Detecting (emergent) continuous symmetry of criticality via subsystem's entanglement spectrum

TL;DR

This paper introduces a numerical method to identify emergent symmetries at critical points in quantum many-body systems by analyzing the entanglement spectrum of small subsystems, bypassing the need for prior theoretical assumptions.

Contribution

It proposes a novel, unbiased approach to detect underlying symmetries of critical points using entanglement spectrum analysis without relying on low-energy effective theories.

Findings

Entanglement spectrum reveals emergent symmetries at criticality.

Method works with small subsystems, making it computationally efficient.

Provides a way to verify symmetries without prior assumptions.

Abstract

The (emergent) symmetry of a critical point is one of the most important information to identify the universality class and effective field theory, which is fundamental for various critical theories. However, the underlying symmetry so far can only be conjectured indirectly from the dimension of the order parameters in symmetry-breaking phases, and its correctness requires further verifications to avoid overlooking hidden order parameters, which by itself is also a difficult task. In this work, we propose an unbiased way to numerically identify the underlying (emergent) symmetry of a critical point in quantum many-body systems, without prior knowledge about its low-energy effective field theory. Through calculating the reduced density matrix in a very small subsystem of the total system numerically, the Anderson tower of states in the entanglement spectrum clearly reflects the underlying (emergent) symmetry of the criticality. It is attributed to the fact that the entanglement spectrum can observe the broken symmetry of the entanglement ground-state after cooling from the critical point along an extra temperature axis.