Anisotropic XY Model Research Articles

Visualizing the quantum phase transition by using quantum steering ellipsoids in the anisotropic spin XY model

Abstract Quantum steering ellipsoids (QSEs) can serve as a useful geometric tool for describing both the strength and type of quantum correlations between two subsystems of a compound system. By employing the quantum renormalization-group method, we focus on investigating the relation between QSEs and the quantum phase transition (QPT) in the anisotropic spin XY model. The results indicate that the QPT is well visualized in terms of the shape of the QSE, i.e. it is an oblate spheroid in the spin-fluid phase and a needle in the Néel phase. Meanwhile, after several iterations of renormalization, the QSE volume V undergoes a contraction mutation, and can develop two saturated values at the critical points associated with the QPT, which correspond to two different phases: the spin-fluid phase and the Néel phase. We also find that the QSE is closely associated with quantum entanglement in the model, i.e. the volume of the QSE between blocks is more than 4π/81 when the system is in the spin-fluid phase, which indicates that the system must be entangled. Furthermore, the nonanalytic and scaling behaviors of the volume of the QSE have been analyzed in detail, and the results convince us that the quantum critical properties are connected with the behavior of the QSE.

Study of the Berezinskii–Kosterlitz–Thouless transition: an unsupervised machine learning approach

The Berezinskii–Kosterlitz–Thouless (BKT) transition in magnetic systems is an intriguing phenomenon, and estimating the BKT transition temperature is a long-standing problem. In this work, we explore anisotropic classical Heisenberg XY and XXZ models with ferromagnetic exchange on a square lattice and antiferromagnetic exchange on a triangular lattice using an unsupervised machine learning approach called principal component analysis (PCA). The earlier PCA studies of the BKT transition temperature ( TBKT ) using the vorticities as input fail to give any conclusive results, whereas, in this work, we show that the proper analysis of the first principal component-temperature curve can estimate TBKT which is consistent with the existing literature. This analysis works well for the anisotropic classical Heisenberg with a ferromagnetic exchange on a square lattice and for frustrated antiferromagnetic exchange on a triangular lattice. The classical anisotropic Heisenberg antiferromagnetic model on the triangular lattice has two close transitions: the TBKT and Ising-like phase transition for chirality at Tc , and it is difficult to separate these transition points. It is also noted that using the PCA method and manipulation of their first principal component not only makes the separation of transition points possible but also determines transition temperature.

Investigating quantum criticality and multipartite entanglement in the anisotropic XY model with staggered Dzyaloshinskii–Moriya interaction

Investigating quantum criticality and multipartite entanglement in the anisotropic XY model with staggered Dzyaloshinskii–Moriya interaction

Quantum otto machine in Lipkin-Meshkov-Glick model with magnetic field and a symmetric cross interaction

This study investigates the quantum heat correlations associated with the quantum Otto machine, considering the discrete sides of the Lipkin-Meshkov-Glick model as the working medium in the presence of a magnetic field and a symmetric cross interaction. The eigenenergy and occupation probabilities of two-sided and three-sided spin interactions are determined at thermal equilibrium. The results reveal symmetrical heat correlations around the coupling of the symmetric cross interaction, regardless of whether the working medium adopts anisotropic XY, Ising model, or mixed ferromagnetism. The work done by two or three sides of the mixed ferromagnetic working substance exhibits symmetry but with different maximum bounds. Furthermore, the efficiency of the two-sided mixed ferromagnetism model improves as the exchange parameter increases, while the maximum efficiency of the anisotropic XY model is lower compared to the efficiency of the Ising model and mixed ferromagnetism. It is also highlighted that a quantum heat engine or refrigerator can be generated by controlling the system’s anisotropy parameter using a three-sided spin interaction.

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.

Generalized phase-space techniques to explore quantum phase transitions in critical quantum spin systems

We apply the generalized Wigner function formalism to detect and characterize a range of quantum phase transitions in several cyclic, finite-length, spin-12 one-dimensional spin-chain models, viz., the Ising and anisotropic XY models in a transverse field, and the XXZ anisotropic Heisenberg model. We make use of the finite system size to provide an exhaustive exploration of each system’s single-site, bipartite and multi-partite correlation functions. In turn, we are able to demonstrate the utility of phase-space techniques in detecting and characterizing first-order, second-order and infinite-order quantum phase transitions, while also enabling an in-depth analysis of the correlations present within critical systems. We also highlight the method’s ability to capture other features of spin systems such as ground-state factorization and critical system scaling. Finally, we demonstrate the generalized Wigner function’s utility for state verification by determining the state of each system and their constituent sub-systems at points of interest across the quantum phase transitions, enabling interesting features of critical systems to be readily analyzed.

