Gapless Modes Research Articles

Gapless nonhydrodynamic modes in relativistic kinetic theory

Gapless nonhydrodynamic modes in relativistic kinetic theory

Impossible symmetries and conformal gravity

We explore the physics of relativistic gapless phases defined by a mixed anomaly between two generalized conserved currents. The gapless modes can be understood as Goldstone modes arising from the nonlinear realization of (generically higher-form) symmetries arising from these currents. In some cases, the anomaly cannot be reproduced by any local and unitary theory, indicating that the corresponding symmetries are impossible, in the sense that they cannot appear in a Lorentzian physical system. We give a general construction and illustrate it with several examples. Most notably, we study conformal gravity from this perspective, describing the higher-form symmetries of the linear theory and showing how it can be understood in terms of anomalies. Along the way we clarify some aspects of electric-magnetic duality in linear conformal gravity. Published by the American Physical Society 2024

Interacting crystalline topological insulators in two-dimensions with time-reversal symmetry

Topology is routinely used to understand the physics of electronic insulators. However, for strongly interacting electronic matter, such as Mott insulators, a comprehensive topological characterization is still lacking. When their ground state only contains short-range entanglement and does not break symmetries spontaneously, they generically realize crystalline fermionic symmetry-protected topological phases (cFSPTs), supporting gapless modes at the boundaries or at the lattice defects. Here, we provide an exhaustive classification of cFSPTs in two dimensions with U(1) charge-conservation and spinful time-reversal symmetries, namely, those generically present in spin-orbit coupled insulators, for any of the 17 wallpaper groups. It has been shown that the classification of cFSPTs can be understood from appropriate real-space decorations of lower-dimensional subspaces, and we expose how these relate to the Wyckoff positions of the lattice. We find that all nontrivial one-dimensional decorations require electronic interactions. Furthermore, we provide model Hamiltonians for various decorations, and discuss the signatures of cFSPTs. This classification paves the way to further explore topological interacting insulators, providing the backbone information in generic model systems and ultimately in experiments. Published by the American Physical Society 2024

Entanglement-enabled symmetry-breaking orders

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wavefunction of some few-body clusters; some standard examples include the simplest ferromagnets and valence bond solids. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any such tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description. For concreteness, we present an infinite family of exactly solvable gapped models on one-dimensional lattices with nearest-neighbor interactions, whose ground states exhibit entanglement-enabled symmetry-breaking orders from a discrete symmetry breaking. In addition, these ground states have gapless edge modes protected by the unbroken symmetries. We also propose a construction to realize entanglement-enabled symmetry-breaking orders with spontaneously broken continuous symmetries. Under the unbroken symmetries, some of our examples can be viewed as symmetry-protected topological states that are beyond the conventional classifications.

Gravitational Landau levels and the chiral anomaly

A popular physical picture of the mechanism behind the four-dimensional chiral anomaly is provided by the massless Dirac equation in the presence of constant electric and magnetic background fields. The magnetic field creates highly degenerate Landau levels, the lowest of which is gapless. Any parallel component of the electric field drives a spectral flow in the gapless mode that causes particles to emerge from, or disappear into, the Dirac sea. Seeking a similar picture for the gravitational contribution to the chiral anomaly, we consider the massless Dirac equation in a background spacetime that creates gravitational Landau levels. We find that in this case the resulting spectral flow, with its explicit particle production, accounts for only a small part of the anomalous creation of chiral charge. The balance is provided by the vacuum expectation charge arising from the spectral asymmetry.

Universal Platform of Point-Gap Topological Phases from Topological Materials.

Whereas point-gap topological phases are responsible for exceptional phenomena intrinsic to non-Hermitian systems, their realization in quantum materials is still elusive. Here, we propose a simple and universal platform of point-gap topological phases constructed from Hermitian topological insulators and superconductors. We show that (d-1)-dimensional point-gap topological phases are realized by making a boundary in d-dimensional topological insulators and superconductors dissipative. A crucial observation of the proposal is that adding a decay constant to boundary modes in d-dimensional topological insulators and superconductors is topologically equivalent to attaching a (d-1)-dimensional point-gap topological phase to the boundary. We furthermore establish the proposal from the extended version of the Nielsen-Ninomiya theorem, relating dissipative gapless modes to point-gap topological numbers. From the bulk-boundary correspondence of the point-gap topological phases, the resultant point-gap topological phases exhibit exceptional boundary states or in-gap higher-order non-Hermitian skin effects.

Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4

The notion of topological insulators (TIs), characterized by an insulating bulk and conducting topological surface states, can be extended to higher-order topological insulators (HOTIs) hosting gapless modes localized at the boundaries of two or more dimensions lower than the insulating bulk. In this work, by performing high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements with submicron spatial and spin resolution, we systematically investigate the electronic structure and spin texture of quasi-one-dimensional (1D) HOTI candidate Bi4Br4. In contrast to the bulk-state-dominant spectra on the (001) surface, we observe gapped surface states on the (100) surface, whose dispersion and spin-polarization agree well with our ab-initio calculations. Moreover, we reveal in-gap states connecting the surface valence and conduction bands, which is a signature of the hinge states inside the (100) surface gap. Our findings provide compelling evidence for the HOTI phase of Bi4Br4. The identification of the higher-order topological phase promises applications based on 1D spin-momentum locked current in electronic and spintronic devices.

Soft phonon theorems

A variety of condensed matter systems describe gapless modes that can be interpreted as Nambu-Goldstone bosons of spontaneously broken Poincaré symmetry. In this paper we derive new soft theorems constraining the tree-level scattering of these degrees of freedom, as exhibited in solids, fluids, superfluids, and framids. These soft theorems are in one-to-one correspondence with various broken symmetries, including spacetime translations, Lorentz boosts, and, for the case of fluids, volume-preserving diffeomorphisms. We also implement a bootstrap in which the enhanced vanishing of amplitudes in the soft limit is taken as an input, thus sculpting out a subclass of exceptional solid, fluid, and framid theories.

Sufficient Condition for Gapless Spin-Boson Lindbladians, and Its Connection to Dissipative Time Crystals.

We discuss a sufficient condition for gapless excitations in the Lindbladian master equation for collective spin-boson systems and permutationally invariant systems. The condition relates a nonzero macroscopic cumulant correlation in the steady state to the presence of gapless modes in the Lindbladian. In phases arising from competing coherent and dissipative Lindbladian terms, we argue that such gapless modes, concomitant with angular momentum conservation, can lead to persistent dynamics in the spin observables with the possible formation of dissipative time crystals. We study different models within this perspective, from Lindbladians with Hermitian jump operators, to non-Hermitian ones composed by collective spins and Floquet spin-boson systems. We also provide a simple analytical proof for the exactness of the mean-field semiclassical approach in such systems based on a cumulant expansion.

Non-Hermitian topological Fermi superfluid near the p -wave unitary limit

We discuss theoretically the non-Hermitian superfluid phase transition in one-dimensional two-component Fermi gases near the $p$-wave Feshbach resonance accompanied by the two-body loss associated with dipolar relaxation. We point out that this system gives us an opportunity to explore the interplay among various nontrivial properties such as universal thermodynamics at divergent $p$-wave scattering lengths, the topological phase transition at vanishing chemical potential, and the non-Hermitian Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) transition, in a unified manner. In the BCS phase, the loss-induced superfluid-normal transition occurs when the exceptional point appears in the effective non-Hermitian Hamiltonian. In the BEC phase, the diffusive gapless mode can be regarded as a precursor of the instability of the superfluid state. Moreover, we show that the superfluid state is fragile against the two-body loss near the topological phase transition point.

Higher rank chirality and non-Hermitian skin effect in a topolectrical circuit

While chirality imbalances are forbidden in conventional lattice systems, non-Hermiticity can effectively avoid the chiral-doubling theorem to facilitate 1D chiral dynamics. Indeed, such systems support unbalanced unidirectional flows that can lead to the localization of an extensive number of states at the boundary, known as the non-Hermitian skin effect (NHSE). Recently, a generalized (rank-2) chirality describing a 2D robust gapless mode with dispersion ω = kxky has been introduced in crystalline systems. Here we demonstrate that rank-2 chirality imbalances can be established in a non-Hermitian (NH) lattice system leading to momentum-resolved chiral dynamics, and a rank-2 NHSE where there are both edge- and corner-localized skin modes. We then experimentally test this phenomenology in a 2-dimensional topolectric circuit that implements a NH Hamiltonian with a long-lived rank-2 chiral mode. Using impedance measurements, we confirm the rank-2 NHSE in this system, and its manifestation in the predicted skin modes and a highly unusual momentum-position locking response. Our investigation demonstrates a circuit-based path to exploring higher-rank chiral physics, with potential applications in systems where momentum resolution is necessary, e.g., in beamformers and non-reciprocal devices.

