Research on topological models unveils fascinating physics, especially in the realm of dynamical quantum phase transitions (DQPTs). However, the understanding of entanglement structures and properties near DQPT in models with longer-range hoppings is far from complete. In this work, we study DQPTs in the quenched extended Su-Schrieffer-Heeger model. Anomalous DQPTs, where the number of critical momenta exceeds the winding number differences between the prequench and postquench phases, are observed. We find that the entanglement exhibits local maximum (minimum) around the anomalous DQPTs, in line with the level crossings (separations) around the middle of the correlation matrix spectrum. We further categorize the phases in the equilibrium model into two classes and distinctive features in the time evolution of the entanglement involving quenches within and across the two classes are identified. The findings pave the way to a better understanding of topological models with longer-range hoppings in the out-of-equilibrium regime.
Research on topological models unveils fascinating physics, especially in the realm of dynamical quantum phase transitions (DQPTs). However, the understanding of entanglement structures and properties near DQPT in models with longer-range hoppings is far from complete. In this work, we study DQPTs in the quenched extended Su-Schrieffer-Heeger model. Anomalous DQPTs, where the number of critical momenta exceeds the winding number differences between the prequench and postquench phases, are observed. We find that the entanglement exhibits local maximum (minimum) around the anomalous DQPTs, in line with the level crossings (separations) around the middle of the correlation matrix spectrum. We further categorize the phases in the equilibrium model into two classes and distinctive features in the time evolution of the entanglement involving quenches within and across the two classes are identified. The findings pave the way to a better understanding of topological models with longer-range hoppings in the out-of-equilibrium regime.
Abstract The dynamics of quantum phase transitions of topological systems has attracted interest. Here we consider the effect of long-range hopping terms on the dynamic behavior. The long-range hoppings preserve chiral symmetry and decay as a function of distance, with an exponent β. We also consider a situation where the hoppings are modulated by oscillations. We compare the results with those obtained for short-range models such as the Su–Schrieffer–Heeger model or its extension to second neighboring cells. While often the lowest critical times coincide with the first peak of the Loschmidt rate, several anomalous cases are identified. Also, the number of critical times often exceeds the absolute value of the change of the winding number in a quench. Various correlation functions are considered, and their time-dependence may often be used to identify the early-time dynamical phase transitions.
We investigate dynamical quantum phase transitions (DQPTs) in both pure and mixed states within the extended Su-Schrieffer-Heeger (SSH) model framework, focusing on the SSH-3 and SSH-4 models, which differ in symmetry properties. The SSH-3 model, characterized by a chiral-like point symmetry rather than true chiral symmetry, supports robust localized edge states tied to its topological nature. Our results show that for pure states, DQPTs occur after quenches crossing the topological transition, even when the energy band gap remains open. For mixed states, DQPT behavior aligns with pure states at low temperatures but undergoes significant changes at higher temperatures, including the emergence of multiple critical times. In contrast, the SSH-4 model, which possesses chiral symmetry, features four distinct energy-spectrum configurations. We find that pure-state DQPTs arise only when the quench starts from the initial state, chosen from a band that becomes gapless with another band at a certain critical point, and crosses the critical point. At finite temperature, mixed-state DQPTs persist at low temperatures only if the corresponding pure-state quench induces DQPTs, but they disappear at elevated temperatures. These findings elucidate the interplay between symmetry, band structures, and temperature in governing DQPTs within generalized SSH models.
We investigate the critical behavior of momentum-space entanglement entropy at dynamical quantum phase transitions (DQPTs) in translationally invariant two-band insulators and superconductors. By analyzing the Su-Schrieffer-Heeger model, the quantum XY chain, and the Haldane model, we establish that the geometric DQPT condition d^ki⋅d^kf=0 manifests as exact degeneracy pk∗=1/2 in the entanglement spectrum defined with respect to the post-quench eigenbasis, yielding a maximal momentum-space entropy of ln2. In one dimension, critical momenta appear as isolated points, whereas in two dimensions they form continuous one-dimensional manifolds, reflecting the dimensional dependence of the underlying critical structure. Importantly, alternative bipartitions such as the sublattice basis produce qualitatively different behavior: the entropy becomes explicitly time-dependent and attains a minimum at DQPT critical times, underscoring the essential role of basis selection. Our results establish that momentum-space entanglement entropy, when evaluated in the appropriate eigenbasis, provides a robust, time-independent diagnostic of DQPTs and offers a unified geometric perspective linking entanglement, topology, and non-equilibrium criticality.
Abstract The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena—topological phases and dynamical quantum phase transitions (DQPTs)—in non-Hermitian systems. Focusing on one-dimensional models with chiral symmetry, we find DQPTs following the quench from a trivial to a non-Hermitian topological phase. Moreover, the critical momenta and critical time of the DQPTs are found to be directly related to the topological invariants of the non-Hermitian system. We further demonstrate our theory in three prototypical non-Hermitian lattice models, the lossy Kitaev chain (LKC), the LKC with next-nearest-neighbor hoppings, and the nonreciprocal Su–Schrieffer–Heeger model. Finally, we suggest a proposal to experimentally verify the found connection by a nitrogen-vacancy center in diamond.
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.
Recent studies of moiré physics have unveiled a wealth of opportunities for significantly advancing the field of quantum phase transitions. However, properties of reentrant phase transitions driven by moiré strength are poorly understood. Here, we investigate the reentrant sequence of phase transitions and the invariant of universality class in moiré-modulated extended Su-Schrieffer-Heeger (SSH) model. For the simplified case with intercell hopping w=0, we analytically derive renormalization relations of Hamiltonian parameters to explain the reentrant phenomenon. For the general case, numerical phase boundaries are calculated in the thermodynamic limit. The bulk boundary correspondence between zero-energy edge modes and entanglement spectrum is revealed from the degeneracy of both quantities. We also address the correspondence between the central charge obtained from entanglement entropy and the change in winding number during the phase transition. Our results shed light on the understanding of universal characteristics and bulk-boundary correspondence for moiré induced reentrant phase transitions in 1D condensed-matter systems.