Bulk-boundary correspondence for intrinsically-gapless SPTs from group
cohomology
- URL: http://arxiv.org/abs/2208.09001v2
- Date: Wed, 11 Jan 2023 17:24:30 GMT
- Title: Bulk-boundary correspondence for intrinsically-gapless SPTs from group
cohomology
- Authors: Rui Wen, Andrew C. Potter
- Abstract summary: Intrinsically gapless symmetry protected topological phases (igSPT) are gapless systems with SPT edge states.
An anomaly in the low-energy (IR) symmetry group emerges from an extended anomaly-free microscopic (UV) symmetry.
In two- and three-dimensional systems, an additional possibility is that the emergent anomaly can be satisfied by an anomalous symmetry-enriched topological order.
- Score: 3.299672391663527
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Intrinsically gapless symmetry protected topological phases (igSPT) are
gapless systems with SPT edge states with properties that could not arise in a
gapped system with the same symmetry and dimensionality. igSPT states arise
from gapless systems in which an anomaly in the low-energy (IR) symmetry group
emerges from an extended anomaly-free microscopic (UV) symmetry We construct a
general framework for constructing lattice models for igSPT phases with
emergent anomalies classified by group cohomology, and establish a direct
connection between the emergent anomaly, group-extension, and topological edge
states by gauging the extending symmetry. In many examples, the edge-state
protection has a physically transparent mechanism: the extending UV symmetry
operations pump lower dimensional SPTs onto the igSPT edge, tuning the edge to
a (multi)critical point between different SPTs protected by the IR symmetry. In
two- and three- dimensional systems, an additional possibility is that the
emergent anomaly can be satisfied by an anomalous symmetry-enriched topological
order, which we call a quotient-symmetry enriched topological order (QSET) that
is sharply distinguished from the non-anomalous UV SETs by an edge phase
transition. We construct exactly solvable lattice models with QSET order.
Related papers
- Intrinsic mixed-state SPT from modulated symmetries and hierarchical structure of anomaly [0.0]
We introduce a class of intrinsic symmetry-protected topological mixed-state in open quantum systems.
The mSPT phases cannot be realized as the ground states of a gapped Hamiltonian under thermal equilibrium.
A detailed comparison of the hierarchical structure of boundary anomalies in both pure and mixed states is presented.
arXiv Detail & Related papers (2024-07-11T18:01:37Z) - Higher-order topology protected by latent crystalline symmetries [0.0]
It is sufficient to have a latent rotation symmetry, which may be revealed upon performing an isospectral reduction on the system.
This work extends the classification of topological crystalline insulators to include latent symmetries.
arXiv Detail & Related papers (2024-05-04T16:21:24Z) - Symmetry Protected Topological Phases of Mixed States in the Doubled Space [0.0]
We study the interplay of symmetry and topology in quantum many-body mixed states.
In a phenomenon not seen in pure states, mixed states can exhibit average symmetries.
We study the patterns of spontaneous symmetry breaking ( SSB) of mixed states.
arXiv Detail & Related papers (2024-03-20T03:40:28Z) - Higher-Order Cellular Automata Generated Symmetry-Protected Topological
Phases and Detection Through Multi-Point Strange Correlators [23.660726551852182]
We introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter.
We show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., line-like subsystems in the 2D cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems.
arXiv Detail & Related papers (2023-12-31T13:56:20Z) - Hidden subsystem symmetry protected states in competing topological
orders [7.912220713730698]
We reveal the connection between two-dimensional subsystem symmetry-protected topological (SSPT) states and two-dimensional topological orders via a self-dual frustrated toric code model.
This model can be mapped to a model defined on the dual lattice with subsystem symmetries and subextensive ground state degeneracy.
arXiv Detail & Related papers (2023-09-05T15:21:48Z) - Fractonic Higher-Order Topological Phases in Open Quantum Systems [12.454257885851737]
We study the generalization of decohered average symmetry-protected topological phases to open quantum systems with a combination of subsystem symmetries and global symmetries.
arXiv Detail & Related papers (2023-07-11T17:58:35Z) - Duality viewpoint of criticality [10.697358928025304]
We study quantum many-body systems which are self-dual under duality transformation connecting different symmetry protected topological phases.
We provide a geometric explanation of the criticality of these self-dual models.
We illustrate our results with several examples in one and two dimensions, which separate two different SPTs.
arXiv Detail & Related papers (2022-09-27T15:13:27Z) - Noise-resilient Edge Modes on a Chain of Superconducting Qubits [103.93329374521808]
Inherent symmetry of a quantum system may protect its otherwise fragile states.
We implement the one-dimensional kicked Ising model which exhibits non-local Majorana edge modes (MEMs) with $mathbbZ$ parity symmetry.
MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism.
arXiv Detail & Related papers (2022-04-24T22:34:15Z) - Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized
rotational symmetry [85.36456486475119]
A non-Hermitian system is protected by the generalized rotational symmetry $H+=UHU+$ of the system.
Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants.
arXiv Detail & Related papers (2021-11-24T15:50:22Z) - Experimentally Detecting Quantized Zak Phases without Chiral Symmetry in
Photonic Lattices [14.450949607717437]
We experimentally realize an extended Su-Schrieffer-Heeger model with broken chiral symmetry.
Our results demonstrate that inversion symmetry protects the quantized Zak phase, but edge states can disappear in the topological nontrivial phase.
Our photonic lattice provides a useful platform to study the interplay among topological phases, symmetries, and the bulk-boundary correspondence.
arXiv Detail & Related papers (2021-09-28T13:35:44Z) - Information retrieval and eigenstates coalescence in a non-Hermitian
quantum system with anti-$\mathcal{PT}$ symmetry [15.273168396747495]
Non-Hermitian systems with parity-time reversal ($mathcalPT$) or anti-$mathcalPT$ symmetry have attracted a wide range of interest owing to their unique characteristics and counterintuitive phenomena.
We implement a Floquet Hamiltonian of a single qubit with anti-$mathcalPT$ symmetry by periodically driving a dissipative quantum system of a single trapped ion.
arXiv Detail & Related papers (2021-07-27T07:11:32Z)
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.