yet unavoidable order of limits of long times first and large system sizes afterwards.
Condensed matter physics plays a crucial role in modern scientific research and technological advancements, providing insights into the behavior of materials and their fundamental properties. Understanding complex phenomena and systems in condensed matter physics poses significant challenges due to their inherent intricacies. Over the years, computational approaches have been pivotal in unraveling the mysteries of condensed matter physics, but they face limitations when dealing with large-scale systems and simulating quantum effects accurately. Quantum simulation and quantum computation techniques have emerged as promising tools for addressing these limitations, offering the potential to revolutionize our understanding of condensed matter physics. In this paper, we focus on the simulation of Anderson localization in the Heisenberg spin chain systems and explore the effects of disorder on closed and open chain systems using quantum computers.
We examine frustrated ferromagnetic S = 1 spin chains at zero temperature by using the density-matrix renormalization group method. In open boundary conditions, the S = 1 quantum spin chains are known to produce fractionalized free spins on each edge, which causes difficulty in the numerical calculation of the thermodynamic ground states. To overcome this, we propose modified open boundary conditions to suppress the formation of fractionalized edge spins. The comparison of the physical properties of the ground states, which are obtained from the modified and the standard open boundary conditions, reveals that the modified open boundary conditions are more effective in improving the convergence behavior and reducing the computational costs.
In few-qubit systems, the quantum Zeno effect arises when measurement occurs sufficiently frequently that the spins are unable to relax between measurements. This can compete with Hamiltonian terms, resulting in interesting relaxation processes which depend nonmonotonically on the ratio of measurement rate to coherent oscillations. While Zeno physics for a single qubit is well understood, an interesting open question is how the Zeno effect is modified by coupling the measured spin to a nontrivial bulk. In this work, we study the effect of coupling a one-dimensional transverse field Ising to a Zeno spin which lives at the boundary. We find that sharp singularities occur in the boundary relaxation dynamics, which can be tied to the emergence or destruction of edge modes that can be found analytically. Finally, we provide numerical indications that the dynamical singularities are stable in the presence of integrability-breaking interactions.
The transfer-matrix method is employed to investigate a spin-1/2 Ising chain under open and periodic boundary conditions. It is demonstrated that finite-size Ising chains with antiferromagnetic coupling may exhibit significantly distinct magnetic behavior under open and periodic boundary conditions. While the open Ising chains display intriguing magnetic features regardless of the system size, mainly due to a specific contribution of boundary spins, the magnetic behavior of closed Ising chains depends basically on the number of spins. The closed Ising chains with an odd number of spins are subject to a geometric spin frustration leading to an additional plateau in the magnetization curve, which is naturally absent in the closed Ising chains with an even number of spins. Despite different microscopic origins, the magnetization curves of open and closed Ising chains with an odd number of spins exhibit an identical intermediate plateau, with only small quantitative differences appearing at moderate temperatures, which means that a geometric spin frustration of odd-membered rings is somewhat similar to the effect of open boundaries. The magnetization curves of the open Ising chains with an even number of spins differ drastically from those of the closed Ising chains due to the presence of an additional intermediate magnetization plateau. Furthermore, the initial susceptibility, inverse initial susceptibility, and susceptibility-temperature product are examined in detail as functions of temperature. These magnetic response functions demonstrate that the Curie constant and Weiss temperature represent fundamental characteristics of the magnetic system that are independent of the choice of boundary conditions.