From orthogonal link to phase vortex in generalized dynamical Hopf insulators

• URL: http://arxiv.org/abs/2309.01344v1
• Date: Mon, 4 Sep 2023 04:03:46 GMT
• Title: From orthogonal link to phase vortex in generalized dynamical Hopf insulators
• Abstract summary: We unravel the quenched two-dimensional (2D) two-band Chern insulators under a parallel quench protocol. We find that whether the dynamical Hopf invariant exists or not, the links in (2+1)D space always keep their standard shape even for topological initial states.
• Score: 5.111942603132791
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the creation of Hopf topological matters, the old paradigm is to conceive the Hopf invariant first, and then display its intuitive topology through links. Here we brush aside this effort and put forward a new recipe for unraveling the quenched two-dimensional (2D) two-band Chern insulators under a parallel quench protocol, which implies that the quench quantities with different momentum k are parallel or antiparallel to each other. We find that whether the dynamical Hopf invariant exists or not, the links in (2+1)D space always keep their standard shape even for topological initial states, and trace out the trajectories of phase vortices. The linking number is exactly equal to the difference between pre- and post-quench Chern numbers regardless of the construction of homotopy groups. We employ two concrete examples to illustrate these results, highlighting the polarity reversal at fixed points.

Related papers

• Unified resonant-manifold framework for dynamical quantum phase transitions [0.0032818514814266144]
  We propose a unified framework addressing the gap in terms of the energy structure of different product state configurations.<n>We show that the (ir)regularity of branch DQPTs is related to the multiplicity of this transitional manifold.<n>We also observe exotic periods of extended degeneracy in the return rate which are also conditioned on the structure of this transitional manifold.
  arXiv  Detail & Related papers  (2026-05-21T18:00:34Z)
• Symmetry-protected topology and deconfined solitons in a multi-link $\mathbb{Z}_2$ gauge theory [45.88028371034407]
  We study a $mathbbZ$ lattice gauge theory defined on a multi-graph with links that can be visualized as great circles of a spherical shell.<n>We show that this leads to state-dependent tunneling amplitudes underlying a phenomenon analogous to the Peierls instability.<n>By performining a detailed analysis based on matrix product states, we prove that charge deconfinement emerges as a consequence of charge-fractionalization.
  arXiv  Detail & Related papers  (2026-03-02T22:59:25Z)
• Theory of the correlated quantum Zeno effect in a monitored qubit dimer [41.94295877935867]
  We show how the competition between two measurement processes give rise to two distinct Quantum Zeno (QZ) regimes.<n>We develop a theory based on a Gutzwiller ansatz for the wavefunction that is able to capture the structure of the Hilbert phase diagram.<n>We show how the two QZ regimes are intimately connected to the topology of the flow of the underlying non-Hermitian Hamiltonian governing the no-click evolution.
  arXiv  Detail & Related papers  (2025-03-28T19:44:48Z)
• Cohomotopy, Framed Links, and Abelian Anyons [0.0]
  We identify cobordism classes of framed links with the fundamental group of the group-completed configuration space of points in the plane.<n>Under Segal's theorem, these classes are integers generated by the Hopf generator in the 2-cohomotopy of the 3-sphere.<n>We close with an outlook on implications for the identification of anyonic solitons in 2D electron gases as exotic flux quantized in Cohomotopy.
  arXiv  Detail & Related papers  (2024-08-21T18:00:02Z)
• Quantum Random Walks and Quantum Oscillator in an Infinite-Dimensional Phase Space [45.9982965995401]
  We consider quantum random walks in an infinite-dimensional phase space constructed using Weyl representation of the coordinate and momentum operators. We find conditions for their strong continuity and establish properties of their generators.
  arXiv  Detail & Related papers  (2024-06-15T17:39:32Z)
• Non-Abelian Hopf-Euler insulators [0.0]
