We study the late time relaxation dynamics of a pure $U(1)$ lattice gauge theory in the form of a dimer model on a bilayer geometry. To this end, we first develop a proper notion of hydrodynamic transport in such a system by constructing a global conservation law that can be attributed to the presence of topological solitons. The correlation functions of local objects charged under this conservation law can then be used to study the universal properties of the dynamics at late times, applicable to both quantum and classical systems. Performing the time evolution via classically simulable automata circuits unveils a rich phenomenology of the system's non-equilibrium properties: For a large class of relevant initial states, local charges are effectively restricted to move along one-dimensional 'tubes' within the quasi-two-dimensional system, displaying fracton-like mobility constraints. The time scale on which these tubes are stable diverges with increasing systems size, yielding a novel mechanism for non-ergodic behavior in the thermodynamic limit. We further explore the role of geometry by studying the system in a quasi-one-dimensional limit, where the Hilbert space is strongly fragmented due to the emergence of an extensive number of conserved quantities. This provides an instance of a recently introduced concept of 'statistically localized integrals of motion', whose universal anomalous hydrodynamics we determine by a mapping to a problem of classical tracer diffusion. We conclude by discussing how our approach might generalize to study transport in other lattice gauge theories.
We consider close-packed tiling models of geometric objects -- a mixture of hardcore dimers and plaquettes -- as a generalisation of the familiar dimer models. Specifically, on an anisotropic cubic lattice, we demand that each site be covered by either a dimer on a z-link or a plaquette in the x-y plane. The space of such fully packed tilings has an extensive degeneracy. This maps onto a fracton-type `higher-rank electrostatics', which can exhibit a plaquette-dimer liquid and an ordered phase. We analyse this theory in detail, using height representations and T-duality to demonstrate that the …
Fractons are emergent particles which are immobile in isolation, but which can move together in dipolar pairs or other small clusters. These exotic excitations naturally occur in certain quantum phases of matter described by tensor gauge theories. Previous research has focused on the properties of small numbers of fractons and their interactions, effectively mapping out the "Standard Model" of fractons. In the present work, however, we consider systems with a finite density of either fractons or their dipolar bound states, with a focus on the $U(1)$ fracton models. We study some of the phases …
Recent work has established the existence of stable quantum phases of matter described by symmetric tensor gauge fields, which naturally couple to particles of restricted mobility, such as fractons. We focus on a minimal toy model of a rank 2 tensor gauge field, consisting of fractons coupled to an emergent graviton (massless spin-2 excitation). We show how to reconcile the immobility of fractons with the expected gravitational behavior of the model. First, we reformulate the fracton phenomenon in terms of an emergent center of mass quantum number, and we show how an effective attraction arise…
We introduce a new quantity, that we term recoverable information, defined for stabilizer Hamiltonians. For such models, the recoverable information provides a measure of the topological information, as well as a physical interpretation, which is complementary to topological entanglement entropy. We discuss three different ways to calculate the recoverable information, and prove their equivalence. To demonstrate its utility, we compute recoverable information for fracton models using all three methods where appropriate. From the recoverable information, we deduce the existence of emergent $Z_2…
Inspired by recent developments generalizing Jordan-Wigner dualities to higher dimensions, we develop a framework of such dualities using an algebraic formalism for translation-invariant Hamiltonians proposed by Haah. We prove that given a translation-invariant fermionic system with general $q$-body interactions, where $q$ is even, a local mapping preserving global fermion parity to a dual Pauli spin model exists and is unique up to a choice of basis. Furthermore, the dual spin model is constructive, and we present various examples of these dualities. As an application, we bosonize fermionic s…
We consider the quench dynamics of a two-dimensional quantum dimer model and determine the role of its kinematic constraints. We interpret the non-equilibrium dynamics in terms of the underlying equilibrium phase transitions consisting of a BKT-transition between a columnar ordered valence bond solid (VBS) and a valence bond liquid (VBL), as well as a first order transition between a staggered VBS and the VBL. We find that quenches from a columnar VBS are ergodic and both order parameters and spatial correlations quickly relax to their thermal equilibrium. By contrast, the staggered side of th…
We introduce and study three-dimensional quantum dimer models with positive resonance terms. We demonstrate that their ground state wave functions exhibit a nonlocal sign structure that can be exactly formulated in terms of loops, and as a direct consequence, monomer excitations obey Fermi statistics. The sign structure and Fermi statistics in these "signful" quantum dimer models can be naturally described by a parton construction, which becomes exact at the solvable point.
