We investigate relaxation in the recently discovered ``fracton'' models and discover that these models naturally host glassy quantum dynamics in the absence of quenched disorder. We begin with a discussion of ``type I'' fracton models, in the taxonomy of Vijay, Haah, and Fu. We demonstrate that in these systems, the mobility of charges is suppressed exponentially in the inverse temperature. We further demonstrate that when a zero-temperature type I fracton model is placed in contact with a finite-temperature heat bath, the approach to equilibrium is a logarithmic function of time over an exponentially wide window of time scales. Generalizing to the more complex ``type II'' fracton models, we find that the charges exhibit subdiffusion up to a relaxation time that diverges at low temperatures as a superexponential function of inverse temperature. This behavior is reminiscent of ``nearly localized'' disordered systems, but occurs with a translation invariant three-dimensional Hamiltonian. We also conjecture that fracton models with conserved charge may support a phase which is a thermal metal but a charge insulator.
We investigate relaxation in the recently discovered fracton'' models and discover that these models naturally host glassy quantum dynamics in the absence of quenched disorder. We begin with a discussion of type I'' fracton models, in the taxonomy of Vijay, Haah, and Fu. We demonstrate that in these systems, the mobility of charges is suppressed exponentially in the inverse temperature. We further demonstrate that when a zero-temperature type I fracton model is placed in contact with a finite-temperature heat bath, the approach to equilibrium is a logarithmic function of time over an exponentially wide window of time scales. Generalizing to the more complex type II'' fracton models, we find that the charges exhibit subdiffusion up to a relaxation time that diverges at low temperatures as a superexponential function of inverse temperature. This behavior is reminiscent of nearly localized'' disordered systems, but occurs with a translation invariant three-dimensional Hamiltonian. We also conjecture that fracton models with conserved charge may support a phase which is a thermal metal but a charge insulator.
We introduce new classes of hydrodynamic theories inspired by the recently discovered fracton phases of quantum matter.Fracton phases are characterized by elementary excitations (fractons) with restricted mobility.The hydrodynamic theories we introduce describe thermalization in systems with fractonlike mobility constraints, including fluids where charge and dipole moment are both locally conserved, and fluids where charge is conserved along every line or plane of a lattice.Each of these fluids is subdiffusive and constitutes a new universality class of hydrodynamic behavior.There are infinitely many such classes, each with distinct subdiffusive exponents, all of which are captured by our formalism.Our framework naturally explains recent results on dynamics with constrained quantum circuits, as well as recent experiments with ultracold atoms in tilted optical lattices.We identify crisp experimental signatures of these novel hydrodynamics and explain how they may be realized in near term ultracold atom experiments.
We study the statistical and dynamical aspects of a translation-invariant Hamiltonian, without quench disorder, as an example of the manifestation of the phenomenon of many-body localization. This is characterized by the breakdown of thermalization and by information preservation of initial preparations at long times. To realize this, we use quasiperiodic long-range interactions, which are now achievable in high-finesse cavity experiments, to find evidence suggestive of a divergent time-scale in which charge inhomogeneities in the initial state survive asymptotically. This is reminiscent of a glassy behavior, which appears in the ground state of this system, being also present at infinite temperatures.
Fractons are topological quasiparticles with limited mobility. While there exist a variety of models hosting these excitations, typical fracton systems require rather complicated many-particle interactions. Here, we discuss fracton behavior in the more common physical setting of classical kagome spin models with frustrated two-body interactions only. We investigate systems with different types of elementary spin degrees of freedom (three-state Potts, XY, and Heisenberg spins) which all exhibit characteristic subsystem symmetries and fractonlike excitations. The mobility constraints of isolated fractons and bound fracton pairs in the three-state Potts model are, however, strikingly different compared to the known type-I or type-II fracton models. One may still explain these properties in terms of type-I fracton behavior and construct an effective low-energy tensor gauge theory when considering the system as a two-dimensional cut of a three-dimensional cubic lattice model. Our extensive classical Monte Carlo simulations further indicate a crossover into a low-temperature glassy phase where the system gets trapped in metastable fracton states. Moving on to XY spins, we find that in addition to fractons the system hosts fractional vortex excitations. As a result of the restricted mobility of both types of defects, our classical Monte Carlo simulations do not indicate a Kosterlitz-Thouless transition but again show a crossover into a glassy low-temperature regime. Finally, the energy barriers associated with fractons vanish in the case of Heisenberg spins, such that defect states may continuously decay into a ground state. These decays, however, exhibit a power-law relaxation behavior which leads to slow equilibration dynamics at low temperatures.
