Fragmentation, Zero Modes, and Collective Bound States in Constrained Models

Kinetically constrained models were originally introduced to capture slow relaxation in glassy systems, where dynamics are hindered by local constraints instead of energy barriers. Their quantum counterparts have recently drawn attention for exhibiting highly degenerate eigenstates at zero energy—known as —stemming from chiral symmetry. Yet, the structure and implications of these zero modes remain poorly understood. In this work, we focus on the properties of the zero mode subspace in quantum kinetically constrained models with a <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>U</a:mi> <a:mo stretchy="false">(</a:mo> <a:mn>1</a:mn> <a:mo stretchy="false">)</a:mo> </a:math> particle-conservation symmetry. We use the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>U</e:mi> <e:mo stretchy="false">(</e:mo> <e:mn>1</e:mn> <e:mo stretchy="false">)</e:mo> </e:math> East, which lacks inversion symmetry, and the inversion-symmetric <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>U</i:mi> <i:mo stretchy="false">(</i:mo> <i:mn>1</i:mn> <i:mo stretchy="false">)</i:mo> </i:math> East-West models to illustrate our two main results. First, we observe that the simultaneous presence of constraints and chiral symmetry generally leads to a in the number of zero modes due to the fragmentation of the many-body Hilbert space into disconnected sectors. Second, we generalize the concept of compact localized states from single-particle physics and introduce the notion of , a special kind of nonergodic eigenstates that are robust to enlarging the system size. We formulate sufficient criteria for their existence, arguing that the degenerate zero mode subspace plays a central role, and demonstrate bound states in both example models and in a two-dimensional model, the <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mi>U</m:mi> <m:mo stretchy="false">(</m:mo> <m:mn>1</m:mn> <m:mo stretchy="false">)</m:mo> </m:math> North-East, and in the pair-flip model, a system without particle conservation. Our results motivate a systematic study of bound states and their relation to ergodicity breaking, transport, and other properties of quantum kinetically constrained models.