arXiv subjects

Wen-Li Yang

Publications and source records attributed to Wen-Li Yang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Embedded Majorana Islands

Mesoscopic superconducting islands hosting Majorana zero modes (MZMs), or Majorana islands in short, offer a prototype of topological qubits. In this work we investigate theoretically the model of a generic Majorana island tunneling-coupled to a single-piece metallic substrate, hence an \textit{embedded Majorana island}. We show the crucial consequences of an interplay between the topological ground states nonlocally addressed by the MZMs and the metallic bath with coherent electron propagation: on the one hand, the topological degeneracy on the Majorana island can be preserved, by virtue of the particle-hole symmetry, despite the apparent bath-induced coupling between MZMs; on the other hand, the electronic interference in the metallic bath may lead to profound alterations to the renormalization group behavior of the hybrid system towards low energy/temperature compared with conventional Kondo physics. This work serves to establish the model of embedded Majorana islands as an experimentally relevant and theoretically intriguing problem particularly in the direction of topological quantum computation.

cond-mat.mes-hall↗

arXiv2024

Surface energy and elementary excitations of the XYZ spin chain with integrable open boundary fields

We study the thermodynamic limit of the anisotropic XYZ spin chain with non-diagonal integrable open boundary conditions. Although the $U(1)$-symmetry is broken, by using the new parametrization scheme, we exactly obtain the surface energy and the excitation energy of the system, which has solved the difficulty in the inhomogeneous $T-Q$ relation. With the boundary parameters in the regions making the Hamiltonian Hermitian, we have obtained the distribution patterns of the zero roots of the eigenvalue of the transfer matrix for the ground state and the excited ones. We find that the surface and excitation energies depend on the parities of sites number $N$, due to the long-range Neel order in the bulk. The spontaneous magnetization and easy-axis for all the regions of boundary parameters are studied. We also obtain the physical quantities in the thermodynamic limit of boundary XXZ model by taking the triangular limit.

math-ph↗

arXiv2024

Local unitary equivalence of arbitrary-dimensional multipartite quantum states

Local unitary equivalence is an important ingredient for quantifying and classifying entanglement. Verifying whether or not two quantum states are local unitary equivalent is a crucial problem, where only the case of multipartite pure states is solved. For mixed states, however, the verification of local unitary equivalence is still a challenging problem. In this paper, based on the coefficient matrices of generalized Bloch representations of quantum states, we find a variety of local unitary invariants for arbitrary-dimensional bipartite quantum states. These invariants are operational and can be used as necessary conditions for verifying the local unitary equivalence of two quantum states. Furthermore, we extend the construction to the arbitrary-dimensional multipartite case. We finally apply these invariants to estimate concurrence, a vital entanglement measure, showing the practicability of local unitary invariants in characterizing entanglement.

quant-ph↗

arXiv2024

Generalized Maxwell equal area law and black holes in complex free energy

Maxwell equal area law is an important and traditional analytical tool in thermodynamic phase transition, especially in the calculation of gas-liquid phase transition, which reconciles the theoretical calculation with the experimental results. Undoubtedly, its importance is also self-evident for the black hole thermodynamic system. In this study, we construct a generalized Maxwell equal area law, which allows different states of thermodynamic systems to be within the generalized free energy. The black hole thermodynamic characteristics are spontaneously emerged in the free energy landscape. Furthermore, by analytic continuation, we utilize the properties of analytical functions to investigate some universal characteristics of thermodynamic phase transitions in black holes, and preliminarily establish the counterpart of thermodynamic phase transitions in the complex domain.

gr-qc↗

arXiv2024

The universality of physical images at relative timescales on multiplex networks

The duration of the accumulation rate (physical image) is a key factor in analysis of counterintuitive phenomena involving relative timescales on multiplex networks. Typically, the relative timescales are represented by multiplying any layer by the same factor. However, researchers often overlook the changes in the relative timescales caused by local parameters, resulting in incomplete analysis of phenomena. This paper examines the survival time of stifler individuals in the information-epidemic model on multiplex networks. The relative timescales can be affected by the survival time (only one parameter), reversing the monotonically increasing phenomenon into a monotonically decreasing one, that is, a counterintuitive phenomenon under incomplete analysis. Additionally, the relative timescales can influence the epidemic threshold, which is different from the previous studies. Our work suggests that considering the physical image of relative timescales is crucial when analyzing multiplex networks, even when only one parameter is altered.