We study the spreading of initially local operators under unitary time evolution in a one-dimensional random quantum circuit model that is constrained to conserve a Uð1Þ charge and also the dipole moment of this charge.These constraints are motivated by the quantum dynamics of fracton phases.We discover that the charge remains localized at its initial position, providing a crisp example of a nonergodic dynamical phase of random circuit dynamics.This localization can be understood as a consequence of the return properties of low-dimensional random walks, through a mechanism reminiscent of weak localization, but insensitive to dephasing.The charge dynamics is well described by a system of coupled hydrodynamic equations, which makes several nontrivial predictions that are all in good agreement with numerics in one dimension.Importantly, these equations also predict localization in two-dimensional fractonic random circuits.We further find that the immobile fractonic charge emits nonconserved operators, whose spreading is governed by exponents that are distinct from those observed in nonfractonic circuits.These nonstandard exponents are also explained by our coupled hydrodynamic equations.Where entanglement properties are concerned, we find that fractonic operators exhibit a short time linear growth of observable entanglement with saturation to an area law, as well as a subthermal volume law for operator entanglement.The entanglement spectrum is found to follow semi-Poisson statistics, similar to eigenstates of many-body localized systems.The nonergodic phenomenology is found to persist to initial conditions containing nonzero density of dipolar or fractonic charge, including states near the sector of maximal charge.Our work implies that low-dimensional fracton systems should preserve forever a memory of their initial conditions in local observables under noisy quantum dynamics, thereby constituting ideal memories.It also implies that one-and two-dimensional fracton systems should realize true many-body localization (MBL) under Hamiltonian dynamics, even in the absence of disorder, with the obstructions to MBL in translationinvariant systems and in spatial dimensions greater than one being evaded by the nature of the mechanism responsible for localization.We also suggest a possible route to new nonergodic phases in high dimensions.
We study the relaxation dynamics of strongly interacting quantum systems that display a kind of many-body localization in spite of their translation-invariant Hamiltonian. We show that dynamics starting from a random initial configuration is nonperturbatively slow in the hopping strength, and potentially genuinely nonergodic in the thermodynamic limit. In finite systems with periodic boundary conditions, density relaxation takes place in two stages, which are separated by a long out-of-equilibrium plateau whose duration diverges exponentially with the system size. We estimate the phase boundary of this quantum glass phase, and discuss the role of local resonant configurations. We suggest experimental realizations and methods to observe the discussed nonergodic dynamics.
While quantum statistical mechanics triumphs in explaining many equilibrium phenomena, there is an increasing focus on going beyond conventional scenarios of thermalization. Traditionally examples of nonthermalizing systems are either integrable or disordered. Recently, examples of translationally invariant physical systems have been discovered whose excited energies avoid thermalization either due to local constraints (whether exact or emergent) or due to higher-form symmetries. In this article, we extend these investigations for the case of 3D U ( 1 ) quantum dimer models, which are lattice gauge theories with finite-dimensional local Hilbert spaces (also generically called quantum link models) with staggered charged static matter. Using a combination of analytical and numerical methods, we uncover a class of athermal states that arise in large winding sectors, when the system is subjected to external electric fields. The polarization of the dynamical fluxes in the direction of applied field traps excitations in 2D planes, while an interplay with the Gauss law constraint in the perpendicular direction causes exotic athermal behavior due to the emergence of new conserved quantities. This causes a geometric fragmentation of the system. We provide analytical arguments showing that the scaling of the number of fragments is exponential in the linear system size, leading to weak fragmentation. Further, we identify sectors which host fractonic excitations with severe mobility restrictions. The unitary evolution of fragments dominated by fractons is qualitatively different from the one dominated by nonfractonic excitations.