We investigate the nonequilibrium dynamics of a one-dimensional interacting system across a transition from a charge-density-wave (CDW) phase to a symmetry-protected topological (SPT) phase. Starting from a CDW initial state, we study both sudden quenches and slow ramps into the SPT regime. While the CDW order melts under both protocols, the fate of topological order is sharply different. Following a sudden quench, long-range SPT order does not emerge because the post-quench state contains a finite density of excitations above the topological ground state. In contrast, slow ramps allow the system to follow the instantaneous ground state away from the critical region, enabling the buildup of SPT order with deviations governed by Kibble-Zurek defect production. The dynamics is solvable via a unitary mapping to a quadratic fermionic Hamiltonian, allowing us to compute the Loschmidt echo, correlation functions, and string correlator. The Loschmidt rate function exhibits cusps signaling dynamical quantum phase transitions, while the correlation dynamics reveal the contrasting mechanisms governing quenches and ramps across the transition. These results demonstrate that entering the topological regime is not sufficient for the emergence of topological order; the decisive factor is the suppression of excitation production during the evolution.
We investigate the nonequilibrium dynamics of a one-dimensional interacting system across a transition from a charge-density-wave (CDW) phase to a symmetry-protected topological (SPT) phase. Starting from a CDW initial state, we study both sudden quenches and slow ramps into the SPT regime. While the CDW order melts under both protocols, the fate of topological order is sharply different. Following a sudden quench, long-range SPT order does not emerge because the post-quench state contains a finite density of excitations above the topological ground state. In contrast, slow ramps allow the system to follow the instantaneous ground state away from the critical region, enabling the buildup of SPT order with deviations governed by Kibble-Zurek defect production. The dynamics is solvable via a unitary mapping to a quadratic fermionic Hamiltonian, allowing us to compute the Loschmidt echo, correlation functions, and string correlator. The Loschmidt rate function exhibits cusps signaling dynamical quantum phase transitions, while the correlation dynamics reveal the contrasting mechanisms governing quenches and ramps across the transition. These results demonstrate that entering the topological regime is not sufficient for the emergence of topological order; the decisive factor is the suppression of excitation production during the evolution.
A structurally coherent pattern emerges across recent preprints in cond-mat.str-el and cond-mat.mes-hall: the question of *when* and *how* topological order emerges in quantum many-body systems cannot be answered by equilibrium phase diagrams alone. The emergence depends jointly on (i) the microscopic excitation production mechanism during dynamical protocols, (ii) the categorical symmetry structure that classifies what phases are even reachable, (iii) the anomaly type encoded in the Lyndon–Hochschild–Serre spectral sequence, (iv) the defect statistics and fusion rules that distinguish topological phases sharing identical anyon content, and (v) the non-Hermitian or interaction-driven amplification of charge instabilities near exceptional points. This is a heuristic reading, not a derivation: the five sources share conceptual architecture but not a common formalism. The thesis, stated as a candidate structural pattern worth investigating, is: **topological order is protocol-sensitive precisely because the categorical invariants that distinguish phases are invisible to local order parameters and can be populated or evacuated only by excitation-density-controlled dynamics**. Concretely, a sudden quench generically populates excitations that are orthogonal to the topological ground-state manifold, while slow ramps suppress this population via Kibble–Zurek mechanisms; categorical symmetry then determines which topological sectors are accessible at all; and anomaly type (E∞^{1,2} vs. E∞^{2,1}) determines whether the transition is dual to ordinary symmetry breaking or to the spontaneous breaking of a non-invertible symmetry. The falsification path is concrete: DMRG or tensor-network simulations of a spin-1/2 chain with D₈ LSM anomaly should show that a sudden quench into the DQCP regime fails to build non-invertible Rep(H₈) order parameters, while an adiabatic ramp does—a prediction that follows from the corpus findings taken together but has not yet been directly tested. Primary categories drawn upon: cond-mat.str-el (seven papers), cond-mat.mes-hall (two papers), cond-mat.dis-nn (one paper, weakly connected). --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.27166, 2605.27672, 2605.29875, 2605.31602, 2606.05856, 2606.06343, 2606.06466, 2606.07241, 2606.07247, 2606.08558, 2606.09722, 2606.09759, 2606.11048, 2606.11303, 2606.11527, 2606.12089, 2606.12180, 2606.12353
A recurring pattern across several recent preprints in condensed-matter physics is that the *density of excitations above the ground state* functions as a decisive control parameter for whether topological order can emerge, persist, or be characterized — and that this density is shaped not only by equilibrium phase boundaries but by the microscopic dynamics of how a system is driven, the boundary conditions imposed, the non-Hermitian structure of the effective Hamiltonian, and the algebraic framework used to classify order parameters. This synthesis draws on six papers from cond-mat.str-el and cond-mat.dis-nn (plus one connecting result from cond-mat.mes-hall) to develop a candidate reading — explicitly heuristic, not a derivation — of how these mechanisms compose. The central thesis is: topological order is not merely a property of a ground-state wave function but a *dynamically conditional* object whose emergence requires simultaneous suppression of excitation density (controlled by ramp protocol [corpus:arxiv:2606.11303]), non-Hermitian boundary-condition sensitivity [corpus:arxiv:2606.06466], and categorical symmetry structure [corpus:arxiv:2605.27672; corpus:arxiv:2606.05856; corpus:arxiv:2606.06343; corpus:arxiv:2605.31601]. The microscopic universal theory of symmetry-enriched topological quantum spin liquids [corpus:arxiv:2606.08558] provides the overarching framework within which these conditions can, in principle, be stated precisely. The falsification path is concrete: DMRG or tensor-network simulation of an interacting non-Hermitian SSH chain under controlled ramp protocols should reveal whether the exceptional-point amplification of charge-density-wave order [corpus:arxiv:2606.06466] suppresses or merely delays SPT order buildup in a manner quantitatively consistent with Kibble-Zurek defect counting. The synthesis is limited by abstract-only reading and by the fact that the papers do not share a common formalism; bridges between them are argued by mechanism, not derived. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.27166, 2605.27672, 2605.29745, 2605.29875, 2605.31540, 2605.31601, 2606.02512, 2606.04651, 2606.04748, 2606.04958, 2606.05856, 2606.06343, 2606.06412, 2606.06432, 2606.06466, 2606.06490, 2606.07241, 2606.08558, 2606.08805, 2606.09722, 2606.09759, 2606.11048, 2606.11060, 2606.11303, 2606.12089, 2606.12180, 2606.12353
The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.
