Quantum Phases of Time Order in Many-Body Ground States

TL;DR

This paper introduces the concept of time order as a new way to classify quantum phases of matter, including time crystalline and time functional orders, demonstrated through specific models.

Contribution

It proposes a novel framework for identifying quantum ground state phases based on temporal structures in auto-correlation functions, expanding beyond traditional symmetry-based classifications.

Findings

Time order phases are characterized in spin-1 BEC and quantum Rabi models.

Time crystalline order (CTC) is detected as a special case of time order.

Non-Hermitian spin models exhibit time functional order.

Abstract

Understanding phases of matter is of both fundamental and practical importance. Prior to the widespread appreciation and acceptance of topological order, the paradigm of spontaneous symmetry breaking, formulated along the Landau-Ginzburg-Wilson (LGW) dogma, is central to understanding phases associated with order parameters of distinct symmetries and transitions between phases. This work proposes to identify ground state phases of quantum many-body system in terms of time order, which is operationally defined by the appearance of nontrivial temporal structure in the two-time auto-correlation function of a symmetry operator (order parameter). As a special case, the (symmetry protected) time crystalline order phase detects continuous time crystal (CTC). Time order phase diagrams for spin-1 atomic Bose-Einstein condensate (BEC) and quantum Rabi model are fully worked out. Besides time crystalline order, the intriguing phase of time functional order is discussed in two non-Hermitian interacting spin models.