arXiv subjects

Vincent P. Flynn

Publications and source records attributed to Vincent P. Flynn.

9 recordsLinked to original sources

arXiv2026

Hidden Frustration in Collinear Altermagnets: Pairing Vortices and Equilibrium Spin Current Loops

We show that a magnet can remain perfectly collinear while its quantum vacuum circulates. In a centrosymmetric altermagnet, a symmetry-allowed locally staggered Dzyaloshinskii-Moriya coupling imprints a gauge-irremovable vortex-antivortex pair into the anomalous magnon pair correlations at high-symmetry points in momentum space. In real space, these hidden vortices produce an antiferrochiral array of equilibrium spin currents circulating oppositely around neighboring plaquettes. Gauge-irremovable frustration therefore survives despite classical collinearity: it exists entirely in the quantum correlations. Our results show that complex pairing, gauge-invariant fluxes, and equilibrium loop currents - structures encountered across electronic flux phases, spin liquids, and frustrated quantum magnets - can be encoded in the squeezed vacuum of a collinear magnet.

cond-mat.mes-hall↗

arXiv2026

Quantum criticality beyond thermodynamic stability

For a many-body system in equilibrium, described by a thermodynamically stable Hamiltonian, quantum criticality is associated with structural changes of the many-body ground state. However, there exist physically relevant models, notably, certain quadratic bosonic Hamiltonians (QBHs), which fail to have a ground state. QBHs can be dynamically stable or unstable. We show the notion of criticality is meaningful for the entire class of QBHs that are dynamically stable or at the boundary of instability, regardless of thermodynamic stability, and that the key state for such QBHs is a naturally and unambiguously defined quasiparticle vacuum (QPV). This state is Gaussian, and coincides with the ground state if the QBH is thermodynamically stable. We identify a relevant spectral gap, the Krein gap, associated to the minimal spectral separation between creation and annihilation operators, and show that the QPV is unique when the Krein gap is positive. We prove that, for dynamically stable QBHs with finite-range couplings, correlations are exponentially bounded unless the Krein gap closes, which is associated with one of two spectral degeneracies: an exceptional point or a Krein collision. Consequently, long-range QPV correlations can ensue. Thus, the Krein gap takes the role of the spectral gap for dynamically stable QBHs, and the boundary of dynamical stability and criticality (associated to exceptional points) or multicriticality (associated to Krein collisions) are the same. We also find that bosonic critical behavior beyond thermodynamic stability is witnessed by the scaling of the entanglement entropy and other indicators of equilibrium criticality from information geometry. Our framework opens the door to investigating all dynamically stable QBHs through the lens of critical phenomena, including thermodynamically unstable ones from photonics, cavity-QED, and magnonics.

quant-ph↗

arXiv2026

Dynamical metastability and transient topological magnons in interacting driven-dissipative magnetic systems

Metastability, i.e., partial relaxation to long-lived, quasi-stationary states before true asymptotic equilibrium sets in, emerges ubiquitously in classical and quantum dynamical systems as a result of timescales separation. In open quantum systems, an intrinsically nonequilibrium analogue, dynamical metastability, can originate from the spectral geometry of a non-Hermitian operator. In noninteracting models, this mechanism produces boundary-sensitive anomalous relaxation, transient amplification, and topologically mandated long-lived edge modes, all of which are enhanced as system size grows. Here we extend dynamical metastability into the nonlinear, interacting regime and identify magnetic heterostructures as a natural platform for its exploration. We introduce an interacting spin Lindbladian whose linearized magnon dynamics map onto a dynamically metastable Hatano-Nelson chain, and show that dynamical metastability in the noninteracting limit seeds genuinely nonlinear phenomena, including size-dependent spin dipping and anomalous attraction to unstable equilibria. Long-lived edge states associated to topologically mandated Dirac bosons persist under nonlinearities and disorder. We further analyze the magnetization dynamics in magnetic multilayers within the classical Landau-Lifshitz-Gilbert-Slonczewski framework, identifying Dzyaloshinskii-Moriya interaction, nonlocal damping, and spin-transfer torque as control parameters governing bulk-boundary stability mismatch and band topology. While all the distinctive dynamical phenomena previously identified reappear in this experimentally relevant setting, the LLGS framework also supports multistability and limit cycles that are absent in the quantum model. Our results constitute the first systematic study of dynamical metastability in nonlinear dynamics, directly relevant to spin-torque oscillator arrays, magnonic devices, and beyond.

cond-mat.mes-hall↗

arXiv2025

Demonstration of a Tunable Non-Hermitian Nonlinear Microwave Dimer

Achieving and controlling non-reciprocity in engineered photonic structures is of fundamental interest in science and engineering. Here, we introduce a tunable, non-Hermitian, nonlinear microwave dimer designed to precisely implement phase-non-reciprocal hopping dynamics between two spatially separated cavities at room temperature. Our system incorporates simple components such as three-dimensional microwave cavities, unidirectional amplifiers, digital attenuators, and a digital phase shifter. By dividing the energy transfer into forward and backward paths, our platform enables precise control over the amplitude and phase of the propagating signals in each direction. Through a combination of theoretical and numerical analysis, we model the dynamics of the system under different operating conditions, including a parameter regime where the gain not only compensates for but significantly exceeds the inherent loss. Our model quantitatively reproduces the observed weak-drive transmission spectra, the amplitude and frequency of self-sustained limit cycles, and the phase locking synchronization effect between the limit cycle and an external microwave tone. Our results may have implications in areas ranging from sensing and synthetic photonic materials to neuromorphic computing and quantum networks, while providing new insight into the interplay between non-Hermitian and nonlinear dynamics.

