Higher-order Topological Parity Anomaly and Half-integer Hall Effect in High-dimensional Synthetic Lattices
- URL: http://arxiv.org/abs/2505.08820v1
- Date: Mon, 12 May 2025 18:44:54 GMT
- Title: Higher-order Topological Parity Anomaly and Half-integer Hall Effect in High-dimensional Synthetic Lattices
- Authors: Xian-Hao Wei, Xi-Wang Luo, Guang-Can Guo, Zheng-Wei Zhou,
- Abstract summary: parity anomaly and associated textithalf-integer quantized Hall conductance can be realized by the boundary states of $n$-th order topological insulators.<n>Our work offers the realization and characterization of parity anomaly in general high-dimensional higher-order topological insulators.
- Score: 0.4374837991804086
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Recent advances in constructing synthetic dimension provide a powerful tool for exploring exotic topological states of matter in high dimensions. Here we report that the parity anomaly and associated \textit{half-integer} quantized Hall conductance, arising in 2$j$+1 (space-time) dimensions with a single or odd number of Dirac cones, can be realized by the boundary states of $n$-th order topological insulators in (2$j$+$n$)-dimensional synthetic lattices. We establish a general bulk-boundary correspondence by integrating the ``nested" Wilson loop theory with the time-reversal polarization at highly-symmetric momenta, a set of $Z_2$ topological invariants are extracted which determines the number of higher-order-boundary Dirac cones and their locations. We develop a general construction procedure for Hamiltonians supporting such higher-order topological parity anomaly. Moreover, we propose an experimental implementation scheme based on photonic synthetic dimensions and provide a method for probing the associated half-integer Hall conductance by the transmission spectra. Our work offers the realization and characterization of parity anomaly in general high-dimensional higher-order topological insulators and opens an avenue for exploring fundamental physics and possible device applications enabled by manipulating Dirac cones.
Related papers
- Entanglement and the density matrix renormalisation group in the generalised Landau paradigm [0.0]
We leverage the interplay between gapped phases and dualities of symmetric one-dimensional quantum lattice models.
For every phase in the phase diagram, the dual representation of the ground state that breaks all symmetries minimises both the entanglement entropy and the required number of variational parameters.
Our work testifies to the usefulness of generalised non-invertible symmetries and their formal category theoretic description for the nuts and bolts simulation of strongly correlated systems.
arXiv Detail & Related papers (2024-08-12T17:51:00Z) - Topological Interfaces of Luttinger Liquids [0.0]
Topological interfaces of two-dimensional conformal field theories exhibit striking spectral and entanglement characteristics.
We show that a topological interface of two Luttinger liquids can be realized by coupling special one-dimensional superconductors.
The proposed lattice model provides an experimentally-realizable alternative to spin and anyon chains for the analysis of several conjectured conformal fixed points.
arXiv Detail & Related papers (2023-12-09T12:41:50Z) - Low-dimensional polaritonics: Emergent non-trivial topology on
exciton-polariton simulators [0.0]
Polaritonic lattice configurations in dimensions $D=2$ are used as simulators of topological phases, based on symmetry class A Hamiltonians.
We provide a comprehensive mathematical framework, which fully addresses the source and structure of topological phases in coupled polaritonic array systems.
arXiv Detail & Related papers (2023-10-31T04:22:58Z) - Higher-order topological Peierls insulator in a two-dimensional
atom-cavity system [58.720142291102135]
We show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state.
The pattern opens a non-trivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states.
Our work shows how atomic quantum simulators can be harnessed to investigate novel strongly-correlated topological phenomena.
arXiv Detail & Related papers (2023-05-05T10:25:14Z) - Fermion production at the boundary of an expanding universe: a cold-atom
gravitational analogue [68.8204255655161]
We study the phenomenon of cosmological particle production of Dirac fermions in a Friedman-Robertson-Walker spacetime.
We present a scheme for the quantum simulation of this gravitational analogue by means of ultra-cold atoms in Raman optical lattices.
arXiv Detail & Related papers (2022-12-02T18:28:23Z) - Constructing higher-order topological states in higher dimension [11.54915189652831]
We show a topological corner state constructed from the edge states in one dimensional lattice.
We also show the dimension-reduction from a four-dimensional topological phase characterized by vector Chern number.
Our work provides a promising tool constructing higher topological phases in higher dimensional structures.
arXiv Detail & Related papers (2020-11-22T14:42:30Z) - Quantum anomalous Hall phase in synthetic bilayers via twistless
twistronics [58.720142291102135]
We propose quantum simulators of "twistronic-like" physics based on ultracold atoms and syntheticdimensions.
We show that our system exhibits topologicalband structures under appropriate conditions.
arXiv Detail & Related papers (2020-08-06T19:58:05Z) - Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range.
For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z) - Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide.
For open boundary condition, we find exotic topological bound-pair edge states with radiative losses.
By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
arXiv Detail & Related papers (2020-02-24T04:44:12Z) - Probing chiral edge dynamics and bulk topology of a synthetic Hall
system [52.77024349608834]
Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states.
Here, we realize a quantum Hall system using ultracold dysprosium atoms, in a two-dimensional geometry formed by one spatial dimension.
We demonstrate that the large number of magnetic sublevels leads to distinct bulk and edge behaviors.
arXiv Detail & Related papers (2020-01-06T16:59:08Z)
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.