physics.soc-ph↗

arXiv2024

Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries

We investigate the thermodynamic limit and exact surface energy of the isotropic spin-1 Heisenberg chain with integrable generic open boundary conditions by a novel Bethe ansatz method. We obtain the homogeneous Bethe ansatz equations for the zero roots of the transfer matrix. Based on the patterns of the zero roots, we analytical calculate the densities of zero roots and the surface energies of the model in all regimes of the boundary parameters.

math-ph↗

arXiv2023

Off-diagonal approach to the exact solution of quantum integrable systems

We investigate the $t$-$W$ scheme for the anti-ferromagnetic XXX spin chain under both periodic and open boundary conditions. We propose a new parametrization of the eigenvalues of transfer matrix. Based on it, we obtain the exact solution of the system. By analyzing the distribution of zero roots at the ground state, we obtain the explicit expressions of the eigenfunctions of the transfer matrix and the associated $\mathbb{W}$ operator (see (2.8) and (3.20)) in the thermodynamic limit. We find that the ratio of the quantum determinant with the eigenvalue of $\mathbb{W}$ operator for the ground state exhibits exponential decay behavior. Thus this fact ensures that the so-called inversion relation (the $t-W$ relation without the $W$-term) can be used to study the ground state properties of quantum integrable systems with/without $U(1)$-symmetry in the thermodynamic limit.

math-ph↗

arXiv2023

Exact physical quantities of a competing spin chain in the thermodynamic limit

We study the exact physical quantities of a competing spin chain which contains many interesting and meaningful couplings including the nearest neighbor, next nearest neighbor, chiral three spins, Dzyloshinsky-Moriya interactions and unparallel boundary magnetic fields in the thermodynamic limit. We obtain the density of zero roots, surface energies and elementary excitations in different regimes of model parameters. Due to the competition of various interactions, the surface energy and excited spectrum show many different pictures from those of the Heisenberg spin chain.

math-ph↗

arXiv2023

Discovery and regulation of chiral magnetic solitons: Exact solution from Landau-Lifshitz-Gilbert equation

The Landau-Lifshitz-Gilbert (LLG) equation has emerged as a fundamental and indispensable framework within the realm of magnetism. However, solving the LLG equation, encompassing full nonlinearity amidst intricate complexities, presents formidable challenges. In this context, we develop a precise mapping through geometric representation, establishing a direct linkage between the LLG equation and an integrable generalized nonlinear Schrödinger equation. This novel mapping provides accessibility towards acquiring a great number of exact spatiotemporal solutions. Notably, exact chiral magnetic solitons, critical for stability and controllability in propagation with and without damping effects are discovered. Our formulation provides exact solutions for the long-standing fully nonlinear problem, facilitating practical control through spin current injection in magnetic memory applications.

nlin.PS↗

arXiv2023

Unveiling Stable One-dimensional Magnetic Solitons in Magnetic Bilayers

We propose a novel model which efficiently describes the magnetization dynamics in a magnetic bilayer system. By applying a particular gauge transformation to the Landau-Lifshitz-Gilbert (LLG) equation, we successfully convert the model into an exactly integrable framework. Thus the obtained analytical solutions allows us to predict a 1D magnetic soliton pair existed by tunning the thickness of the spacing layer between the two ferrimagnetic layers. The decoupling-unlocking-locking transition of soliton motion is determined at various interaction intensitiy. Our results have implications for the manipulation of magnetic solitons and the design of magnetic soliton-based logic devices.

cond-mat.mes-hall↗

arXiv2023

Spectrum of the transfer matrices of the spin chains associated with the $A^{(2)}_3$ Lie algebra

We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion technique, we obtain the closed recursive relations of the fused transfer matrices. Based on them, together with the asymptotic behaviors and the values at special points, we obtain the eigenvalues and Bethe ansatz equations of the system. We also show that the method is universal and valid for the periodic boundary condition where the $U(1)$ symmetry is reserved. The results in this paper can be applied to studying the exact solution of the $A^{(2)}_n$-related integrable models with arbitrary $n$.

math-ph↗

arXiv2023

Exact solution of the $q$-deformed $D^{(1)}_3$ vertex model with open boundaries

In this paper, we study the exact solution of the $q$-deformed $D^{(1)}_3$ quantum lattice model with non-diagonal open boundary condition. We demonstrate the crossing symmetry of the transfer matrix and obtain the quantum determinant. We construct the independent transfer matrix fusion identities and show that the fusion processes can be closed. Based on the fusion hierarchies and polynomial analysis, we obtain the inhomogeneous $T-Q$ relations, exact energy spectrum and Bethe ansatz equations of the system.

