Motivated by conjectures in holography relating the entanglement of purification and reflected entropy to the entanglement wedge cross section, we introduce two related non-negative measures of ...tripartite entanglement g and h. We prove structure theorems which show that states with nonzero g or h have nontrivial tripartite entanglement. We then establish that in one dimension these tripartite entanglement measures are universal quantities that depend only on the emergent low-energy theory. For a gapped system, we argue that either g≠0 and h=0 or g=h=0, depending on whether the ground state has long-range order. For a critical system, we develop a numerical algorithm for computing g and h from a lattice model. We compute g and h for various CFTs and show that h depends only on the central charge whereas g depends on the whole operator content.
The nature of entanglement in many-body systems is a focus of intense research with the observation that entanglement holds interesting information about quantum correlations in large systems and ...their relation to phase transitions. In particular, it is well known that although generic, many-body states have large, extensive entropy, ground states of reasonable local Hamiltonians carry much smaller entropy, often associated with the boundary length through the so-called area law. Here we introduce a continuous family of frustration-free Hamiltonians with exactly solvable ground states and uncover a remarkable quantum phase transition whereby the entanglement scaling changes from area law into extensively large entropy. This transition shows that entanglement in many-body systems may be enhanced under special circumstances with a potential for generating “useful” entanglement for the purpose of quantum computing and that the full implications of locality and its restrictions on possible ground states may hold further surprises.
In this study, we study the (2+1)-dimensional nonlinear Schrödinger kind equation which illustrates the non-linear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic spin chains (HFSCs) ...through bilinear and anisotropic interactions in the semi-classical limit. This model also illustrates the ferromagnetic materials of magnetic ordering. Two analytical schemes are employed to study the equation namely, improved auxiliary equation and generalized Riccati mapping methods. We construct dark and bright solitons, combined bright–dark solitons, periodic waves, solitary waves and elliptic solutions to this equation. We give graphical presentations of the 2D and 3D of some achieved solutions. The obtained results of this investigation might be useful to explain the physical structure of this model. The achieved results of HFSC show the effectiveness and reliability of the proposed techniques.
•Applications of mathematical physics models.•Higher order resonant NLSE with Quadratic Cubic nonlinearity.•The hydrodynamic mathematical methods.•Modulation instability analysis.
The nonlinear Schrodinger equation (NLSE) in (2 + 1) dimensions with beta derivative evolution is considered here to study nonlinear coherent structures for Heisenberg models of ferromagnetic spin ...chain with magnetic exchanges. Such structures are studied by determining the analytical solutions of NLSE having beta derivative evolution via two different mathematical techniques. The dynamical behaviors of equilibrium points are also studied by deriving the planar dynamical system from the considered equation. Some of obtained analytical solutions are described with graphical representation by varying beta derivative parameter (BDP) and obliqueness. It is revealed that the obliqueness is extensively affected both on the plane wave dynamics as well as equilibrium points of the system, whereas the equilibrium points are independent of BDP.
The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We ...thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs2CoCl4, a close realization of the S = 1/2 transverse-field X X Z spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.
Based on the Bethe ansatz approach and inelastic neutron scattering experiments, we reveal the evolution of confinement of many-body Bethe strings in ordered regions of the quasi-one-dimensional ...antiferromagnet YbAlO3. In the antiferromagnetic phase, the spin dynamics is dominated by confined length-1 Bethe strings, whose dominancy in the high-energy branch of the excitation spectrum yields to confined length-2 Bethe strings when the material is tuned to the spin-density-wave phase. In the thermal-induced disordered region, the confinement effect disappears, and the system restores the conventional quantum integrable physics of the one-dimensional Heisenberg model. Finally, our results establish a unified picture based on a Bethe string for the spin dynamics in different magnetic phases of YbAlO3, and thus provide profound insight into many-body quantum magnetism.
Abstract We address quantum characterization of anisotropic spin chains in the presence of anti-symmetric exchange, and investigate whether the Hamiltonian parameters of the chain may be estimated ...with precision approaching the ultimate limit imposed by quantum mechanics. At variance with previous approaches, we focus on the information that may be extracted by measuring only two neighboring spins rather than a global observable on the entire chain. We evaluate the Fisher information (FI) of a two-spin magnetization measure, and the corresponding quantum Fisher information (QFI), for all the relevant parameters, i.e. the spin coupling, the anisotropy, and the Dzyaloshinskii–Moriya (DM) parameter. Our results show that the reduced system made of two neighboring spins may be indeed exploited as a probe to characterize global properties of the entire system. In particular, we find that the ratio between the FI and the QFI is close to unit for a large range of the coupling values. The DM coupling is beneficial for coupling estimation, since it leads to the presence of additional bumps and peaks in the FI and QFI, which are not present in a model that neglects exchange interaction and may be exploited to increase the robustness of the overall estimation procedure. Finally, we address the multiparameter estimation problem, and show that the model is compatible but sloppy, i.e. both the Uhlmann curvature and the determinant of the QFI matrix vanish. Physically, this means that the state of the system actually depends only on a reduced numbers of combinations of parameters, and not on all of them separately.
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