A central question in modern quantum matter is not merely *which* topological phases exist, but *how* and *when* they become accessible — the dynamical, microscopic, and symmetry-theoretic conditions under which topological order can actually emerge, be diagnosed, or be destroyed. This synthesis identifies a structural pattern across five specific findings from recent cond-mat.str-el, cond-mat.dis-nn, and cond-mat.mes-hall preprints: (1) non-Hermitian delocalization generically realizes random Dirac criticality in 1D, providing a topological mechanism for criticality without fine-tuning [corpus:arxiv:2606.12089]; (2) the fate of symmetry-protected topological order under nonequilibrium drives is governed by excitation density rather than by which phase regime is entered, with Kibble-Zurek defect production as the decisive control parameter [corpus:arxiv:2606.11303]; (3) exceptional points in interacting non-Hermitian systems amplify charge-density-wave instabilities under open boundary conditions, demonstrating that non-Hermitian boundary topology actively reshapes interaction-driven phase competition [corpus:arxiv:2606.06466]; (4) sequential-circuit invariants of non-invertible symmetry defects provide a purely operator-theoretic diagnostic of 't Hooft anomalies and identify genuinely new loop excitations with non-Abelian fermionic statistics in (3+1)D [corpus:arxiv:2606.11527]; and (5) deconfined quantum critical points in spin chains with Lieb-Schultz-Mattis anomalies are dual, via gauging, to spontaneous breaking of non-invertible symmetries, with the full fusion category — not merely the fusion ring — encoding inequivalent universality classes [corpus:arxiv:2606.05856, corpus:arxiv:2606.06343]. The synthesis argues, as a heuristic reading rather than a derivation, that excitation production, boundary-condition sensitivity, and categorical symmetry structure constitute three interlocking control axes for topological order accessibility. A concrete falsification path is proposed for each claim. The abstract-only reading methodology is acknowledged as a structural limitation throughout. --- Authorship: Saluca Agentic AI Research Team (Saluca LLC). AI-drafted from arXiv preprint corpus on the date in the filename. Cited arXiv preprints: 2605.27166, 2605.29745, 2605.29875, 2606.04651, 2606.04748, 2606.04958, 2606.05856, 2606.06343, 2606.06412, 2606.06432, 2606.06466, 2606.07041, 2606.07241, 2606.07247, 2606.08558, 2606.08805, 2606.09759, 2606.11048, 2606.11303, 2606.11527, 2606.12089, 2606.12353
Dynamical quantum phase transitions (DQPTs) manifested in the nonanalyticities in the temporal evolution of a closed quantum system generated by the time-independent final Hamiltonian, following a quench (or ramping) of a parameter of the Hamiltonian, is an emerging frontier of nonequilibrium quantum dynamics. We, here, introduce the notion of a dynamical topological order parameter (DTOP) that characterizes these DQPTs occurring in quenched (or ramped) two-dimensional closed quantum systems; this is quite a nontrivial generalization of the notion of DTOP introduced in Budich and Heyl [Phys. Rev. B 93, 085416 (2016)] for one-dimensional situations. This DTOP is obtained from the ``gauge-invariant'' Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time-evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur. What is remarkable is that while the topology of the equilibrium model is characterized by the Chern number, the emergent topology associated with the DQPTs is characterized by a generalized winding number.
We use infinite matrix-product-state techniques to study the time evolution of the charge-density-wave (CDW) order after a quench or a light pulse in a fundamental fermion-boson model. The motion of fermions in the model is linked to the creation of bosonic excitations, which counteracts the melting of the CDW order. For low-energy quenches corresponding to a change of the boson relaxation rate, we find behavior similar to that in an effective t−V model. When the boson energy is quenched instead or a light pulse is applied to the system, the transient dynamics are more complex, with the CDW order first quickly decreasing to an intermediate value while the density-wave-like order of the bosons rises. In the case of pulse irradiation, the subsequent time evolution of the CDW order depends strongly on the photon frequency. For frequencies slightly below the boson energy, we observe a temporary increase of the CDW order parameter. Our results reveal the complex physics of driven Mott insulators in low-dimensional systems with strong correlations. Published by the American Physical Society 2024