Quantum kinetically constrained models can exhibit a wealth of dynamical phenomena ranging from anomalous transport to Hilbert-space fragmentation (HSF). We study a class of one-dimensional particle-number-conserving systems in which particle hoppings are subjected to an East-like constraint, akin to facilitated spin models in classical glasses. While such a kinetic constraint leads to HSF, we find that the degree of fragmentation exhibits a sharp transition as the average particle density is varied. Below a critical density, the system transitions from being weakly fragmented where most of the initial states thermalize diffusively to strongly fragmented where the dynamics are frozen and the system fails to thermalize. Remarkably, the East model allows for both efficient numerical simulations and analytic solutions of various diagnostics of the phase transition, from which we obtain a set of exact critical exponents. We find that the freezing transition in particle-conserving East models belongs to the same universality class as dipole-conserving fracton systems. Our results provide a tractable minimal model for filling-induced freezing transitions associated with HSF, which can be readily tested on state-of-the-art quantum platforms.
Quantum kinetically constrained models can exhibit a wealth of dynamical phenomena ranging from anomalous transport to Hilbert-space fragmentation (HSF). We study a class of one-dimensional particle-number-conserving systems in which particle hoppings are subjected to an East-like constraint, akin to facilitated spin models in classical glasses. While such a kinetic constraint leads to HSF, we find that the degree of fragmentation exhibits a sharp transition as the average particle density is varied. Below a critical density, the system transitions from being weakly fragmented where most of the initial states thermalize diffusively to strongly fragmented where the dynamics are frozen and the system fails to thermalize. Remarkably, the East model allows for both efficient numerical simulations and analytic solutions of various diagnostics of the phase transition, from which we obtain a set of exact critical exponents. We find that the freezing transition in particle-conserving East models belongs to the same universality class as dipole-conserving fracton systems. Our results provide a tractable minimal model for filling-induced freezing transitions associated with HSF, which can be readily tested on state-of-the-art quantum platforms.
We study a stochastic lattice gas of particles in one dimension with strictly finite-range interactions that respect the fractonlike conservation laws of total charge and dipole moment. As the charge density is varied, the connectivity of the system's charge configurations under the dynamics changes qualitatively. We find two distinct phases: Near half filling the system thermalizes subdiffusively, with almost all configurations belonging to a single dynamically connected sector. As the charge density is tuned away from half filling there is a phase transition to a frozen phase, where locally active finite bubbles cannot exchange particles and the system fails to thermalize. The two phases exemplify what has recently been referred to as weak and strong Hilbert space fragmentation, respectively. We study the static and dynamic scaling properties of this weak-to-strong fragmentation phase transition in a kinetically constrained classical Markov circuit model, obtaining some conjectured exact critical exponents.
Quantum kinetically constrained models have recently attracted significant attention due to their anomalous dynamics and thermalization. In this work, we introduce a hitherto unexplored family of kinetically constrained models featuring conserved particle number and strong inversion-symmetry breaking due to facilitated hopping. We demonstrate that these models provide a generic example of so-called quantum Hilbert space fragmentation, that is manifested in disconnected sectors in the Hilbert space that are not apparent in the computational basis. Quantum Hilbert space fragmentation leads to an exponential in system size number of eigenstates with exactly zero entanglement entropy across several bipartite cuts. These eigenstates can be probed dynamically using quenches from simple initial product states. In addition, we study the particle spreading under unitary dynamics launched from the domain wall state, and find faster than diffusive dynamics at high particle densities, that crosses over into logarithmically slow relaxation at smaller densities. Using a classically simulable cellular automaton, we reproduce the logarithmic dynamics observed in the quantum case. Our work suggests that particle conserving constrained models with inversion symmetry breaking realize so far unexplored dynamical behavior and invite their further theoretical and experimental studies.