We show how a finite number of conservation laws can globally `shatter' Hilbert space into exponentially many dynamically disconnected subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a `fractonic' model of quantum dynamics constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic model dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. This shattering can occur in a…
The classical cubic-lattice dimer model undergoes an unconventional transition between a columnar crystal and a dimer liquid, in the same universality class as the deconfined quantum critical point in spin-1/2 antiferromagnets but with very different microscopic physics and microscopic symmetries. Using Monte Carlo simulations, we show that this transition has an emergent SO(5) symmetry relating quantities characterizing the two adjacent phases. While the low-temperature phase has a conventional order parameter, the defining property of the Coulomb liquid on the high-temperature side is deconf…
We introduce a quantum spin-1/2 model with many-body correlated Heisenberg-type interactions on the 2D square lattice, designed to host a plaquette valence-bond solid (PVBS) ground state breaking $\mathbb{Z}_4$ symmetry. We carry out a detailed quantum Monte Carlo study of the quantum phase transition between the antiferromagnetic (AFM) and PVBS states. We find a first-order transition, in contrast to previously studied continuous 'deconfined' transitions between the AFM and columnar valence-bond solids. We show that the coexistence state at the AFM--PVBS transition is unexpectedly associated …
In many active matter systems, particle trajectories have a well-defined handedness or chirality. Whether such chiral activity can introduce stereoselective interactions between particles is not known. Here we developed a strategy to tune the nature of chiral activity of 3D-printed granular ellipsoids without altering their shape or size. In vertically agitated monolayers of these particles, we observed two types of dimers form depending on the chirality of the pairing monomers. Heterochiral dimers moved collectively as a single achiral active unit, while homochiral ones formed a translational…
Collections of interacting, self-propelled particles have been extensively studied as minimal models of many living and synthetic systems from bird flocks to active colloids. However, the influence of active rotations in the absence of self-propulsion i.e. spinning without walking) remains less explored. Here, we numerically and theoretically investigate the behaviour of ensembles of self-spinning dimers. We find that geometric frustration of dimer rotation by interactions yields spatiotemporal order and active melting with no equilibrium counterparts. At low density, the spinning dimers self-…
We propose a height-conserving quantum dimer model (hQDM) such that the lattice sum of its associated height field is conserved, and that it admits a Rokhsar-Kivelson (RK) point. The hQDM with minimal interaction range on the square lattice exhibits Hilbert space fragmentation and maps exactly to the XXZ spin model on the square lattice in certain Krylov subspaces. We obtain the ground-state phase diagram of hQDM via quantum Monte Carlo simulations, and demonstrate that a large portion of it is within the Krylov subspaces which admit the exact mapping to the XXZ model, with dimer ordered phase…
We present detailed analytic calculations of finite-volume energy spectra, mean field theory, as well as a systematic low-energy effective field theory for the square lattice quantum dimer model. The analytic considerations explain why a string connecting two external static charges in the confining columnar phase fractionalizes into eight distinct strands with electric flux $\frac{1}{4}$. An emergent approximate spontaneously broken $SO(2)$ symmetry gives rise to a pseudo-Goldstone boson. Remarkably, this soft phonon-like excitation, which is massless at the Rokhsar-Kivelson (RK) point, exist…
Short-time critical dynamics in the classical cubic dimer model
School of Physics, Sun Yat-sen University（中山大学物理学院）；Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University（西湖大学理学院物理系及未来产业研究中心）；Institute of Natural Sciences, Westlake Institute for Advanced Study（西湖高等研究院自然科学研究院）；Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, School of Physics, Sun Yat-sen University（中山大学物理学院广东省磁电物理与器件重点实验室）
Unraveling the Emergence of Slow Dynamics in U(1) Lattice Gauge Theories
International School for Advanced Studies (SISSA)（高级研究国际学院）；The Abdus Salam International Centre for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Jožef Stefan Institute（约瑟夫·斯蒂芬研究所）；INFN, Sezione di Trieste（意大利国家核物理研究所的里雅斯特分部）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文系）；INFN, sezione di Bologna（意大利国家核物理研究所博洛尼部分部）
Some of the exciting phenomena uncovered in strongly correlated systems in recent years - for instance quantum topological order, deconfined quantum criticality, and emergent gauge symmetries -- appear in systems in which the Hilbert space is effectively projected at low energies in a way that imposes local constraints on the original degrees of freedom. Cases in point include spin liquids, valence bond systems, dimer models, and vertex models. In this work, we use a slave boson description coupled to a large-$S$ path integral formulation to devise a generalised route to obtain effective field…
We study the mechanism of decay of a topological (winding-number) excitation due to finite-size effects in a two-dimensional valence-bond solid state, realized in an $S=1/2$ spin model ($J$-$Q$ model) and studied using projector Monte Carlo simulations in the valence bond basis. A topological excitation with winding number $|W|>0$ contains domain walls, which are unstable due to the emergence of long valence bonds in the wave function, unlike in effective descriptions with the quantum dimer model. We find that the life time of the winding number in imaginary time diverges as a power of the sys…
