Related papers: Computing classification of interacting fermionic …
We study symmetry-protected topological (SPT) phase transitions induced by stacking two gapped one-dimensional subsystems in BDI symmetry class. The topological invariant of the entire system is a sum of three topological invariants: two…
Symmetry topological field theory (SymTFT) gives a holographic correspondence between systems with a global symmetry and a higher-dimensional topological field theory. In this framework, classification of gapped phases of matter in…
We study the classification of symmetry protected topological (SPT) phases with crystalline symmetry (cSPT phases). Focusing on bosonic cSPT phases in two and three dimensions, we introduce a simple family of cSPT states, where the system…
We construct and compute a homotopy-theoretic model for the Bott spiral of symmetry-protected topological phases (SPTs) studied by Queiroz--Khalaf--Stern. We model free and interacting fermionic SPTs using K-theory and reflection-positive…
Using the decorated domain wall procedure, we construct Finite Depth Local Unitaries (FDLUs) that realize Fermionic Symmetry-Protected Topological (SPT) phases. This results in explicit 'full' commuting projector Hamiltonians, where 'full'…
It is demonstrated by explicit construction that three-dimensional bosonic crystalline symmetry protected topological (cSPT) phases are classified by $H_{\phi}^{5}(G;\mathbb{Z})\oplus H_{\phi}^{1}(G;\mathbb{Z})$ for all 230 space groups…
In this paper we show how the classification of topological phases in insulators and superconductors is changed by interactions, in the case of 1D systems. We focus on the TR-invariant Majorana chain (BDI symmetry class). While the band…
The topological invariant of a topological insulator (or superconductor) is given by the number of symmetry-protected edge states present at the Fermi level. Despite this fact, established expressions for the topological invariant require…
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…
Persistent (co)homology is a central construction in topological data analysis, where it is used to quantify prominence of features in data to produce stable descriptors suitable for downstream analysis. Persistence is challenging to…
The realization of novel phases of matter on quantum simulators is a topic of intense interest. Digital quantum computers offer a route to prepare topological phases with interactions that do not naturally arise in analog quantum…
We investigate the physics of one-dimensional symmetry protected topological (SPT) phases protected by symmetries whose symmetry generators exhibit spatial modulation. We focus in particular on phases protected by symmetries with linear…
Going beyond the conventional classification rule of Altland-Zirnbauer symmetry classes, $PT$ symmetric topological phases are classified by $(PT)^2=1$ or $-1$. The interconversion between the two $PT$-symmetric topological classes is…
Topological phases in non-Hermitian systems have become fascinating subjects recently. In this paper, we attempt to classify topological phases in 1D interacting non-Hermitian systems. We begin with the non-Hermitian generalization of the…
Symmetry protected topological phases exhibit nontrivial short-ranged entanglement protected by symmetry and cannot be adiabatically connected to trivial product states while preserving the symmetry. In contrast, intrinsic topological…
We classify one-dimensional symmetry-protected topological (SPT) phases protected by dipole symmetries. A dipole symmetry comprises two sets of symmetry generators: charge and dipole operators, which together form a non-trivial algebra with…
We investigate (1+1)d symmetry-protected topological (SPT) phases with fusion category symmetries. We emphasize that the UV description of an anomaly-free fusion category symmetry must include the fiber functor, giving rise to a local…
We consider topological phases in periodically driven (Floquet) systems exhibiting many-body localization, protected by a symmetry $G$. We argue for a general correspondence between such phases and topological phases of undriven systems…
Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery…
In this work we investigate the decorated domain wall construction in bosonic group-cohomology symmetry-protected topological (SPT) phases and related quantum anomalies in bosonic topological phases. We first show that a general decorated…