Field-theoretic functional renormalization group formalism for non-Fermi liquids and its application to the antiferromagnetic quantum critical metal in two dimensions

To capture the universal low-energy physics of metals within effective field theories, one has to generalize the usual notion of scale invariance and renormalizable field theory due to the presence of intrinsic scales (Fermi momenta). In this paper, we develop a field-theoretic functional renormalization group formalism for full low-energy effective field theories of non-Fermi liquids that include all gapless modes around the Fermi surface. The formalism is applied to the non-Fermi liquid that arises at the antiferromagnetic quantum critical point in two space dimensions. In the space of coupling functions, an interacting fixed point arises at a point with momentum-independent couplings and vanishing nesting angle. In theories deformed with non-zero nesting angles, coupling functions acquire universal momentum profiles controlled by the bare nesting angles at low energies before flowing to superconducting states in the low-energy limit. The superconducting instability is unavoidable because lukewarm electrons that are coherent enough to be susceptible to pairing end up being subject to a renormalized attractive interaction with its minimum strength set by the nesting angle irrespective of the bare four-fermion coupling. Despite the inevitable superconducting instability, theories with small bare nesting angles and bare four-fermion couplings that are repulsive or weakly attractive must pass through the region with slow RG flow due to the proximity to the non-Fermi liquid fixed point. The bottleneck region controls the scaling behaviours of the normal state and the quasi-universal pathway from the non-Fermi liquid to superconductivity. In the limit that the nesting angle is small, the non-Fermi liquid scaling dictates the physics over a large window of energy scale above the superconducting transition temperature.

Nearly critical holographic superfluids

We study the nearly critical behaviour of holographic superfluids at finite temperature and chemical potential in their probe limit. This allows us to examine the coupled dynamics of the full complex order parameter with the charge density of the system. We derive an effective theory for the long wavelength limit of the gapless and pseudo-gapped modes by using analytic techniques in the bulk. We match our construction with Model F in the classification of Hohenberg and Halperin and compute the complex dissipative kinetic transport coefficient in terms of thermodynamics and black hole horizon data. We carry out an analysis of the corresponding modes and argue that at finite density the dispersion relations are discontinuous between the normal and the broken phase. We compare and contrast our results with earlier numerical work.

Physical origin of current partition at a topological trifurcation

In gated bilayer graphene, topological zero-line modes (ZLMs) appear along lines separating regions with opposite valley Hall topologies. Although it is experimentally difficult to design the electric gates to realize ZLMs due to the extremely challenging techniques, twisted bilayer graphene provides a natural platform to produce ZLMs in the presence of uniform electric field. In this Letter, we develop a set of wavepacket dynamics, which can be utilized to characterize various gapless edge modes and can quantitatively reproduce the electronic transport properties at topological intersections. To our surprise, in the minimally twisted bilayer graphene where a topological trifurcation intersection naturally arises, we show that the counterintuitive current partition (i.e., the direct transport propagation) originates from the microscopic mechanism "bypass jump". Our method can be applied to understand the microscopic pictures of the electronic transport features of all kinds of topological states.