math-ph↗

arXiv2023

Rate of the phase transition for a charged anti-de Sitter black hole

Phase transition is a core content of black hole thermodynamics. This study adopted the Kramer's escape rate method for describing the Brownian motion of particles in an external field to investigate the intensity of the phase transition between small and large black hole states. Some existing studies mostly focused on the formal analysis of the thermodynamic phase transition of black holes, but they neglected the detailed description of the phase transition process. Our results show that the phase transition between small and large black holes for charged anti-de Sitter (AdS) black holes presents serious asymmetric features, and the overall process is dominated by the transition from a small black hole to a large black hole. This study filled a research gap of a stochastic process analysis on the issue of the first-order phase transition rate in the AdS black hole.

gr-qc↗

arXiv2022

Off-diagonal Bethe Ansatz for the $D^{(1)}_3$ model

The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the $T-Q$ relations for the periodic case and by the inhomogeneous $T-Q$ one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the $D^{(1)}_{n}$ model directly.

math-ph↗

arXiv2022

Entanglement, Coherence, and Extractable Work in Quantum Batteries

We investigate the connection between quantum resources and extractable work in quantum batteries. We demonstrate that quantum coherence in the battery or the battery-charger entanglement is a necessary resource for generating nonzero extractable work during the charging process. At the end of the charging process, we also establish a tight link of coherence and entanglement with the final extractable work: coherence naturally promotes the coherent work while coherence and entanglement inhibit the incoherent work. We also show that obtaining maximally coherent work is faster than obtaining maximally incoherent work. Examples ranging from the central-spin battery and the Tavis-Cummings battery to the spin-chain battery are given to illustrate these results.

quant-ph↗

arXiv2022

Exact surface energy of the $D^{(1)}_2$ spin chain with generic non-diagonal boundary reflections

The exact solution of the $D^{(1)}_2$ quantum spin chain with generic non-diagonal boundary reflections is obtained. It is found that the generating functional of conserved quantities of the system can be factorized as the product of transfer matrices of two anisotropic $XXZ$ spin chains with open boundary conditions. By using the factorization identities and the fusion technique, the eigenvalues and the Bethe ansatz equations of the model are obtained. The eigenvalues are also parameterized by the zero roots of the transfer matrix, and the patterns of root distributions are obtained. Based on them, ground states energy and the surface energies induced by the twisted boundary magnetic fields in the thermodynamic limit are obtained. These results are checked by the numerical calculations. The corresponding isotropic limit is also discussed. The results given in this paper are the foundation to study the exact physical properties of high rank $D^{(1)}_{n}$ model by using the nested processes.

math-ph↗

arXiv2022

Entanglement and work extraction in the central-spin quantum battery

We consider a central-spin battery where $N_b$ central spins serve as battery cells and $N_c$ bath spins serve as charging units. It is shown that the energy stored in the battery that can be extractable is quantified by the ergotropy, and that battery-charger entanglement is quantified via the Von Neumann entropy. By using an exact approach to a one-cell and two-cell battery, our analytical results suggest that, during the charging process, the extractable work slowly increases before the battery-charger entanglement reaches its maximum and then it will rapidly increase when the entanglement begins to decrease. In particular, we rigorously show that there is an inverse relationship between the extractable work and the entanglement at the end of the charging process. Moreover, we investigate different approaches to realize optimal work extraction without wasted energy. Among them a central-spin battery with an unpolarized Dicke state as the charger possesses a universal charging time $\propto 1/N_c$, large extractable work, and $\sqrt{N_c}$-improvement of charging power compared with the battery in the Tavis-Cummings limit. The above-mentioned results have also been numerically verified in multi-cell batteries. Our results pave the way to improve extractable work storage in the central-spin battery and highlight a competitive relation between the extractable work and the battery-charger entanglement.

quant-ph↗

arXiv2022

A Necessary and Sufficient Entanglement Criterion of N-qubit System Based on Correlation Tensor

Great advances have been achieved in studying characteristics of entanglement for fundamentals of quantum mechanics and quantum information processing. However, even for N-qubit systems, the problem of entanglement criterion has not been well solved. In this Letter, using the method of state decomposition and high order singular value decomposition (HOSVD), we propose a necessary and sufficient entanglement criterion for general N-qubit systems. As an example, we apply our method to study the multi-qubit W state with white noise. We not only obtain the separability critical point, which is tight and thus better than known results, but also the separate states ensemble for decomposition. More examples are presented to show our criterion is accurate, which is tighter than the well-known positive partial transpose criterion. For two-qubit case, we can provide an entanglement measurer which gives similar results with concurrence up to a factor. Our results pave the way to solve the entanglement-separability criterion for more general cases.

quant-ph↗