Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
- URL: http://arxiv.org/abs/2410.03821v1
- Date: Fri, 4 Oct 2024 18:00:01 GMT
- Title: Electric polarization and discrete shift from boundary and corner charge in crystalline Chern insulators
- Authors: Yuxuan Zhang, Maissam Barkeshli,
- Abstract summary: We provide a general formula in terms of $mathscrS_texto$ and $vecmathscrP_texto$ for the total charge of any subregion of the system.
Results hold for Chern insulators, despite their gapless chiral edge modes, and for which an unambiguous definition of an intrinsically two-dimensional electric polarization has been unclear until recently.
- Score: 7.694970944345054
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Recently, it has been shown how topological phases of matter with crystalline symmetry and $U(1)$ charge conservation can be partially characterized by a set of many-body invariants, the discrete shift $\mathscr{S}_{\text{o}}$ and electric polarization $\vec{\mathscr{P}}_{\text{o}}$, where $\text{o}$ labels a high symmetry point. Crucially, these can be defined even with non-zero Chern number and/or magnetic field. One manifestation of these invariants is through quantized fractional contributions to the charge in the vicinity of a lattice disclination or dislocation. In this paper, we show that these invariants can also be extracted from the length and corner dependence of the total charge (mod 1) on the boundary of the system. We provide a general formula in terms of $\mathscr{S}_{\text{o}}$ and $\vec{\mathscr{P}}_{\text{o}}$ for the total charge of any subregion of the system which can include full boundaries or bulk lattice defects, unifying boundary, corner, disclination, and dislocation charge responses into a single general theory. These results hold for Chern insulators, despite their gapless chiral edge modes, and for which an unambiguous definition of an intrinsically two-dimensional electric polarization has been unclear until recently. We also discuss how our theory can fully characterize the topological response of quadrupole insulators.
Related papers
- Fractionally Quantized Electric Polarization and Discrete Shift of Crystalline Fractional Chern Insulators [7.694970944345054]
Fractional Chern insulators (FCI) with crystalline symmetry possess topological invariants that fundamentally have no analog in continuum fractional quantum Hall (FQH) states.
We demonstrate through numerical calculations on model wave functions that FCIs possess a fractionally quantized electric polarization.
arXiv Detail & Related papers (2024-11-06T19:00:00Z) - Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
We show how to reduce the geometry of degenerate states to the non-abelian connection $A$.
We find independent invariants associated with each triple of subspaces.
Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
arXiv Detail & Related papers (2024-04-04T06:39:28Z) - Characterization and classification of interacting (2+1)D topological
crystalline insulators with orientation-preserving wallpaper groups [0.0]
We develop a characterization and classification of interacting, invertible fermionic topological phases in (2+1) dimensions.
We derive a topological response theory in terms of background crystalline gauge fields.
We derive an explicit map between the free and interacting classifications.
arXiv Detail & Related papers (2023-09-21T18:00:01Z) - Small-time controllability for the nonlinear Schr\"odinger equation on
$\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields.
In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
arXiv Detail & Related papers (2023-07-28T21:30:44Z) - Quantum Current and Holographic Categorical Symmetry [62.07387569558919]
A quantum current is defined as symmetric operators that can transport symmetry charges over an arbitrary long distance.
The condition for quantum currents to be superconducting is also specified, which corresponds to condensation of anyons in one higher dimension.
arXiv Detail & Related papers (2023-05-22T11:00:25Z) - Complete crystalline topological invariants from partial rotations in
(2+1)D invertible fermionic states and Hofstadter's butterfly [6.846670002217106]
We show how to extract many-body invariants $Theta_textopm$, where $texto$ is a high symmetry point, from partial rotations in (2+1)D invertible fermionic states.
Our results apply in the presence of magnetic field and Chern number $C neq 0$, in contrast to previous work.
arXiv Detail & Related papers (2023-03-29T18:00:00Z) - Exact solution of a non-Hermitian $\mathscr{PT}$-symmetric Heisenberg
spin chain [0.0]
We construct the exact solution of a non-Hermitian $mathscrPT$-symmetric isotropic Heisenberg spin chain with integrable boundary fields.
We find that both $A$ and $B$ type phases can be further divided into sub-phases which exhibit different ground states.
arXiv Detail & Related papers (2023-01-15T02:32:44Z) - Quantized charge polarization as a many-body invariant in (2+1)D
crystalline topological states and Hofstadter butterflies [14.084478426185266]
We show how to define a quantized many-body charge polarization $vecmathscrP$ for (2+1)D topological phases of matter, even in the presence of non-zero Chern number and magnetic field.
We derive colored Hofstadter butterflies, corresponding to the quantized value of $vecmathscrP$, which further refine the colored butterflies from the Chern number and discrete shift.
arXiv Detail & Related papers (2022-11-16T19:00:00Z) - Annihilating Entanglement Between Cones [77.34726150561087]
We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied.
Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
arXiv Detail & Related papers (2021-10-22T15:02:39Z) - Spectrum of localized states in fermionic chains with defect and
adiabatic charge pumping [68.8204255655161]
We study the localized states of a generic quadratic fermionic chain with finite-range couplings.
We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
arXiv Detail & Related papers (2021-07-20T18:44:06Z) - Anisotropy-mediated reentrant localization [62.997667081978825]
We consider a 2d dipolar system, $d=2$, with the generalized dipole-dipole interaction $sim r-a$, and the power $a$ controlled experimentally in trapped-ion or Rydberg-atom systems.
We show that the spatially homogeneous tilt $beta$ of the dipoles giving rise to the anisotropic dipole exchange leads to the non-trivial reentrant localization beyond the locator expansion.
arXiv Detail & Related papers (2020-01-31T19:00:01Z)
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.