Deconfined quantum critical point with nonlocality

The deconfined quantum critical point (DQCP) between the N\'{e}el and valence bond solid (VBS) order was originally proposed in quantum spin systems with a local Hamiltonian. In the last few years analogues of DQCPs with nonlocal interactions have been explored, which can lead to rich possibilities. The nonlocal interactions can either arise from an instantaneous long range interaction in the Hamiltonian, or from gapless modes that reside in one higher spatial dimension. Here we consider another mechanism of generating nonlocal interactions by coupling the DQCP to the "hot spots" of a Fermi surface. We demonstrate that at least within a substantial energy window, the physics of the DQCP is controlled by a new fixed point with dynamical exponent $z > 1$

Bulk and surface critical behavior of a quantum Heisenberg antiferromagnet on two-dimensional coupled diagonal ladders

Using Quantum Monte Carlo simulations, we study the spin-1/2 Heisenberg model on a two-dimensional lattice formed by coupling diagonal ladders. The model hosts an antiferromagnetic N\'eel phase, a rung singlet product phase, and a topological none trivial Haldane phase, separated by two quantum phase transitions. We show that the two quantum critical points are all in the three-dimensional O(3) universality class. The properties of the two gapped phases, including the finite-size behavior of the string orders in the Haldane phase, are studied. We show that the surface formed by the ladders ends is gapless, while the surface exposed along the ladders is gapful, in the Haldane phase. Conversely, in the gapped rung singlet phase, the former surface is gapped, and the latter is gapless. We demonstrate that, although mechanisms of the two gapless modes are different, nonordinary surface critical behaviors are realized at both critical points on the gapless surfaces exposed by simply cutting bonds without fine-tuning the surface coupling required to reach a multicritical point in classical models. We also show that, on the gapped surfaces, the surface critical behaviors are in the ordinary class.

Dynamics Reflect Gapless Edge Modes for Topological Superconductor

AbstractThe dynamical feature for a p‐wave superconductor model in different parameter regions in terms of the appearance of topologically gapless edge modes in reel geometry is investigated. First, the parameter region with gapless edge modes versus a parameter and quasi‐momentum is shown. The parameter diagram can be reflected by the expectations of Pauli matrices in global manners. In another view, the dynamical feature of the excitation behave differently in the parameter regions with topological gapless edge modes and not. And the cusps of dynamical return rate vanish as the parameter pass the topological phase boundary slowly enough. It is found that the dynamics in the parameter region with gapless edge modes behaves differently to that without edge modes and related mostly to the eigenenergy gap between the pre‐and post‐quench eigenstates. The cusps of the dynamical return rate behave robustly against the noise occurs during evolution in the lattice until localization behavior dominates. This work benefits detecting topological edge modes by dynamical manners.

Stability of the smectic phase in arrays of parallel quantum wires

Using bosonization, we study a microscopic 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 wavefunctions $\ell$ 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 taken into account. Perturbative studies on phenomenological models have shown that the smectic fixed point is unstable towards a variety of phases such as superconductivity, stripe, smectic and Fermi liquid phases. Here, we show that the considered microscopic 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 $\ell\to0$. For finite $\ell$, we find a critical Coulomb coupling $\alpha_{c}$ 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 microscopic models. Finally, we discuss the physical realization of this model with moire heterostructures.

Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions

We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent \alphaα. Using large scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken N'eel phase. We find evidence that the transition is second order. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons – bound states of spinons across the legs. We obtain the momentum resolved spin dynamic structure factor numerically and find a well defined triplon band that evolves into a gapless magnon dispersion across the transition. We further discuss the possibility of deconfined criticality in this model.

Skyrmion lattice hosted in synthetic antiferromagnets and helix modes

Thin ferromagnetic films can possess unconventional magnetic properties, opening a new road for using them in spintronic technologies. In the present work exploiting three different methods, we comprehensively analyze phason excitations of a skyrmion lattice in synthetic antiferromagnets. To analyze phason excitations of the skyrmion lattice, we have constructed an analytical model based on three coupled helices and found a linear gapless mode. Micromagnetic simulations also support this result. Moreover, a similar result has been achieved within the rigid skyrmion lattice model based on the coupled Thiele's equations, when the coupling between skyrmions in different layers of the synthetic antiferromagnetic is comparable to or larger than the intralayer coupling. In addition, we also consider the orbital angular momentum and spin pumping current associated with phason excitations. Due to the gapless excitations in the case of skyrmion lattice, the pumping current is nonzero for the arbitrary frequency of pumping microwaves. In the case of individual skyrmions, no current is pumped when microwave frequency is inside the gap of the spectrum of individual skyrmions.