We consider theories of fractons with $N$ fields. These theories have exotic spacetime symmetries, including a conserved dipole moment. Using collective fields we solve these models to leading order in large $N$. The large $N$ solution reveals that these models are strongly correlated, and that interactions generate a momentum-dependent self-energy. Dipole symmetry is spontaneously broken throughout the phase diagram of these models, leading to a low-energy Goldstone description of what we dub "dipole superfluids."
We consider theories of fractons with N fields. These theories have exotic spacetime symmetries, including a conserved dipole moment. Using collective fields we solve these models to leading order in large N. The large N solution reveals that these models are strongly correlated, and that interactions generate a momentum-dependent self-energy. Dipole symmetry is spontaneously broken throughout the phase diagram of these models, leading to a low-energy Goldstone description of what we dub "dipole superfluids."
We consider theories of N-component fields with exotic spacetime symmetries, including a conserved dipole moment. Microscopic charges are immobile by symmetry, and so resemble fractons. Using collective fields we solve these models to leading order in large N. The large N solution reveals that these models are strongly correlated, and that interactions dress the microscopic charges so that they become mobile, long-lived quasiparticles. Dipole symmetry is spontaneously broken throughout the phase diagram of these models, leading to a low-energy Goldstone description.
Fractonic superfluids are featured by the interplay of spontaneously broken charge symmetry and mobility constraints on single-particle kinematics due to the conservation of higher moments, such as dipoles, angular charge moments, and quadrupoles. Building on prior studies by Yuan [] and Chen [], we study a class of fractonic superfluids, termed (HFS), in which bosons of multiple species interact while moment hybridization is conserved. We explore the consequences of hybridization via two model series: , conserving total moments of the same order across species, and , conserving total moments of different orders. In Model Series A, we analyze dipole moment hybridization and extend the discussion to higher-order moments, examining the ground state, Goldstone modes, correlation functions, and so on. We compute the minimal spatial dimensions, where the total charge symmetry begins to get partially broken via particle-hole condensation, leading to true off-diagonal long-range order. In Model Series B, we focus on HFS with hybrid dipole-quadrupole conservation. For both series, we introduce Bose-Hubbard–type lattice models that reduce to either of both series in the weak Hubbard interaction regime. We perform a mean-field analysis on the global phase diagram and discuss experimental realizations in strongly tilted optical lattices via a third-order perturbation theory. This work, alongside prior studies, completes a trilogy on fractonic superfluids, uncovering symmetry-breaking physics emerging from higher moment conservation, leaving various promising studies for future investigation.
Fractonic superfluids are exotic phases of matter in which bosons are subject to mobility constraints, resulting in features beyond those of conventional superfluids. These exotic phases arise from the spontaneous breaking of higher-rank symmetry (HRS) in many-body systems with higher-moment conservation, such as dipoles, quadrupoles, and angular moments. The aim of this paper is to introduce exciting developments on the theory of spontaneous symmetry breaking in such systems, which we refer to as ``many-fracton systems''. More specifically, we introduce exciting progress on general aspects of HRS, minimal model construction, realization of symmetry-breaking ground states, order parameter, off-diagonal long-range order (ODLRO), Noether currents with continuity equations, Gross-Pitaevskii equations, quantum fluctuations, Goldstone modes, specific heat, generalized Mermin-Wagner theorem, critical current, Landau criterion, symmetry defects, and Kosterlitz-Thouless (KT)-like physics, hydrodynamics, and dipolar Hubbard model realization. This paper is concluded with several future directions.
We examine the hydrodynamics of systems with spontaneously broken multipolar symmetries using a systematic effective field theory. We focus on the simplest nontrivial setting: a system with charge and dipole symmetry, but without momentum conservation. When no symmetries are broken, our formalism reproduces the quartic subdiffusion ($\ensuremath{\omega}\ensuremath{\sim}\ensuremath{-}i{k}^{4}$) characteristic of ``fracton hydrodynamics'' with conserved dipole moment. Our formalism also captures spontaneous breaking of charge and/or dipole symmetry. When charge symmetry is spontaneously broken, the hydrodynamic modes are quadratically propagating and quartically relaxing ($\ensuremath{\omega}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}{k}^{2}\ensuremath{-}i{k}^{4}$). When the dipole symmetry is spontaneously broken but the charge symmetry is preserved, then we find quadratically relaxing (diffusive) transverse modes, plus another mode which, depending on parameters, may be either purely diffusive ($\ensuremath{\omega}\ensuremath{\sim}\ensuremath{-}i{k}^{2}$) or quadratically propagating and quadratically relaxing ($\ensuremath{\omega}\ensuremath{\sim}\ifmmode\pm\else\textpm\fi{}{k}^{2}\ensuremath{-}i{k}^{2}$). Our work provides concrete predictions that may be tested in near-term cold atom experiments, and also lays out a general framework that may be applied to study systems with spontaneously broken multipolar symmetries.
The emergence of fractonic topological phases and novel universality classes for quantum dynamics highlights the importance of dipolar symmetry in condensed matter systems. In this work, we study the properties of symmetry-breaking phases of the dipolar symmetries in fermionic models in various spatial dimensions. In such systems, fermions obtain energy dispersion through dipole condensation. Due to the nontrivial commutation between the translation symmetry and dipolar symmetry, the Goldstone modes of the dipolar condensate are strongly coupled to the dispersive fermions and naturally give rise to non-Fermi liquids at low energies. The infrared description of the dipolar symmetry-breaking phase is analogous to the well-known theory of a Fermi surface coupled to an emergent U(1) gauge field. We also discuss the crossover behavior when the dipolar symmetry is slightly broken and the cases with anisotropic dipolar conservation.
We investigate the thermodynamics of equilibrium thermal states and their near-equilibrium dynamics in systems with fractonic symmetries in arbitrary curved space. By explicitly gauging the fracton algebra we obtain the geometry and gauge fields that field theories with conserved dipole moment couple to. We use the resultant fracton geometry to show that it is not possible to construct an equilibrium partition function for global thermal states unless part of the fractonic symmetries is spontaneously broken. This leads us to introduce two classes of fracton superfluids with conserved energy and momentum, namely p p -wave and s s -wave fracton superfluids. The latter phase is an Aristotelian superfluid at ideal order but with a velocity constraint and can be split into two separate regimes: The U(1) fracton superfluid and the pinned s s -wave superfluid regimes. For each of these classes and regimes we formulate a hydrodynamic expansion and study the resultant modes. We find distinctive features of each of these phases and regimes at ideal order in gradients, without introducing dissipative effects. In particular we note the appearance of a sound mode for s s -wave fracton superfluids. We show that previous work on fracton hydrodynamics falls into these classes. Finally, we study ultra-dense p p -wave fracton superfluids with a large kinetic mass in addition to studying the thermodynamics of ideal Aristotelian superfluids.