arXiv subjects

Yu-Liang Xu

Publications and source records attributed to Yu-Liang Xu.

6 recordsLinked to original sources

arXiv2023

Ground-state and thermal entanglements in a non-Hermitian XY system with real and imaginary magnetic fields

In this manuscript, we study the non-Hermitian spin-1/2 XY model in the presence of the alternating, imaginary and transverse magnetic fields. For the two-site spin system, we solve exactly the energy spectrum and phase diagram, also calculate the ground-state and thermal entanglements by using the concept of the concurrence. It is found that the two-site concurrence in the eigenstate which only depends on the imaginary magnetic field η is always equal to one in the region of PT symmetry, while it decreases with η in the PT-symmetric broken region. Especially, the concurrence shows the non-analytic behavior at the exceptional point, and the same is true in the case of the biorthogonal basis, which indicates that the concurrence can characterize the phase transition in this non-Hermitian system. The interesting thing is that η weakens the thermal entanglement when the system is isotropic and enhances the entanglement when the system becomes the Ising model. For the one-dimensional spin chain, the magnetization and entanglement are further studied by using the two-spin cluster mean-field approximation. The results show that their variations have opposite trends with the magnetic fields. Moreover, the system exists the first-order quantum phase transitions for some anisotropic parameters in the PT-symmetry region, and the entanglement changes suddenly at the quantum phase transition point.

cond-mat.stat-mech↗

arXiv2021

Phase diagrams, quantum correlations and critical phenomena of antiferromagnetic Heisenberg model on diamond-type hierarchical lattices

The spin-1/2 antiferromagnetic Heisenberg systems are studied on three typical diamond-type hierarchical lattices (systems A, B and C) with fractal dimensions 1.63, 2 and 2.58, respectively, and the phase diagrams, critical phenomena and quantum correlations are calculated by a combination of the equivalent transformation and real-space renormalization group methods. We find that there exist a reentrant behavior for system A and a finite temperature transition in the isotropic Heisenberg limit for system C (not for system B). Unlike the ferromagnetic case, the Neel temperatures of antiferromagnetic systems A and B are inversely proportional to ln(Delta_c-Delta) (when Delta->Delta_c) and ln Delta (when Delta->0), respectively. And we also find that there is a turning point of quantum correlation in the isotropic Heisenberg limit Delta=0 where there is a peak of the contour and no matter how large the size of system is, quantum correlation will change to zero in the Ising limit for the three systems. The quantum correlation decreases with the increase of lattice size L and it is almost zero when L>=30 for system A, and for systems B and C, they still exist when L is larger than that of system A. Moreover, as an example, we discuss the error of result in system A, which is induced by the noncommutativity.

cond-mat.stat-mech↗

arXiv2021

Single-ion anisotropy effects on the critical behaviors of quantum entanglement and correlation in the spin-1 Heisenberg chain

Quantum entanglement and correlations in the spin-1 Heisenberg chain with single-ion anisotropy are investigated using the quantum renormalization group method. Negativity and quantum discord (QD) are calculated with various anisotropy parameters $\bigtriangleup$ and single-ion anisotropy parameters $D$. We focus on the relations between two abovementioned physical quantities and on transitions between the Néel, Haldane, and Large-D phases. It is found that both negativity and QD exhibit step-like patterns in different phases as the size of the system increases. Interestingly, the single-ion anisotropy parameter $D$, which can be modulated using nuclear electric resonance (2020 \textit{Nature} \textbf{579} 205), plays an important role in tuning the quantum phase transition (QPT) of the system. Both the first partial derivative of the negativity and quantum discord with respect to $D$ or $\bigtriangleup$ exhibit nonanalytic behavior at the phase transition points, which corresponds directly to the divergence of the correlation length. The quantum correlation critical exponents derived from negativity and QD are equal, and are the reciprocal of the correlation length exponent at each critical point. This work extends the application of quantum entanglement and correlations as tools for depicting QPTs in spin-1 systems.

cond-mat.str-el↗

arXiv2021

Quantum Quench dynamics in XY spin chain with ferromagnetic and antiferromagnetic interactions

In this manuscript we investigate the one-dimensional anisotropic XY model with ferromagnetic and antiferromagnetic interactions, which gives more interesting phase diagrams and dynamic critical behaviors. By using quantum renormalization-group method, we find that there are three phases in the system: antiferromagnetic Ising phase ordered in "x direction", spin-fluid phase and ferromagnetic Ising phase ordered in "y direction". In order to study the dynamical critical behaviors of the system, two quantum quenching methods are used. In both cases, the concurrence, a measure of entanglement, oscillates periodically over time. We show that the periods are the same and can be used as a new order parameter for quantum phase transitions. For further discussion, we derive the scaling exponent, θ, and correlation length exponent, ν, from the scaling behavior of the evolution period.

cond-mat.stat-mech↗

arXiv2020

Dynamics of entanglement in the one-dimensional anisotropic XXZ model

The dynamics of entanglement in the one-dimensional spin-1/2 anisotropic XXZ model is studied using the quantum renormalization-group method. We obtain the analytical expression of the concurrence, for two different quenching methods, it is found that initial state plays a key role in the evolution of system entanglement, i.e., the system returns completely to the initial state every other period. Our computations and analysis indicate that the first derivative of the characteristic time at which the concurrence reaches its maximum or minimum with respect to the anisotropic parameter occurs nonanalytic behaviors at the quantum critical point. Interestingly, the minimum value of the first derivative of the characteristic time versus the size of the system exhibits the scaling behavior which is the same as the scaling behavior of the system ground-state entanglement in equilibrium. In particular, the scaling behavior near the critical point is independent of the initial state.

cond-mat.stat-mech↗

arXiv2012

Thermal entanglement between non-nearest-neighbor spins on fractal lattices

We investigate thermal entanglement between two non-nearest-neighbor sites in ferromagnetic Heisenberg chain and on fractal lattices by means of the decimation renormalization-group (RG) method. It is found that the entanglement decreases with increasing temperature and it disappears beyond a critical value T_{c}. Thermal entanglement at a certain temperature first increases with the increase of the anisotropy parameter Δ and then decreases sharply to zero when Δ is close to the isotropic point. We also show how the entanglement evolves as the size of the system L becomes large via the RG method. As L increases, for the spin chain and Koch curve the entanglement between two terminal spins is fragile and vanishes when L\geq17, but for two kinds of diamond-type hierarchical (DH) lattices the entanglement is rather robust and can exist even when L becomes very large. Our result indicates that the special fractal structure can affect the change of entanglement with system size.

cond-mat.stat-mech↗