This paper explores the effect of the strong-to-weak fragmentation transition, namely, the freezing transition, and its rich characteristics in a family of one-dimensional spinless fermionic models with facilitated hoppings involving short-to-long-range East constraints. Focusing on this family of models with range-q constraints, our investigation furnishes an exhaustive understanding of the fragmented Hilbert space utilizing the enumerative combinatorics and transfer-matrix methods. This further allows us to get insight into the freezing transition in this family of models with the help of the generalization of Catalan numbers introduced by Frey and Sellers for q>1, further revealing that increasing the range of constraints drives the transition to transpire at lower filling fractions as nc=1/(q+1). This distinct fragmentation structure also yields the emergence of ground states at multiple fillings, which can be explained from the root structure of the largest fragment within the full Hilbert space. Furthermore, the ground state exhibits signatures of criticality with logarithmic scaling of entanglement entropy. Thereafter, our investigation exemplifies that the above transition has a profound impact on the thermalization of bulk and boundary autocorrelators at long times, which includes intricate filling-dependent inhomogeneous long-time autocorrelation profiles across the chain in open boundary conditions (OBCs). Finally, we probe the effect of the strong-to-weak fragmentation transition on the transport at intermediate times in periodic boundary conditions (PBCs), restricting ourselves to models up to range-3 constraints. This investigation discloses a vast range of anomalous transport possibilities, ranging from size-stretched exponential relaxation through superdiffusive to subdiffusive behaviors, akin to the fragmentation structure supported by the filling fraction and range of constraints. In brevity, our paper reveals intriguing possibilities conspired by constraints with varying ranges, and those-induced Hilbert-space fragmentation and freezing transition, thus offering exciting avenues for future explorations.
We demonstrate the existence of a universal phase diagram of quantum chains with range- k interactions subject to the conservation of a total charge and its dipole moment. These systems exhibit “freezing” transitions between strongly and weakly Hilbert-space-fragmented phases as the charge filling ν is varied. We show that these continuous phase transitions occur at a critical charge filling of ν c = ( k − 2 ) − 1 of the on-site Hilbert-space dimension d . To this end, we analytically prove that, for any d , any state with ν < ν c hosts a finite density of sites belonging to “blockages,” which we define as subregions of the chain across which transport of charge and dipole moment cannot occur. Some blockages arise from sequences of frozen sites, i.e., sites with an unchanging on-site charge, while others do not involve frozen sites at all. We prove that the presence of blockages implies strong fragmentation of typical symmetry sectors into Krylov subspaces, each of which forms an exponentially vanishing fraction of the total sector. By studying the distribution of blockages we analytically characterize how typical states are subdivided into dynamically disconnected local “active bubbles” and prove that typical eigenstates at these charge fillings exhibit area-law entanglement entropy, while there exist rare eigenstates featuring non-area-law scaling. We also numerically show that for ν > ν c and arbitrary d , typical symmetry sectors are weakly fragmented, with their dominant Krylov sectors constituted of states that are free of blockages. We analytically derive some critical exponents characterizing the transition and numerically determine the density of blockages at ν = ν c , with clear implications for transport at the critical point. Finally, we investigate the properties of special-case models for which no phase transitions occur.
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 U ( 1 ) particle-conservation symmetry. We use the U ( 1 ) East, which lacks inversion symmetry, and the inversion-symmetric U ( 1 ) 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 U ( 1 ) 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.
We investigate a one-dimensional correlated-hopping model of spinless fermions with an East constraint. We first analytically unravel the complete fragmentation structure of this model by labeling each fragment by a unique root configuration and utilizing the transfer matrix method. We show that the growth of the size of each fragment of the model follows the widely studied Dyck sequence and is therefore analytically tractable with the help of Catalan triangles. While the eigenstate thermalization hypothesis (ETH) does not hold within the full Hilbert space which exhibits Poisson statistics of the energy level spacing, an examination of various quantities restricted to the largest fragments shows that a weaker version of the subspace-restricted thermalization holds. This weaker violation of the ETH within the largest fragments is supported by the presence of subspace-restricted quantum many-body scars due to quantum fragmentation. Our analysis further reveals that the filling fraction at which the model has the largest fragment shifts with increasing system sizes from half-filling due to the distinct fragmentation structure. Next, we show that the inclusion of a nearest-neighbor density-density interaction with strength V induces a spectral transition within the largest fragment from a weakly ETH-violating phase containing scars to a statistical bubble localized phase as V increases. In particular, the $V\ensuremath{\rightarrow}\ensuremath{\infty}$ limit produces an integrable model. We find that the addition of finite-V stabilizes the ground state near half-filling while keeping intact the fragmentation structure of the East model. However, this behavior abruptly changes exactly at $V=\ensuremath{\infty}$ due to the emergence of a distinct fragmentation structure; we analytically explore this in a comprehensive manner. The infinite-V model has many interesting properties, among which the appearance of the ground state and the largest fragment at two different filling fractions is specially noteworthy. Finally, we propose an experimental setup to realize the infinite-V model as a particular limit of a special kind of $t\text{\ensuremath{-}}V$ model with an on-site potential.