Thermal local quantum Fisher and Wigner–Yanase correlations in an anisotropic two-qubit Heisenberg XY model

Thermal local quantum Fisher and Wigner–Yanase correlations in an anisotropic two-qubit Heisenberg XY model

Non-Hermitian Ising model at finite temperature

As a very simple model, the Ising model plays an important role in statistical physics. In the paper, with the help of quantum Liouvillian statistical theory, we study the one-dimensional non-Hermitian Ising model at finite temperature and give its analytical solutions. We find that the non-Hermitian Ising model shows quite different properties from those of its Hermitian counterpart. For example, the ‘pseudo-phase transition’ is explored between the ‘topological’ phase and the ‘non-topological’ phase, at which the Liouvillian energy gap is closed rather than the usual energy gap. In particular, we point out that the one-dimensional non-Hermitian Ising model at finite temperature can be equivalent to an effective anisotropic XY model in the transverse field. This work will help people understand quantum statistical properties of non-Hermitian systems at finite temperatures.

Quantum criticality in spin-1/2 anisotropic XY model with staggered Dzyaloshinskii–Moriya interaction

By utilizing the infinite time evolving block decimation method in infinite matrix product state representation, the quantum criticality and critical exponents varying are investigated in the spin-1/2 anisotropic XY chain with staggered Dzyaloshinskii–Moriya interaction. The phase diagram is obtained from the entanglement measurement, where a XY phase line δ=0 separates the Néel phase. Along this critical line, the central charge c=1 is extracted from the finite entanglement and the finite correlation length. In addition, the characteristic critical exponents are obtained from the local transverse magnetization, nonlocal transverse Néel order, and the correlation length, respectively. It is found that all the critical exponents are varying continuously along the phase transition line δ=0, and the ratios of critical exponents imply that the phase transition is in conformity with the weak universality. The linear relations of the critical exponents are able to illustrate the dependence between the critical exponents and the Dzyaloshinskii–Moriya interaction.

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...

Distribution of entanglement with variable range interactions

Distribution of quantum entanglement is investigated for an anisotropic quantum XY model with variable range interactions and in the presence of a uniform transverse magnetic field. We report the possibility of qualitative growth in entanglement between distant sites with an increase in the range of interactions that vary either exponentially or polynomially as the distance between the sites increases. Interestingly, we find that such entanglement enhancement is not ubiquitous and is dependent on the factorization points, a specific set of system parameters where the zero-temperature state of the system is fully separable. In particular, we observe that at zero-temperature, when the system parameters are chosen beyond the pair of factorization points, the increments in entanglement length due to variable range interactions are more pronounced compared to the situation when the parameters lie in between the factorization points. By employing the sum of all the bipartite entanglements with respect to a single site, we also show that the shareability of the bipartite entanglements is constrained, thereby establishing their monogamous nature. Furthermore, we note that the factorization points get reallocated depending on the laws of interaction fall-offs and provide an ansatz for the same. We reveal that the temperature at which the canonical equilibrium state becomes entangled from an unentangled one increases with the increase in the range of interactions, thereby demonstrating enhanced robustness in entanglement against temperature in the presence of long-range interactions and only when the system parameters are chosen between the pair of factorization points. We apply an energy-based entanglement witness to provide a justification to the observed robustness with temperature.

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.

Finite-time two-spin quantum Otto engines: Shortcuts to adiabaticity vs. irreversibility

We propose a quantum Otto cycle in a two spin-1/2 anisotropic XY model in a transverse external magnetic field. We first characterize the parameter regime that the working medium operates as an engine in the adiabatic regime. Then, we consider finite-time behavior of the engine with and without utilizing a shortcut to adiabaticity (STA) technique. STA schemes guarantee that the dynamics of a system follows the adiabatic path, at the expense of introducing an external control. We compare the performance of the nonadiabatic and STA engines for a fixed adiabatic efficiency but different parameters of the working medium. We observe that, for certain parameter regimes, the irreversibility, as measured by the efficiency lags, due to finite-time driving is so low that nonadiabatic engine performs quite close to the adiabatic engine, leaving the STA engine only marginally better than the nonadiabatic one. This suggests that by designing the working medium Hamiltonian one may spare the difficulty of dealing with an external control protocol.

Quantum criticality and excitations of a long-range anisotropic XY chain in a transverse field

The critical breakdown of a one-dimensional quantum magnet with long-range interactions is studied by investigating the high-field polarized phase of the anisotropic XY model in a transverse field for the ferromagnetic and antiferromagnetic cases. While for the limiting case of the isotropic long-range XY model we can extract the elementary one-quasiparticle dispersion analytically and calculate two-quasiparticle excitation energies quantitatively in a numerical fashion, for the long-range Ising limit as well as in the intermediate regime we use perturbative continuous unitary transformations on white graphs in combination with classical Monte Carlo simulations for the graph embedding to extract high-order series expansions in the thermodynamic limit. This enables us to determine the quantum-critical breakdown of the high-field polarized phase by analyzing the gap closing including associated critical exponents and multiplicative logarithmic corrections. In addition, for the ferromagnetic isotropic XY model we determined the critical exponents $z$ and $\ensuremath{\nu}$ analytically by a bosonic quantum-field theory.

