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arXiv:2602.01259

The Intrinsic Connection between Dynamical Phase Transitions and Magnetization in the 1D XY Model

Lin-Yue Luo, Wei-Lin Li, Bao-Ming Xu, Zhi Li

quant-phcond-mat.otherSubmitted Feb 1, 2026• Announced Feb 3, 2026• 0 citations
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Abstract

In this manuscript, we study the quench dynamics of a transverse-field XY model starting from coherent Gibbs states. The results reveal that the initial strength of magnetization plays a crucial role in the emergence of dynamical quantum phase transitions. In concrete terms, when quenching within the same phase, through the properties of observables such as Fisher zeros and magnetization, we show that the stronger the initial magnetization, the more difficult the emergence of dynamical quantum phase transitions. The underlying mechanism is that the strong initial magnetization provides a directional effect, which inhibits the spin flipping in the process of quantum quench, making the dynamical quantum phase transition difficult to emerge. Since dynamical quantum phase transitions can be experimentally realized in various artificial systems, we hope that the physics predicted here can be experimentally verified in tabletop platforms.

Comments
13 pages, 8 figures

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In this manuscript, we study the quench dynamics of a transverse-field XY model starting from coherent Gibbs states. The results reveal that the initial strength of magnetization plays a crucial role in the emergence of dynamical quantum phase transitions. In concrete terms, when quenching within the same phase, through the properties of observables such as Fisher zeros and magnetization, we show that the stronger the initial magnetization, the more difficult the emergence of dynamical quantum phase transitions. The underlying mechanism is that the strong initial magnetization provides a directional effect, which inhibits the spin flipping in the process of quantum quench, making the dynamical quantum phase transition difficult to emerge. Since dynamical quantum phase transitions can be experimentally realized in various artificial systems, we hope that the physics predicted here can be experimentally verified in tabletop platforms.
Abstract Quantum coherence will undoubtedly play a fundamental role in understanding the dynamics of quantum many-body systems; therefore, to be able to reveal its genuine contribution is of great importance. In this paper, we focus our discussions on the one-dimensional transverse field quantum Ising model initialized in the coherent Gibbs state, and investigate the effects of quantum coherence on dynamical quantum phase transition (DQPT). After quenching the strength of the transverse field, the effects of quantum coherence are studied using Fisher zeros and the rate function of the Loschmidt echo. We find that quantum coherence not only recovers DQPT destroyed by thermal fluctuations, but also generates some entirely new DQPTs, which are independent of the equilibrium quantum critical point. We also find that the Fisher zero cutting the imaginary axis is not sufficient to generate DQPT because it also requires the Fisher zeros to be tightly bound close enough to the neighborhood of the imaginary axis. It can be manifested that DQPTs are rooted in quantum fluctuations. This work reveals new information on the fundamental connection between quantum critical phenomena and quantum coherence.
Based on the obtained exact results we systematically study the quench dynamics of a one-dimensional spin-1/2 transverse field Ising model with zero- and finite-temperature initial states. We focus on the magnetization of the system after a sudden change of the external field and a coherent time-evolution process. With a zero-temperature initial state, the quench magnetic susceptibility as a function of the initial field strength exhibits strongly similar scaling behaviors to those of the static magnetic susceptibility, and the quench magnetic susceptibility as a function of the final field strength shows a discontinuity at the quantum critical point. This discontinuity remains robust and always occurs at the quantum critical point even for the case of finite-temperature initial systems, which indicates a great advantage of employing quench dynamics to study quantum phase transitions.
We study the influence of disorder on the dynamical quantum phase transitions (DQPTs) in the transverse-field anisotropic XY chain after a sudden quench. The formulas to calculate the Loschmidt echo and Fisher zeros of the inhomogeneous XY chain are derived in real space. It is found that new DQPTs appear in the presence of weak disorder for the quenches across the Ising transition and two quantum phase transitions (Ising and anisotropic transitions). As the disorder strength increases, it's demonstrated that the Fisher zeros coalesce to regions on the imaginary axis in the thermodynamic limit. The DQPTs occur at the critical times corresponding to the boundaries of the Fisher zeros regions on the imaginary axis. However, for the quench across the anisotropic transition, the Fisher zeros regions appear even for the very weak disorder. Finally, for the quench within the same phase, the weak disorder is found having no effect on the DQPTs, but the DQPTs will be washed out in the presence of strong disorder.