quant-ph↗

arXiv2024

Topological zero modes and edge symmetries of metastable Markovian bosonic systems

Tight bosonic analogs of free-fermionic symmetry-protected topological phases, and their associated edge-localized excitations, have long evaded the grasp of condensed-matter and AMO physics. In this work, building on our initial exploration [PRL 127, 245701 (2021)], we identify a broad class of quadratic bosonic systems subject to Markovian dissipation that realize tight bosonic analogs of the Majorana and Dirac edge modes characteristic of topological superconductors and insulators, respectively. To this end, we establish a general framework for topological metastability for these systems, by leveraging pseudospectral theory as the appropriate mathematical tool for capturing the non-normality of the Lindbladian generator. The resulting dynamical paradigm, which is characterized by both a sharp separation between transient and asymptotic dynamics and a nontrivial topological invariant, is shown to host edge-localized modes, which we dub Majorana and Dirac bosons. Generically, these consist of one conserved mode and a canonically conjugate generator of an approximate symmetry of the dynamics. The general theory is exemplified through several models exhibiting a range of exotic boundary physics that topologically metastable systems can engender. In particular, we explore the extent to which Noether's theorem is violated in this dissipative setting and the interplay between symmetries and these edge modes. We also demonstrate the possibility of anomalous parity dynamics for a bosonic cat state prepared in a topologically metastable system. Observable multitime signatures in the form of anomalously long-lived quantum correlations and divergent zero-frequency power spectral peaks are proposed and discussed in detail. Our results point to a new paradigm of genuine symmetry-protected topological physics in free bosons, embedded deeply in the long-lived transient regimes of metastable dynamics.

quant-ph↗

arXiv2021

Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics

Majorana bosons, that is, tight bosonic analogs of the Majorana fermionic quasiparticles of condensed matter physics, are forbidden for gapped free bosonic matter within a standard Hamiltonian scenario. We show how the interplay between dynamical metastability and nontrivial bulk topology makes their emergence possible in noninteracting bosonic chains undergoing Markovian dissipation. This leads to a distinctive form of topological metastability, whereby a conserved Majorana boson localized on one edge is paired, in general, with a symmetry generator localized on the opposite edge. We argue that Majorana bosons are robust against disorder and identifiable by signatures in the zero-frequency steady-state power spectrum. Our results suggest that symmetry-protected topological phases for free bosons may arise in transient metastable regimes, which persist over practical timescales.

quant-ph↗

arXiv2020

Restoring number conservation in quadratic bosonic Hamiltonians with dualities

Number-non-conserving terms in quadratic bosonic Hamiltonians can induce unwanted dynamical instabilities. By exploiting the pseudo-Hermitian structure built in to these Hamiltonians, we show that as long as dynamical stability holds, one may always construct a non-trivial dual (unitarily equivalent) number-conserving quadratic bosonic Hamiltonian. We exemplify this construction for a gapped harmonic chain and a bosonic analogue to Kitaev's Majorana chain. Our duality may be used to identify local number-conserving models that approximate stable bosonic Hamiltonians without the need for parametric amplification and to implement non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric dynamics in non-dissipative number-conserving bosonic systems. Implications for computing topological invariants are addressed.

quant-ph↗

arXiv2020

Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians

Unlike their fermionic counterparts, the dynamics of Hermitian quadratic bosonic Hamiltonians are governed by a generally non-Hermitian Bogoliubov-de Gennes effective Hamiltonian. This underlying non-Hermiticity gives rise to a dynamically stable regime, whereby all observables undergo bounded evolution in time, and a dynamically unstable one, whereby evolution is unbounded for at least some observables. We show that stability-to-instability transitions may be classified in terms of a suitably generalized $\mathcal{P}\mathcal{T}$ symmetry, which can be broken when diagonalizability is lost at exceptional points in parameter space, but also when degenerate real eigenvalues split off the real axis while the system remains diagonalizable. By leveraging tools from Krein stability theory in indefinite inner-product spaces, we introduce an indicator of stability phase transitions, which naturally extends the notion of phase rigidity from non-Hermitian quantum mechanics to the bosonic setting. As a paradigmatic example, we fully characterize the stability phase diagram of a bosonic analogue to the Kitaev-Majorana chain under a wide class of boundary conditions. In particular, we establish a connection between phase-dependent transport properties and the onset of instability, and argue that stable regions in parameter space become of measure zero in the thermodynamic limit. Our analysis also reveals that boundary conditions that support Majorana zero modes in the fermionic Kitaev chain are precisely the same that support stability in the bosonic chain.

quant-ph↗

arXiv2020

Squaring the fermion: The threefold way and the fate of zero modes

We investigate topological properties and classification of mean-field theories of stable bosonic systems. Of the three standard classifying symmetries, only time-reversal represents a real symmetry of the many-boson system, while the other two, particle-hole and chiral, are simply constraints that manifest as symmetries of the effective single-particle problem. For gapped systems in arbitrary space dimension we establish three fundamental no-go theorems that prove the absence of: parity switches, symmetry-protected-topological quantum phases, and localized bosonic zero modes under open boundary conditions. We then introduce a squaring, kernel-preserving map connecting non-interacting Hermitian theories of fermions and stable boson systems, which serves as a playground to reveal the role of topology in bosonic phases and their localized midgap boundary modes. Finally, we determine the symmetry classes inherited from the fermionic tenfold-way classification, unveiling an elegant threefold-way topological classification of non-interacting bosons. We illustrate our main findings in one- and two-dimensional bosonic lattice and field-theory models.

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