One-dimensional Anisotropic XY Model Research Articles

Spectral crossovers in non-Hermitian spin chains: Comparison with random matrix theory.

We present a systematic investigation of the short-range spectral fluctuation properties of three non-Hermitian spin-chain Hamiltonians using complex spacing ratios (CSRs). Specifically, we focus on the non-Hermitian variants of the standard one-dimensional anisotropic XY model having intrinsic rotation-time (RT) symmetry that has been explored analytically by Zhang and Song [Phys. Rev. A 87, 012114 (2013)1050-294710.1103/PhysRevA.87.012114]. The corresponding Hermitian counterpart is also exactly solvable and has been widely employed as a toy model in several condensed matter physics problems. We show that the presence of a random field along the x direction together with the one along the z direction facilitates integrability and RT-symmetry breaking, leading to the emergence of quantum chaotic behavior. This is evidenced by a spectral crossover closely resembling the transition from Poissonian to Ginibre unitary ensemble (GinUE) statistics of random matrix theory. Additionally, we consider two phenomenological random matrix models in this paper to examine 1D Poisson to GinUE and 2D Poisson to GinUE crossovers and the associated signatures in CSRs. Here 1D and 2D Poisson correspond to real and complex uncorrelated levels, respectively. These crossovers reasonably capture spectral fluctuations observed in the spin-chain systems within a certain range of parameters.

Quantum Coherence and Skew Information with Quantum Phase Transition in One-Dimensional Anisotropic XY Model under Renormalization Group Method

We investigate the behaviors of Wigner–Yanase skew information and the l1 norm, as two different measures of quantum coherence, in a tripartite ground state of the anisotropic spin-1/2 XY model. Fo...

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 diagram 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. It if found that in the both cases the periods are the same and can be used as a order parameter for quantum phase transitions. It is also found that there is a scaling behavior for the evolution period and a reciprocal relation for the evolution period exponent, θ and correlation length exponent, ν.

Emergence of entanglement with temperature and time in factorization-surface states

There exist zero-temperature states in quantum many-body systems that are fully factorized, thereby possessing vanishing entanglement, and hence being of no use as resource in quantum information processing tasks. Such states can become useful for quantum protocols when the temperature of the system is increased, and when the system is allowed to evolve under either the influence of an external environment, or a closed unitary evolution driven by its own Hamiltonian due to a sudden change in the system parameters. Using the one-dimensional anisotropic XY model in a uniform and an alternating transverse magnetic field, we show that entanglement of the thermal states, corresponding to the factorization points in the space of the system parameters, revives once or twice with increasing temperature. We also study the closed unitary evolution of the quantum spin chain driven out of equilibrium when the external magnetic fields are turned off, and show that considerable entanglement is generated during the dynamics, when the initial state has vanishing entanglement. Interestingly, we find that creation of entanglement for a pair of spins is possible when the system is made open to an external heat bath, interacting through that spin-pair having a repetitive quantum interaction.

Exact work statistics of quantum quenches in the anisotropic XY model.

We derive exact analytic expressions for the average work done and work fluctuations in instantaneous quenches of the ground and thermal states of a one-dimensional anisotropic XY model. The average work and a quantum fluctuation relation is used to determine the amount of irreversible entropy produced during the quench, eventually revealing how the closing of the excitation gap leads to increased dissipated work. The work fluctuation is calculated and shown to exhibit nonanalytic behavior as the prequench anisotropy parameter and transverse field are tuned across quantum critical points. Exact compact formulas for the average work and work fluctuation in ground state quenches of the transverse field Ising model allow us to calculate the first singular field derivative at the critical field values.