Characterization of an operational quantum resource in a critical many-body system

Quantum many-body systems have been extensively studied from the perspective of quantum technology, and conversely, critical phenomena in such systems have been characterized by operationally relevant resources like entanglement. In this paper, we investigate robustness of magic (RoM), the resource in magic state injection based quantum computation schemes, in the context of the transverse field anisotropic XY model. We show that the the factorizable ground state in the symmetry broken configuration is composed of an enormous number of highly magical H states. We find the existence of a point very near the quantum critical point where magic contained explicitly in the correlation between two distant qubits attains a sharp maxima. Unlike bipartite entanglement, this persists over very long distances, capturing the presence of long range correlation near the phase transition. We derive scaling laws and extract corresponding exponents around criticality. Finally, we study the effect of temperature on two-qubit RoM and show that it reveals a crossover between dominance of quantum and thermal fluctuations.

Effect of exciton-phonon coupling on regular spin conductivity in the anisotropic three-dimensional XY model

In this work, we investigate the effect of spin-phonon coupling on continuum spin conductivity in the spin-1 quantum three-dimensional XY model with single-ion anisotropy in the cubic lattice and in the neighborhood of a quantum phase transition by using Schwinger bosons formalism. It is well known that there is a phase transition in the model from a Néel phase to the paramagnetic phase. Since the model with Dzyaloshinskii-Moriya interaction plus single anisotropy term is a source of anomalous effects such as spin Hall effect, it is important to know the spin transport properties of this model.

Scaling of Einstein–Podolsky–Rosen steering in spin chains

Symmetric quantum properties and correlations have been often used earlier to study quantum phase transitions in many body systems and spin models. However, the use of asymmetric quantum features, such as steering, have attracted smaller amount of attention in this context, so far. We study EPR steering and quantum phase transitions in the Ising model in transverse field and in the anisotropic XY model by using steering robustness and quantum renormalization group method. The key ingredients of the quantum criticality near the critical points, such as finite-size scaling behaviour and critical exponents, are investigated in detail with two commonly used spin models. Our results show that the first derivative of steering robustness between two blocks diverges near the quantum phase transition points for both models, and exhibits a finite-size scaling effect. Moreover, we explore in detail the asymmetric character of EPR steering, by taking into accounts finite-size effects and measurement number, in the reduced block state in the anisotropic XY model. The results imply that one-way EPR steering does not exist in large system under the limit despite the fact that EPR steering for the reduced block state is asymmetric.

A comparative study of local quantum Fisher information and local quantum uncertainty in Heisenberg XY model

Recently, it has been shown that the quantum Fisher information via local observables and via local measurements (i.e., local quantum Fisher information (LQFI)) is a central concept in quantum estimation and quantum metrology and captures the quantumness of correlations in multi-component quantum system (Kim et al. (2018) [28]). This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In the present study, we have revealed that LQU is bounded by LQFI in the phase estimation protocol. Also, a comparative study between these two quantum correlations quantifiers is addressed for the quantum Heisenberg XY model. Two distinct situations are considered. The first one concerns the anisotropic XY model and the second situation concerns isotropic XY model submitted to an external magnetic field. Our results confirm that LQFI reveals more quantum correlations than LQU.

Einstein–Podolsky–Rosen steering in critical systems

We explore Einstein–Podolsky–Rosen steering, measured by steering robustness, in the ground states of several typical models that exhibit a quantum phase transition. For the anisotropic XY model, steering robustness approaches zero around the critical point and vanishes in the ferromagnetic phase despite the fact that there exist other quantum nonlocalities, e.g. quantum entanglement. For the Heisenberg XXZ model, steering robustness exhibits some similar behavior as entanglement around the infinite-order quantum phase transition point Δ = 1, e.g. reaching its maximum. As a further example, we also consider steering robustness in the Lipkin–Meshkov–Glick collective spin model. It is then shown that steering robustness disappears at the transition point and remains at zero in the fully polarized symmetric phase, just like the behavior of entanglement and Bell nonlocality.

Phase boundaries in an alternating-field quantum XY model with Dzyaloshinskii-Moriya interaction: Sustainable entanglement in dynamics

We report all phases and corresponding critical lines of the quantum anisotropic transverse XY model with Dzyaloshinskii-Moriya (DM) interaction along with uniform and alternating transverse magnetic fields (ATXY) by using appropriately chosen order parameters. We prove that when DM interaction is weaker than the anisotropy parameter, it has no effect at all on the zero-temperature states of the XY model with uniform transverse magnetic field which is not the case for the ATXY model. However, when DM interaction is stronger than the anisotropy parameter, we show appearance of a new gapless phase - a chiral phase - in the XY model with uniform as well as alternating field. We further report that first derivatives of nearest neighbor two-site entanglement with respect to magnetic fields can detect all the critical lines present in the system. We also observe that the factorization surface at zero-temperature present in this model without DM interaction becomes a volume on the introduction of the later. We find that DM interaction can generate bipartite entanglement sustainable at large times, leading to a proof of ergodic nature of bipartite entanglement in this system, and can induce a transition from non-monotonicity of entanglement with temperature to a monotonic one.