We investigate the edge properties of Abelian topological phases in two spatial dimensions. We discover that many of them support multiple fully chiral edge phases, with surprising and measurable experimental consequences. Using the machinery of conformal field theory and integral quadratic forms we establish that distinct chiral edge phases correspond to genera of positive-definite integral lattices. This completes the notion of bulk-boundary correspondence for topological phases. We establish that by tuning inter-channel interactions the system can be made to transition between the different edge phases without closing the bulk gap.Separately we construct a family of one-dimensional models, called Perfect Metals, with no relevant mass-generating operators. These theories describe stable quantum critical phases of interacting fermions, bosons or spins in a quantum nanowire. These models rigorously answer a long-standing question about the existence of stable metallic phases in one and two spatial dimensions in the presence of generic disorder. Separately, they are the first example of a stable phase of an infinite parallel array of coupled Luttinger liquids. We perform a detailed study of the transport properties of Perfect Metals and show that in addition to violating the Wiedemann-Franz law, they naturally exhibit low power-law dependence of electric and thermal conductivities on temperature all the way to zero temperature. We dub this phenomenological set of properties a hyperconductor because in some sense, hyperconductors are better conductors that superconductors, which may have thermal conductivities that are exponentially small in temperature.
We show that a one-dimensional quantum wire with as few as two channels of interacting fermions can host metallic states of matter that are stable against all perturbations up to qth order in fermion creation or annihilation operators for any fixed finite q. Thus, the leading relevant perturbations are complicated operators that are expected to modify the physics only at very low energies, below accessible temperatures. The stability of these non-Fermi liquid fixed points is due to strong interactions between the channels, which can (but need not) be chosen to be purely repulsive. Our results might enable elementary physical realizations of these phases.
Metallic phases have been observed in several disordered two-dimensional (2D) systems, including thin films near superconductor-insulator transitions and quantum Hall systems near plateau transitions. The existence of 2D metallic phases at zero temperature generally requires an interplay of disorder and interaction effects. Consequently, experimental observations of 2D metallic behavior have largely defied explanation. We formulate a general stability criterion for strongly interacting, massless Dirac fermions against disorder, which describe metallic ground states with vanishing density of states. We show that (2+1)-dimensional quantum electrodynamics (
QED3) with a large, even number of fermion flavors remains metallic in the presence of weak scalar potential disorder due to the dynamic screening of disorder by gauge fluctuations. We also show that
QED3 with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.
Using bosonization, we study a model of parallel quantum wires constructed from two-dimensional Dirac fermions in the presence of periodic topological domain walls. The model accounts for the lateral spread of the wave functions $\ensuremath{\ell}$ in the transverse direction to the wires. The gapless modes confined to each domain wall are shown to form Luttinger liquids, which realize a well-known smectic non-Fermi liquid fixed point when interwire Coulomb interactions are considered. Perturbative studies on phenomenological models have shown that the smectic fixed point is unstable toward a variety of phases such as superconductivity, stripe, smectic, and Fermi liquid phases. Here, we show that the considered model leads to a phase diagram with only smectic metal and Fermi liquid phases. The smectic metal phase is stable in the ideal quantum wire limit $\ensuremath{\ell}\ensuremath{\rightarrow}0$. For finite $\ensuremath{\ell}$, we find a critical Coulomb coupling separating the strong coupling smectic metal from a weak coupling Fermi liquid phase. We conjecture that the absence of superconductivity should be a generic feature of similar models. We discuss the relevance of this model for quantum wires created with moir\'e heterostructures.
A fermionic disordered one-dimensional wire in the presence of attractive interactions is known to have two distinct phases, a localized and superconducting, depending on the strength of interaction and disorder. The localized region may also exhibit a metallic behavior if the system size is shorter than the localization length. Here we show that the superconducting phase has a distribution of the entanglement entropy distinct from the metallic regime. The entanglement entropy distribution is strongly asymmetric with a Lévy α-stable distribution (compared to the Gaussian metallic distribution), as is seen also for the second Rényi entropy distribution. Thus, entanglement properties may reveal properties which cannot be detected by other methods.
We analyze an anisotropic spin-1/2 two-leg ladder in the presence of various types of random perturbations. The generic phase diagram for the pure system, in a way similar to spin one chains, consists of four phases: an antiferromagnet, a Haldane gap or a singlet phase (depending on the sign of interchain coupling), and two
XY phases designated by
XY1 and
XY2. The effects of disorder depend crucially on whether it preserves
XY symmetry (random field along
z and random exchange) or not (random anisotropy or random
XY fields). In all cases we computed the new phase diagram and the correlation length for the disordered system. The ladder exhibits a remarkable stability to disorder with
XY symmetry. Not only the singlet phases but also the massless
XY1 phase are totally unaffected by disorder in stark contrast with the single chain case. Even in the presence of an external magnetic field breaking the spin gap most of the phase diagram (including the
XY point) remains unaffected by the disorder, again in opposition with the single chain case. This stabilization towards disorder is similar, albeit stronger, to the one occurring for fermionic ladders. On the other hand, the
XY2 phase is very strongly suppressed. Disorder breaking
XY symmetry has much stronger effects and most of the phases at the exception of the singlet one are now destroyed. Interestingly, the disordered
XY1 phase has a much shorter correlation length than the disordered
XY2 phase contrarily with the case of perturbations preserving the rotation symmetry around the
z axis. The ladder system is thus in fact much more anisotropic than its single chain counterpart with identical exchanges. Finally we examine the case of strong disorder or weak interchain exchange for
XY symmetric disorder. Close to the isotropic point, when the interchain exchange is increased the system undergoes a transition between two decoupled disordered spin-1/2 chains to a singlet ladder unaffected by disorder. For more
XY like systems, the transition occurs in two steps with a nondisordered
XY1 phase occurring between the decoupled chains and the singlet phase. Comparison with other disordered gapped systems such as spin one chains is discussed.