Dynamical quantum phase transitions (DQPTs) are an exciting paradigm of out-of-equilibrium criticality in many-body systems manifested in nonanalytic behavior in the return rate to the initial state following a sudden quench. While previous work has tried to distinguish between distinct types of DQPTs, such as regular and anomalous, or manifold and branch, a comprehensive understanding of why each type appears in a given scenario is still lacking. In this work, we propose a unified framework addressing this gap in terms of the energy structure of different product state configurations. In particular, while manifold DQPTs are governed by resonances within the initial state manifold, branch DQPTs are governed by resonances with a transitional manifold of states dynamically connected to the initial manifold by low-order processes. We show that the (ir)regularity of branch DQPTs is related to the multiplicity of this transitional manifold, and we also observe exotic periods of extended degeneracy in the return rate (beyond the conventional level crossing of a DQPT) which are also conditioned on the structure of this transitional manifold. We demonstrate this by studying quenches of two different configurations in the 1 + 1D Z_2 LGT to various parameter regimes. Our findings provide a dynamical mechanism underlying branch DQPTs and frames DQPTs as probes of resonant connectivity in constrained Hilbert spaces, paving the way to a more complete understanding of the multifaceted nature of dynamical criticality.
Dynamical quantum phase transitions (DQPTs) are an exciting paradigm of out-of-equilibrium criticality in many-body systems manifested in nonanalytic behavior in the return rate to the initial state following a sudden quench. While previous work has tried to distinguish between distinct types of DQPTs, such as regular and anomalous, or manifold and branch, a comprehensive understanding of why each type appears in a given scenario is still lacking. In this work, we propose a unified framework addressing this gap in terms of the energy structure of different product state configurations. In particular, while manifold DQPTs are governed by resonances within the initial state manifold, branch DQPTs are governed by resonances with a transitional manifold of states dynamically connected to the initial manifold by low-order processes. We show that the (ir)regularity of branch DQPTs is related to the multiplicity of this transitional manifold, and we also observe exotic periods of extended degeneracy in the return rate (beyond the conventional level crossing of a DQPT) which are also conditioned on the structure of this transitional manifold. We demonstrate this by studying quenches of two different configurations in the 1 + 1D Z_2 LGT to various parameter regimes. Our findings provide a dynamical mechanism underlying branch DQPTs and frames DQPTs as probes of resonant connectivity in constrained Hilbert spaces, paving the way to a more complete understanding of the multifaceted nature of dynamical criticality.
Global quenches of quantum many-body models can give rise to periodic dynamical quantum phase transitions (DQPTs) directly connected to the zeros of a Landau order parameter (OP). The associated dynamics has been argued to bear a close resemblance to Rabi oscillations characteristic of two-level systems. Here, we address the question of whether this DQPT behavior is merely a manifestation of the limit of an effective two-level system or if it can arise as part of a more complex dynamics. We focus on quantum many-body scarring as a useful toy model allowing us to naturally study state transfer in an otherwise chaotic system. We find that a DQPT signals a change in the dominant contribution to the wave function in the degenerate initial-state manifold, with a direct relation to an OP zero only in the special case of occurring at the midpoint of an evenly degenerate manifold. Our work generalizes previous results and reveals that, in general, periodic DQPTs comprise complex many-body dynamics fundamentally beyond that of two-level systems.
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′, the critical mode kc, and its energy gap Δkc, following the scaling relation τ∝Δkcλ′−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.
Dynamical quantum phase transitions (DQPTs) are a powerful concept of probing far-from-equilibrium criticality in quantum many-body systems. With the strong ongoing experimental drive to quantum simulate lattice gauge theories, it becomes important to investigate DQPTs in these models in order to better understand their far-from-equilibrium properties. In this work, we use infinite matrix product state techniques to study DQPTs in spin-SU(1) quantum link models. Although we are able to reproduce literature results directly connecting DQPTs to a sign change in the dynamical order parameter in the case of S=1/2 for quenches starting in a vacuum initial state, we find that for different quench protocols or different values of the link spin length S>1/2 this direct connection is no longer present. In particular, we find that there is an abundance of different types of DQPTs not directly associated with any sign change of the order parameter. Our findings indicate that DQPTs are fundamentally different between the Wilson-Kogut-Susskind limit and its representation through the quantum link formalism.
Abstract Dynamical quantum phase transitions (DQPTs), which serve as a theoretical framework for understanding far-from-equilibrium physics in quantum many-body systems, have recently been observed experimentally. Their topological properties are typically characterized by the winding number, which acts as an order parameter. While DQPTs exhibiting both integer and half-integer jumps in the winding number have been reported, the underlying mechanisms behind these distinct topological behaviors, as well as the potential existence of other topological classes, remain open questions. To address this, we investigate DQPTs in the one-dimensional (1D) XY model under a quench protocol. We show that the observed topological diversity originates from the nature of the critical modes, which we classify into two categories: boundary modes and interior modes. Specifically, critical interior modes always lead to DQPTs with an integer winding number, while critical boundary modes always result in DQPTs characterized by a half-integer winding number. By analyzing the number and classification of critical modes, we provide a classification of the topological properties of DQPTs in the 1D XY model. According to their distinct topological features, we categorize DQPTs into six types, three of which have not been previously identified in the literature. We discuss in detail the conditions associated with each type and present the corresponding dynamical phase diagrams. Our framework is not restricted to the XY model; it is applicable to other two-band models in 1D systems, including the SSH model, Kitaev chain, Rice–Mele model, and Creutz model.
Dynamical quantum phase transitions (DQPTs), which refer to the criticality in time of a quantum many-body system, have attracted much theoretical and experimental research interest recently. Despite that DQPTs are defined and signaled by the nonanalyticities in the Loschmidt rate, its interrelation with various correlation measures such as the equilibrium order parameters of the system remains unclear. In this work, by considering the quench dynamics in an interacting topological model, we find that the equilibrium order parameters of the model in general exhibit signatures around the DQPT, in the short time regime. The first extrema of the equilibrium order parameters are connected to the first Loschmidt rate peak. By studying the unequal-time two-point correlation, we also find that the correlation between the nearest neighbors decays while that with neighbors further away builds up as time grows in the noninteracting case, and upon the addition of repulsive intracell interactions. On the other hand, the intercell interaction tends to suppress the two-site correlations. These findings could provide us insights into the characteristic of the system around DQPTs, and pave the way to a better understanding of the dynamics in nonequilibrium quantum many-body systems.
Confinement is an intriguing phenomenon prevalent in condensed matter and high-energy physics. Exploring its effect on the far-from-equilibrium criticality of quantum many-body systems is of great interest from both a fundamental and a technological point of view. Here, we employ large-scale uniform matrix product state calculations to show that a qualitative change in the type of dynamical quantum phase transitions (DQPTs) accompanies the confinement-deconfinement transition in three paradigmatic models: the power-law interacting quantum Ising chain, the two-dimensional quantum Ising model, and the spin- S U ( 1 ) quantum link model. By tuning a confining parameter in these models, it is found that () DQPTs arise as a signature of (de)confinement. Whereas manifold DQPTs are associated with a sign change of the order parameter, their branch counterparts are not, but rather occur even when the order parameter exhibits considerably constrained dynamics. Our conclusions can be tested in modern quantum-simulation platforms, such as ion-trap setups and cold-atom experiments of gauge theories.