This work investigates dynamical quantum phase transitions (DQPTs) in a one-dimensional Ising model subjected to a periodically modulated transverse field. In contrast to sudden quenches, we demonstrate that a DQPT can be induced in two distinct ways. First, when the system remains within a given phase--ferromagnetic (FM) or paramagnetic (PM), a resonant periodic drive can trigger a DQPTs when its frequency matches the energy-level transition of the system. This DQPT is intimately connected to the emergence of Floquet topological phases. The timescale for the transition is governed by the perturbation strength λ′λ'λ′, the critical mode kck_ckc​, and its energy gap ΔkcΔ_{k_c}Δkc​​, following the scaling relation τ∝Δkcλ′−1csc⁡kcτ\proptoΔ_{k_c}λ'^{-1}\csc k_cτ∝Δkc​​λ′−1csckc​. Second, for drives across the critical point between the FM and PM phases, low frequencies can always induce DQPT, regardless of resonance. This behavior stems from the degeneracy of the energy-level at the critical point, which ensures that any drive with a frequency lower than the system's intrinsic transition frequency will inevitably excite the system. However, in the high-frequency regime, such excitation will be strongly suppressed, thereby inhibiting the occurrence of DQPTs. This study provides deeper insight into the nonequilibrium dynamics of quantum spin chains.
We review quantum phase transitions of spin systems in transverse magnetic fields taking the examples of the spin-1/2 Ising and XY models in a transverse field. Beginning with an overview of quantum phase transitions, we introduce a number of model Hamiltonians. We provide exact solutions in one spatial dimension connecting them to conformal field theoretical studies. We also discuss Kitaev models and some other exactly solvable spin systems. Studies of quantum phase transitions in the presence of quenched randomness and with frustrating interactions are presented in detail. We discuss novel phenomena like Griffiths-McCoy singularities. We then turn to more recent topics like information theoretic measures of the quantum phase transitions in these models such as concurrence, entanglement entropy, quantum discord and quantum fidelity. We then focus on non-equilibrium dynamics of a variety of transverse field systems across quantum critical points and lines. After mentioning rapid quenching studies, we dwell on slow dynamics and discuss the Kibble-Zurek scaling for the defect density following a quench across critical points and its modifications for quenching across critical lines, gapless regions and multicritical points. Topics like the role of different quenching schemes, local quenching, quenching of models with random interactions and quenching of a spin chain coupled to a heat bath are touched upon. The connection between non-equilibrium dynamics and quantum information theoretic measures is presented at some length. We indicate the connection between Kibble-Zurek scaling and adiabatic evolution of a state as well as the application of adiabatic dynamics as a tool of a quantum optimization technique known as quantum annealing. The final section is dedicated to a detailed discussion on recent experimental studies of transverse Ising-like systems.
Abstract Ergodicity sits at the heart of the connection between statistical mechanics and dynamics of a physical system. By fixing the initial state of the system into the ground state of the Hamiltonian at zero temperature and tuning a control parameter, we consider the occurrence of the ergodicity with quench dynamics in the one-dimensional (1D) spin-1/2 XY model in a transverse magnetic field. The ground-state phase diagram consists of two ferromagnetic and paramagnetic phases. It is known the magnetization in this spin system is non-ergodic. We set up two different experiments as we call them single and double quenches and test the dynamics of the magnetization along the Z-axis and the spin-spin correlation function along the X-axis which are the order parameters of the zero-temperature phases . Our exact results reveal that for single quenches at zero-temperature, the ergodicity depends on the initial state and the order parameter. In single quenches for a given order parameter, ergodicity will be observed with an ergodic-region for quenches from another phase, non-correspond to the phase of the order parameter, into itself. In addition, a quench from a ground-state phase point corresponding to the order parameter into or very close to the quantum critical point, hc = 1.0, discloses an ergodic behavior. Otherwise, for all other single quenches, the system behaves non-ergodic. Interestingly on the other setup, a double quench on a cyclic path, ergodicity is completely broken for starting from the phase corresponding to the order parameter. Otherwise, it depends on the first quenched point, and the quench time T when the model spent before a second quench in the way back which gives an ability to controlling the ergodicity in the system. Therefore, and contrary to expectations, in the mentioned model the ergodicity can be observed with probing quench dynamics at zero-temperature. Our results provide further insight into the zero-temperature dynamical behavior of quantum systems and their connections to the ergodicity phenomenon.