Maissam Barkeshli

Many-Body Chern Number from Statistical Correlations of Randomized Measurements

Physical Review Letters · 2021 · 69 citations

One of the main topological invariants that characterizes several topologically ordered phases is the many-body Chern number (MBCN). Paradigmatic examples include several fractional quantum Hall phases, which are expected to be realized in different atomic and photonic quantum platforms in the near future. Experimental measurement and numerical computation of this invariant are conventionally based on the linear-response techniques that require having access to a family of states, as a function…

Higher-group symmetry in finite gauge theory and stabilizer codes

SciPost Physics · 2024-04-03 · 35 citations

A large class of gapped phases of matter can be described by topological finite group gauge theories. In this paper, we show how such gauge theories possess a higher-group global symmetry, which we study in detail. We derive the d <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>d</mml:mi> </mml:math> -group global symmetry and its ’t Hooft anomaly for topological finite group gauge theories in (d+1) <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" displ…

Complete Crystalline Topological Invariants from Partial Rotations in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mi mathvariant="normal">D</mml:mi></mml:mrow></mml:math> Invertible Fermionic States and Hofstadter’s Butterfly

Physical Review Letters · 2023-10-23 · 17 citations

The theory of topological phases of matter predicts invariants protected only by crystalline symmetry, yet it has been unclear how to extract these from microscopic calculations in general. Here, we show how to extract a set of many-body invariants ${{\mathrm{\ensuremath{\Theta}}}_{o}^{\ifmmode\pm\else\textpm\fi{}}}$, where $o$ is a high symmetry point, from partial rotations in $(2+1)\mathrm{D}$ invertible fermionic states. Our results apply in the presence of magnetic field and Chern number $C…

Higher-group symmetry of (3+1)D fermionic $\mathbb{Z}_2$ gauge theory: Logical CCZ, CS, and T gates from higher symmetry

SciPost Physics · 2024-05-07 · 16 citations

It has recently been understood that the complete global symmetry of finite group topological gauge theories contains the structure of a higher-group. Here we study the higher-group structure in (3+1)D \mathbb{Z}_2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>ℤ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> gauge theory with an emergent fermion, and point out that pumping chiral p+ip <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" di…

Characterization and classification of interacting (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>2</mml:mi><mml:mo>+</mml:mo><mml:mi>1</mml:mi></mml:math>)-dimensional topological crystalline insulators with orientation-preserving wallpaper groups

Physical review. B./Physical review. B · 2024-01-31 · 15 citations

While free fermion topological crystalline insulators have been largely classified, the analogous problem in the strongly interacting case has been only partially solved, and the relationship between the free and interacting classifications is not well understood. In this paper, we develop a characterization and classification of interacting, invertible fermionic topological phases in ($2+1$) dimensions with charge conservation, discrete magnetic translation, and $M$-fold point group rotation sy…