Unveiling $${\pi }$$ π -tangle and quantum phase transition in the one-dimensional anisotropic XY model

In this paper, the relationship between $${\pi }$$?-tangle and quantum phase transition (QPT) is investigated by employing the quantum renormalization-group method in the one-dimensional anisotropic XY model. The results show that all the 1-tangles increase firstly and then decrease with the anisotropy parameter $$\gamma $$? increasing, and the Coffman---Kundu---Wootters monogamy inequality is always tenable for this system. The entanglement's status of subsystems depends on its site position, and this proposition can be generalized to a multipartite system. Meanwhile, with the increasing of the size of the system, the $${\pi }$$?-tangle decreases slowly and tends to a fixed value finally. Additionally, it exhibits a QPT and a maximum value for the next-nearest-neighbor entanglement at the critical point in our model, which is different from the case of two-body system. After several iterations of the renormalization, the quantum entanglement measure can develop two saturated values, which are associated with two different phases: spin-fluid phase and the Neel phase. To gain further insight, the nonanalytic and scaling behaviors of $${\pi }$$?-tangle have also been analyzed in detail.

Probing [formula omitted]-tangle and quantum phase transition in the one-dimensional anisotropic XY model with Dzyaloshinskii–Moriya interaction

In this paper, the effect of Dzyaloshinskii–Moriya interaction and anisotropy on the π-tangle and quantum phase transition (QPT) by employing the QRG method in the one-dimensional anisotropic XY model is investigated. In our model the anisotropy and DM interaction parameters can influence the phase diagrams. While the anisotropy suppresses the entanglement due to favoring of the alignment of spins, the DM interaction restores the spoiled entanglement via creation of the quantum fluctuations. When the value of DM interaction is certain, the π-tangle develops into two different values which separate the system into two phases i.e. the spin-fluid phase and the Néel phase with the number of QRG iterations increased. Meanwhile, the π-tangle decreases slowly as the sites of the chain became larger, but the π-tangle tends to be a fixed value finally. Additionally, it exhibits a maximum for the next-nearest-neighbor entanglement at the critical point in our model which is different from the situation of the two-body system. To gain further insight, the nonanalytic and scaling behaviors of π-tangle have also been analyzed in detail and this phenomenon indicates that the behavior of the entanglement can perfectly help one to observe the quantum critical properties of the model.

Factorization and Criticality in the Anisotropic XY Chain via Correlations

In this review, we discuss the zero and finite temperature behavior of various bipartite quantum and total correlation measures, the skew information-based quantum coherence and the local quantum uncertainty in the thermal ground state of the one-dimensional anisotropic XY model in a transverse magnetic field. We compare the ability of the considered measures to correctly detect or estimate the quantum critical point and the non-trivial factorization point possessed by the spin chain.

Monogamy of quantum correlations in the one-dimensional anisotropic XY model

In this paper, the monogamy properties of some quantum correlations, including the geometric quantum discord, concurrence, entanglement of formation and entropy quantum discord, in the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii—Moriya (DM) interaction have been investigated using the quantum renormalization group (QRG) method. We summarize the monogamy relation for different quantum correlation measures and make an explicit comparison. Through mathematical calculations and analysis, we obtain that no matter whether the QRG steps are carried out, the monogamy of the given states are always unaltered. Moreover, we conclude that the geometric quantum discord and concurrence obey the monogamy property while other quantum correlation measures, such as entanglement of formation and quantum discord, violate it for this given model.

Stability of the Bloch wall via the Bogomolnyi decomposition in elliptic coordinates

We consider the one-dimensional anisotropic XY model in the continuum limit. Stability analysis of its Bloch wall solution is hindered by the non-diagonality of the associated linearized operator and the Hessian of energy. We circumvent this difficulty by showing that the energy admits a Bogomolnyi bound in elliptic coordinates and that the Bloch wall saturates it—that is, the Bloch wall renders the energy minimum. Our analysis provides a simple but nontrivial application of the BPS (Bogomolnyi–Prasad–Sommerfield) construction in one dimension, where its use is often believed to be limited to reproducing results obtainable by other means.

