We introduce a new type of 3D compressible quantum phase, in which the U(1) charge conservation symmetry is weakly broken by a rigid string-like order parameter, and no local order parameter exists. We show that this gapless phase is completely stable and described at low energy by an infinite-component Chern-Simons-Maxwell theory. We determine the emergent symmetry group, which contains U(1) 0-form planar symmetries and an unusual subgroup of the dual U(1) 1-form symmetry supported on cylindrical surfaces. Through the associated 't Hooft anomaly, we examine how the filling condition is fulfilled in the low-energy theory. We also demonstrate that the phase exhibits a kind of fractonic topological order, signified by extensively many different types of topologically nontrivial quasiparticles formed out of vortices of the weak superfluid. A microscopic model realizing the weak superfluid phase is constructed using an array of strongly coupled Luttinger liquid wires, and the connection to the field theory is established through boson-vortex duality.
We introduce a new type of 3D compressible quantum phase, in which the U(1) charge conservation symmetry is weakly broken by a rigid string-like order parameter, and no local order parameter exists. We show that this gapless phase is completely stable and described at low energy by an infinite-component Chern-Simons-Maxwell theory. We determine the emergent symmetry group, which contains U(1) 0-form planar symmetries and an unusual subgroup of the dual U(1) 1-form symmetry supported on cylindrical surfaces. Through the associated 't Hooft anomaly, we examine how the filling condition is fulfilled in the low-energy theory. We also demonstrate that the phase exhibits a kind of fractonic topological order, signified by extensively many different types of topologically nontrivial quasiparticles formed out of vortices of the weak superfluid. A microscopic model realizing the weak superfluid phase is constructed using an array of strongly coupled Luttinger liquid wires, and the connection to the field theory is established through boson-vortex duality.
We consider a weakly coupled gauge theory where charged particles all have large gaps (ie no Higgs condensation to break the gauge "symmetry") and the field strength fluctuates only weakly. We ask what kind of topological terms can be added to the Lagrangian of such a weakly coupled gauge theory. In this paper, we systematically construct quantized topological terms which are generalization of the Chern-Simons terms and F∧F terms, in space-time dimensions d and for any gauge groups (continuous or discrete), using each element of the topological cohomology classes Hd+1(BG,Z) on the classifying space BG of the gauge group G. In 3d or for finite gauge groups above 3d, the weakly coupled gauge theories are gapped. So our results on topological terms can be viewed as a systematic construction of gapped topologically ordered phases of weakly coupled gauge theories. In other cases, the weakly coupled gauge theories are gapless. So our results can be viewed as an attempt to systematically construct different gapless phases of weakly coupled gauge theories. Amazingly, the bosonic symmetry protected topological (SPT) phases with a finite on-site symmetry group G are also classified by the same Hd+1(BG,Z). (SPT phases are gapped quantum phases with a symmetry and trivial topological order.) In this paper, we show an explicit duality relation between topological gauge theories with the quantized topological terms and the bosonic SPT phases, for any finite group G and in any dimensions; a result first obtained by Levin and Gu. We also study the relation between topological lattice gauge theory and the string-net states with non-trivial topological order and no symmetry.
A quantum ground state of matter is realized in a bosonic model on a three-dimensional fcc lattice with emergent low energy excitations. The phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the graviton, although they have a soft $\ensuremath{\omega}\ensuremath{\sim}{k}^{2}$ dispersion relation. There are three branches of gapless excitations in this phase, one of which is gapless scalar trace mode, the other two have the same polarization and gauge symmetries as the gravitons. The dynamics of this phase is described by a set of Maxwell's equations. The defects carrying gauge charges can drive the system into the superfluid order when the defects are condensed; also the topological defects are coupled to the dual gauge field in the same manner as the charge defects couple to the original gauge field, after the condensation of the topological defects, the system is driven into the Mott insulator phase. In the two-dimensional case, the gapless soft graviton as well as the algebraic liquid phase are destroyed by the vertex operators in the dual theory, and the stripe order is most likely to take place close to the two-dimensional quantum critical point at which the vertex operators are tuned to zero.
