Topological Modes in Monitored Quantum Dynamics

• URL: http://arxiv.org/abs/2411.04191v1
• Date: Wed, 06 Nov 2024 19:00:06 GMT
• Title: Topological Modes in Monitored Quantum Dynamics
• Authors: Haining Pan, Hassan Shapourian, Chao-Ming Jian,
• Abstract summary: We investigate novel topological phenomena in the monitored dynamics through the lens of free-fermion systems. We identify the topological area-law-entangled phases in the former setting through the topological classification of disordered insulators and superconductors. We find that the domain wall between topologically distinct area-law phases hosts dynamical topological modes whose entanglement is protected from being quenched by the measurements in the monitored dynamics.
• Score: 0.23408308015481666
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: Dynamical quantum systems both driven by unitary evolutions and monitored through measurements have proved to be fertile ground for exploring new dynamical quantum matters. While the entanglement structure and symmetry properties of monitored systems have been intensively studied, the role of topology in monitored dynamics is much less explored. In this work, we investigate novel topological phenomena in the monitored dynamics through the lens of free-fermion systems. Free-fermion monitored dynamics were previously shown to be unified with the Anderson localization problem under the Altland-Zirnbauer symmetry classification. Guided by this unification, we identify the topological area-law-entangled phases in the former setting through the topological classification of disordered insulators and superconductors in the latter. As examples, we focus on 1+1D free-fermion monitored dynamics in two symmetry classes, DIII and A. We construct quantum circuit models to study different topological area-law phases and their domain walls in the respective symmetry classes. We find that the domain wall between topologically distinct area-law phases hosts dynamical topological modes whose entanglement is protected from being quenched by the measurements in the monitored dynamics. We demonstrate how to manipulate these topological modes by programming the domain-wall dynamics. In particular, for topological modes in class DIII, which behave as unmeasured Majorana modes, we devise a protocol to braid them and study the entanglement generated in the braiding process.

Related papers

• Free Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States [0.0]
  We develop a general framework for classifying fermionic dynamical systems with measurements using symmetry and topology.<n>In the free-fermion limit, these two frameworks are in one-to-one correspondence and yield equivalent topological classifications of area-law entangled dynamical phases.
  arXiv  Detail & Related papers  (2025-07-17T18:00:01Z)
• Topology of Monitored Quantum Dynamics [5.388986285256996]
  We classify Kraus operators and their effective non-Hermitian dynamical generators. Our classification elucidates the role of topology in measurement-induced phase transitions. We establish the bulk-boundary correspondence in monitored quantum dynamics.
  arXiv  Detail & Related papers  (2024-12-09T01:27:26Z)
• Exceptional Points and Stability in Nonlinear Models of Population Dynamics having $\mathcal{PT}$ symmetry [49.1574468325115]
  We analyze models governed by the replicator equation of evolutionary game theory and related Lotka-Volterra systems of population dynamics.<n>We study the emergence of exceptional points in two cases: (a) when the governing symmetry properties are tied to global properties of the models, and (b) when these symmetries emerge locally around stationary states.
  arXiv  Detail & Related papers  (2024-11-19T02:15:59Z)
• Measuring Non-Hermitian Topological Invariants Directly from Quench Dynamics [6.33906375869588]
  Non-Hermitian (NH) topological phases and phenomena have been observed across various quantum systems. We present a generic and unified framework for the direct measurement of various NH topological invariants in odd-dimensional systems. This work paves the way for the direct measurement of NH topological invariants in quantum systems.
  arXiv  Detail & Related papers  (2024-10-17T05:48:45Z)
• Geometric Trajectory Diffusion Models [58.853975433383326]
  Generative models have shown great promise in generating 3D geometric systems. Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
  arXiv  Detail & Related papers  (2024-10-16T20:36:41Z)
• Visualizing Dynamics of Charges and Strings in (2+1)D Lattice Gauge Theories [103.95523007319937]
  We study the dynamics of local excitations in a lattice of superconducting qubits. For confined excitations, the magnetic field induces a tension in the string connecting them. Our method allows us to experimentally image string dynamics in a (2+1)D LGT.
  arXiv  Detail & Related papers  (2024-09-25T17:59:05Z)
• Scheme for measuring topological transitions in a continuous variable system [2.6417473952498116]
  We propose a scheme for measuring topological properties in a two-photon-driven Kerr-nonlinear resonator (KNR) subjected to a single-photon modulation. The topological properties are revealed through the observation of the Berry curvature and hence the first Chern number. The scheme, with such continuous variable states in mesoscpic systems, provides a new perspective for exploration of the geometry and the related topology with complex systems.
  arXiv  Detail & Related papers  (2024-07-13T04:35:50Z)
• Dynamical topology of chiral and nonreciprocal state transfers in a non-Hermitian quantum system [11.467872077398688]
  We study topological chiral and nonreciprocal dynamics by encircling the exceptional points (EPs) of non-Hermitian Hamiltonians in a trapped ion system. These dynamics are topologically robust against external perturbations even in the presence dissipation-induced nonadiabatic processes. Our results mark a significant step towards exploring topological properties of open quantum systems.
  arXiv  Detail & Related papers  (2024-06-05T07:51:58Z)
• Long-range entanglement and topological excitations [0.0]
  Topological order comes in different forms, and its classification and detection is an important field of modern research. We show that the Disconnected Entanglement Entropy, a measure originally introduced to identify topological phases, is also able to unveil the long-range entanglement carried by a single excitation.
  arXiv  Detail & Related papers  (2023-10-24T18:00:07Z)
• SEGNO: Generalizing Equivariant Graph Neural Networks with Physical Inductive Biases [66.61789780666727]
  We show how the second-order continuity can be incorporated into GNNs while maintaining the equivariant property. We also offer theoretical insights into SEGNO, highlighting that it can learn a unique trajectory between adjacent states. Our model yields a significant improvement over the state-of-the-art baselines.
  arXiv  Detail & Related papers  (2023-08-25T07:15:58Z)
• Topological zero modes and edge symmetries of metastable Markovian bosonic systems [0.0]
  We study tight bosonic analogs of the Majorana and Dirac edge modes characteristic of topological superconductors and insulators. We show the possibility of anomalous parity dynamics for a bosonic cat state prepared in a topologically metastable system. Our results point to a new paradigm of genuine symmetry-protected topological physics in free bosons.
  arXiv  Detail & Related papers  (2023-06-23T18:00:03Z)
• Spreading of a local excitation in a Quantum Hierarchical Model [62.997667081978825]
  We study the dynamics of the quantum Dyson hierarchical model in its paramagnetic phase. An initial state made by a local excitation of the paramagnetic ground state is considered. A localization mechanism is found and the excitation remains close to its initial position at arbitrary times.
  arXiv  Detail & Related papers  (2022-07-14T10:05:20Z)
• 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)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)

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.