Pattern Dynamics Associated with Dynamic Phase Transitions: Domain Walls, Phase Waves, and Spatio-Temporal Chaos: Domain Walls, Phase Waves, and Spatio-Temporal Chaos

We study pattern dynamics in a one-dimensional anisotropic XY model driven by a rotating external field. We find that the dynamical properties change qualitatively through a dynamic phase transition, which is a bifurcation of the spatially uniform states under a periodic external field. When two stable uniform limit cycles coexist, we observe a domain wall structure. Furthermore, there is a domain wall connecting domains of different phases of one limit cycle attractor. We find a periodic structure which is caused by the collapse of the domain wall. We derive approximate equations that describe the long time behavior of the domain walls and find that some results based on this approximation are qualitatively in agreement with those of numerical simulations. The properties of the interaction between the two domain walls depend on the symmetry of the wall. We observe a propagation of the phase wave in the quasi-periodic phase. This result implies the possibility of a phase description in non-autonomous systems. We find two chaotic patterns with different statistical properties in the symmetry-broken chaos region.

Emptiness formation probability for the anisotropic XY spin chain in a magnetic field

We study an asymptotic behavior of the probability of formation of a ferromagnetic string (referred to as EFP) of length n in the ground state of the one-dimensional anisotropic XY model in a transversal magnetic field as n→∞. We find that it is exponential everywhere in the phase diagram of the XY model except at the critical lines where the spectrum is gapless. One of those lines corresponds to the isotropic XY model where EFP decays in a Gaussian way, as was shown in [J. Phys. Soc. Jpn. 70 (2001) 3535]. The other lines are at the critical value of the magnetic field. There, we show that EFP is still exponential but acquires a non-trivial power-law prefactor with a universal exponent.

Autocorrelation function of the x-component of the magnetization in the one-dimensional XY-model

Exact expressions are derived for the time-dependent correlation functions of the x and y component of the magnetization for the one-dimensional anisotropic XY-model ( S= 1 2 ) in zero field in the high-temperature limit. As a corollary, the correlation functions for the Ising chain in a transverse field are obtained.

On a soluble model of an antiferromagnetic chain with Dzyaloshinsky interactions. I

The one-dimensional anisotropic XY model with antisymmetric nearest-neighbour interactions (Dzyaloshinsky interactions) in the presence of a magnetic field B in the z direction is investigated. Special attention is given to the critical behaviour of the system. In the ground state, the susceptibility χ zz has a logarithmic singularity as B → 1 provided that the strength Δ of the Dzyaloshinsky interaction obeys the inequality |Δ| ≤ |γ|, where γ is the anisotropy parameter. However, if |Δ| #62; |γ|, χ zz diverges with a power - 1 2 singularity as B ↑ (1 + Δ 2 - γ 2) 1 2 . The specific heat is studied for low temperatures. Furthermore for a few special values of γ and B the static correlation functions 〈 S α j S β k 〉 are evaluated in the low-temperature limit, for α, β = x, y, z and | j - k| = 1, 2. Finally we consider the chain with Dzyaloshinsky interactions only.

On a soluble model of an antiferromagnetic chain with alternating interactions and magnetic moments

The one-dimensional anisotropic XY model with alternating nearest-neighbour interactions and magnetic moments is investigated. The singularities of the susceptibility χ zz in the ground state are studied in detail. In the general anisotropic case χ zz can exhibit two logarithmic singularities at two different values of the applied magnetic field b. If the interactions satisfy a certain relation which will be reffered to as the pseudoisotropic condition (which includes the isotropic case), χ zz can have two power- 1 2 singularities at the upper side of the lower critical field and the lower side of the upper critical field. Deviations from this behaviour which occur for special values of the interaction constants are discussed in some detail. Finally the specific heat is studied in the low- and high-temperature limits.

Antiferromagnetic chain with Dzyaloshinsky interactions

Some exact results for a one-dimensional anisotropic XY-model with antisymmetric exchange are presented.