In three dimensions, gapped phases can support "fractonic" quasiparticle excitations, which are either completely immobile or can only move within a low-dimensional submanifold, a peculiar topological phenomenon going beyond the conventional framework of topological quantum field theory.In this work we explore fractonic topological phases using three-dimensional coupled wire constructions, which have proven to be a successful tool to realize and characterize topological phases in two dimensions.We find that both gapped and gapless phases with fractonic excitations can emerge from the models.In the gapped case, we argue that fractonic excitations are mobile along the wire direction, but their mobility in the transverse plane is generally reduced.We show that the excitations in general have infinite-order fusion structure, distinct from previously known gapped fracton models.Like the two-dimensional coupled-wire constructions, many models exhibit gapless (or even chiral) surface states, which can be described by infinite-component Luttinger liquids.However, the universality class of the surface theory strongly depends on the surface orientation, thus revealing a different type of bulk-boundary correspondence unique to fracton phases.
Emergent QED3 at the bosonic Laughlin state to superfluid transition
Quantum phase transitions between topologically ordered and symmetry-broken phases lie beyond Landau theory. A prime example is the conjectured continuous transition from the bosonic ν=1/2 Laughlin state to a superfluid, proposed to be governed by a QED3--Chern--Simons (CS) critical point whose stability remains uncertain. We study half-filled bosons in the lowest Landau level subject to a lattice potential. Infinite-cylinder DMRG reveals a single continuous Laughlin--to--superfluid transition. Adiabatic flux insertion collapses the many-body gap and exposes massless Dirac quasiparticles, while momentum-resolved correlation lengths show that three lattice-related density modes share the same critical exponent, evidencing an emergent SO(3) symmetry. The joint appearance of Dirac dispersion and symmetry enlargement provides microscopic support for a stable QED3--CS fixed point. Our numerical strategy also offers a blueprint for exploring Landau-forbidden transitions in fractional Chern insulators and composite Fermi liquids realised in moire and cold-atom systems.
A system with charge conservation and lattice translation symmetry has a well-defined filling ν, which is a real number representing the average charge per unit cell.We show that if ν is fractional (i.e., not an integer), this imposes very strong constraints on the low-energy theory of the system and give a framework to understand such constraints in great generality, vastly generalizing the Luttinger and Lieb-Schultz-Mattis theorems.The most powerful constraint comes about if ν is continuously tunable (i.e., the system is charge compressible), in which case, we show that the low-energy theory must have a very large emergent symmetry group-larger than any compact Lie group.An example is the Fermi surface of a Fermi liquid, where the charge at every point on the Fermi surface is conserved.We expect that in many, if not all, cases, even exotic non-Fermi liquids will have the same emergent symmetry group as a Fermi liquid, even though they could have very different dynamics.We call a system with this property an ersatz Fermi liquid.We show that ersatz Fermi liquids share a number of properties in common with Fermi liquids, including Luttinger's theorem (which is thus extended to a large class of non-Fermi liquids) and periodic "quantum oscillations" in the response to an applied magnetic field.We also establish versions of Luttinger's theorem for the composite Fermi liquid in quantum Hall systems and for spinon Fermi surfaces in Mott insulators.Our work makes a connection between filling constraints and the theory of symmetry-protected topological phases, in particular through the concept of "'t Hooft anomalies."
A bosonic model on a 3 dimensional fcc lattice with emergent low energy excitations, with the same polarization and gauge symmetries as gravitons is constructed. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries. The gapless collective excitation of this phase closely resembles gravitons, although they have a soft ω∼k2 dispersion relation. The dynamics of this novel phase is described by new set of Maxwell equations. This phase also possesses an intricate topological order, requiring 18 winding numbers to specify each topological sector.