(2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes

• URL: http://arxiv.org/abs/2403.18887v1
• Date: Wed, 27 Mar 2024 18:00:00 GMT
• Title: (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes
• Authors: Ryohei Kobayashi, Yuxuan Zhang, Yan-Qi Wang, Maissam Barkeshli,
• Abstract summary: We consider many-body systems of interacting fermions with fermionic symmetry groups $G_f mathbbZf times mathbbZ$. We show that (2+1)D invertible fermionic phases with these symmetries have a $mathbbZ times mathbbZ_8$, $mathbbZ_8$, $mathbbZ2 times mathbbZ$, and $mathbbZ2
• Score: 6.267386954898001
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: It is common in condensed matter systems for reflection ($R$) and time-reversal ($T$) symmetry to both be broken while the combination $RT$ is preserved. In this paper we study invariants that arise due to $RT$ symmetry. We consider many-body systems of interacting fermions with fermionic symmetry groups $G_f = \mathbb{Z}_2^f \times \mathbb{Z}_2^{RT}$, $U(1)^f \rtimes \mathbb{Z}_2^{RT}$, and $U(1)^f \times \mathbb{Z}_2^{RT}$. We show that (2+1)D invertible fermionic topological phases with these symmetries have a $\mathbb{Z} \times \mathbb{Z}_8$, $\mathbb{Z}^2 \times \mathbb{Z}_2$, and $\mathbb{Z}^2 \times \mathbb{Z}_4$ classification, respectively, which we compute using the framework of $G$-crossed braided tensor categories. We provide a many-body $RT$ invariant in terms of a tripartite entanglement measure, and which we show can be understood using an edge conformal field theory computation in terms of vertex states. For $G_f = U(1)^f \rtimes \mathbb{Z}_2^{RT}$, which applies to charged fermions in a magnetic field, the non-trivial value of the $\mathbb{Z}_2$ invariant requires strong interactions. For symmetry-preserving boundaries, the phases are distinguished by zero modes at the intersection of the reflection axis and the boundary. Additional invariants arise in the presence of translation or rotation symmetry.

Related papers

• 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)
• Quantum charges of harmonic oscillators [55.2480439325792]
  We show that the energy eigenfunctions $psi_n$ with $nge 1$ are complex coordinates on orbifolds $mathbbR2/mathbbZ_n$. We also discuss "antioscillators" with opposite quantum charges and the same positive energy.
  arXiv  Detail & Related papers  (2024-04-02T09:16:18Z)
• Vacuum Force and Confinement [65.268245109828]
  We show that confinement of quarks and gluons can be explained by their interaction with the vacuum Abelian gauge field $A_sfvac$.
  arXiv  Detail & Related papers  (2024-02-09T13:42:34Z)
• A Unified Framework for Uniform Signal Recovery in Nonlinear Generative Compressed Sensing [68.80803866919123]
  Under nonlinear measurements, most prior results are non-uniform, i.e., they hold with high probability for a fixed $mathbfx*$ rather than for all $mathbfx*$ simultaneously. Our framework accommodates GCS with 1-bit/uniformly quantized observations and single index models as canonical examples. We also develop a concentration inequality that produces tighter bounds for product processes whose index sets have low metric entropy.
  arXiv  Detail & Related papers  (2023-09-25T17:54:19Z)
• 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)
• DHR bimodules of quasi-local algebras and symmetric quantum cellular automata [0.0]
  We show that for the double spin flip action $mathbbZ/2mathbbZtimes mathbbZ/2mathbbZZcurvearrowright mathbbC2otimes mathbbC2$, the group of symmetric QCA modulo symmetric finite depth circuits in 1D contains a copy of $S_3$, hence is non-abelian.
  arXiv  Detail & Related papers  (2023-03-31T18:33:07Z)
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D [0.0]
  In (1)D topological phases, unpaired Majorana zero modes (MZMs) can arise only if the internal symmetry group $G_f$ of the ground state splits as $G_f = G_b times mathbbZf$. In contrast, (2+1)D topological superconductors (TSC) can host unpaired MZMs at defects even when $G_f$ is not of the form $G_b times mathbbZf$.
  arXiv  Detail & Related papers  (2022-10-05T18:00:00Z)
• Global Convergence of Gradient Descent for Asymmetric Low-Rank Matrix Factorization [49.090785356633695]
  We study the asymmetric low-rank factorization problem: [mathbfU in mathbbRm min d, mathbfU$ and mathV$.
  arXiv  Detail & Related papers  (2021-06-27T17:25:24Z)
• Non-Abelian fracton order from gauging a mixture of subsystem and global symmetries [0.0]
  We demonstrate a general gauging procedure of a pure matter theory on a lattice with a mixture of subsystem and global symmetries. This mixed symmetry can be either a semidirect product of a subsystem symmetry and a global symmetry, or a non-trivial extension of them.
  arXiv  Detail & Related papers  (2021-03-15T18:00:01Z)
• ${\mathbb Z}_2\times {\mathbb Z}_2$-graded parastatistics in multiparticle quantum Hamiltonians [0.0]
  Non-statistics physics can be detected in the multiparticle sector of a theory. $mathbb Ztimes mathbb Z$-graded mechanics has experimentally testable consequences.
  arXiv  Detail & Related papers  (2020-08-26T13:35:23Z)

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.