Renormalization Group Circuits for Gapless States

TL;DR

This paper demonstrates that many gapless states can be constructed as renormalization group fixed points using local unitaries, expanding understanding of their scale-invariant properties beyond conformal field theories.

Contribution

It introduces a new class of gapless states that are RG fixed points, constructed via local unitaries, and relates their wavefunctions to local statistical models.

Findings

Many gapless states are RG fixed points.

The states' wavefunctions relate to local statistical models.

Examples include states in Ising magnetism.

Abstract

We show that a large class of gapless states are renormalization group fixed points in the sense that they can be grown scale by scale using local unitaries. This class of examples includes some theories with dynamical exponent different from one, but does not include conformal field theories. The key property of the states we consider is that the ground state wavefunction is related to the statistical weight of a local statistical model. We give several examples of our construction in the context of Ising magnetism.