Short-range entanglement and invertible field theories

TL;DR

This paper explores how short-range entangled quantum systems can be characterized by invertible topological quantum field theories, providing new, finer invariants for classifying gapped phases using stable homotopy theory.

Contribution

It introduces a novel approach to classify short-range entangled phases via invertible topological theories and stable homotopy, leading to more refined invariants than previously available.

Findings

Concrete topological invariants for gapped SRE phases

Effective use of stable homotopy theory for classification

Successful computations demonstrating invariant effectiveness

Abstract

Quantum field theories with an energy gap can be approximated at long-range by topological quantum field theories. The same should be true for suitable condensed matter systems. For those with short range entanglement (SRE) the effective topological theory is invertible, and so amenable to study via stable homotopy theory. This leads to concrete topological invariants of gapped SRE phases which are finer than existing invariants. Computations in examples demonstrate their effectiveness.