  A class of non-Abelian topological insulators in three dimensions carry a single bulk Hopf index protected by insulator ($mathcalPT$) inversion symmetry. Such systems naturally realize nodal structures in the three-dimensional Brillou zonein, providing a physical manifestation of the linking number described by the Hopf invariant. Our findings pave the way for novel experimental realizations of real-space quantum-geometry.
  arXiv  Detail & Related papers  (2024-05-27T16:07:47Z)
• From Lindblad master equations to Langevin dynamics and back [0.0]
  A case study of the non-equilibrium dynamics of open quantum systems is presented. The quantum Langevin equations are derived from an identical set of physical criteria. The associated Lindblad equations are derived but only one of them is completely positive.
  arXiv  Detail & Related papers  (2023-05-10T16:59:48Z)
• Quantum quenches in a pseudo-Hermitian Chern insulator [1.0093662416275693]
  We show the bulk-surface duality of the pseudo-Hermitian phases, then build a concrete relation between the static band topology and quench dynamics. We propose a possible scheme to realize the seemingly challenging model in a bilayer lattice and detect the dynamics with a double-quench protocol.
  arXiv  Detail & Related papers  (2022-09-30T03:20:45Z)
• Symplectic Polar Duality, Quantum Blobs, and Generalized Gaussians [0.0]
  We show that quantum blobs are the smallest symplectic invariant regions of the phase space compatible with the uncertainty principle in its strong Robertson--Schr"odinger form. We show that these phase space units can be characterized by a simple condition of reflexivity using polar duality, thus improving previous results.
  arXiv  Detail & Related papers  (2022-06-13T17:32:05Z)
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping [45.873301228345696]
  localization problem in the crossover regime for the dimension $d=2$ and hopping $V(r) propto r-2$ is not resolved yet. We show that for the hopping determined by two-dimensional anisotropic dipole-dipole interactions there exist two distinguishable phases at weak and strong disorder.
  arXiv  Detail & Related papers  (2022-05-29T16:53:20Z)
• Phase diagram of Rydberg-dressed atoms on two-leg square ladders: Coupling supersymmetric conformal field theories on the lattice [52.77024349608834]
  We investigate the phase diagram of hard-core bosons in two-leg ladders in the presence of soft-shoulder potentials. We show how the competition between local and non-local terms gives rise to a phase diagram with liquid phases with dominant cluster, spin, and density-wave quasi-long-range ordering.
  arXiv  Detail & Related papers  (2021-12-20T09:46:08Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Geometric phase in a dissipative Jaynes-Cummings model: theoretical explanation for resonance robustness [68.8204255655161]
  We compute the geometric phases acquired in both unitary and dissipative Jaynes-Cummings models. In the dissipative model, the non-unitary effects arise from the outflow of photons through the cavity walls. We show the geometric phase is robust, exhibiting a vanishing correction under a non-unitary evolution.
  arXiv  Detail & Related papers  (2021-10-27T15:27:54Z)
• Entanglement dynamics of spins using a few complex trajectories [77.34726150561087]
  We consider two spins initially prepared in a product of coherent states and study their entanglement dynamics. We adopt an approach that allowed the derivation of a semiclassical formula for the linear entropy of the reduced density operator.
  arXiv  Detail & Related papers  (2021-08-13T01:44:24Z)
• Tuning the topology of $p$-wave superconductivity in an analytically solvable two-band model [0.0]
  We introduce and solve a two-band model of spinless fermions with $p_x$-wave pairing on a square lattice. We show that its phase diagram contains a topologically nontrivial weak pairing phase as well as a trivial strong pairing phase.
  arXiv  Detail & Related papers  (2020-10-01T01:20:46Z)
• Relevant OTOC operators: footprints of the classical dynamics [68.8204255655161]
  The OTOC-RE theorem relates the OTOCs summed over a complete base of operators to the second Renyi entropy. We show that the sum over a small set of relevant operators, is enough in order to obtain a very good approximation for the entropy. In turn, this provides with an alternative natural indicator of complexity, i.e. the scaling of the number of relevant operators with time.
  arXiv  Detail & Related papers  (2020-07-31T19:23:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.