Massless Excitations Research Articles

Vortex-strings in mathcal{N}=2 SQCD and bulk-string decoupling

We study vortex-strings in four-dimensional mathcal{N}=2 supersymmetric SU(Nc) × U(1) gauge theories with Nf hypermultiplets in the fundamental representation of SU(Nc) and general U(1) charges. If Nf> Nc, the vacuum is not gapped and the low-energy theory contains both the vacuum massless excitations and the string zero-modes. The question we address in this work is whether the vacuum and the string moduli decouple at low energies, allowing a description of the low-energy dynamics in terms of a two-dimensional theory on the string worldsheet. We find a simple condition controlling the bulk-string coupling: if there exist two flavors such that the product of their U(1) charge difference with the magnetic flux carried by the string configuration is not an integer multiple of 2π, the string has zero-modes that decay slower than 1/r, where r is the radial distance from the string core. These modes are coupled to the vacuum massless excitations even at low energies. If, however, all such products are integer multiples of 2π, long-range modes of this type do not exist and the string moduli decouple from the bulk at low energies. This condition turns out to coincide with the condition of trivial Aharonov-Bohm phases for the particles in the spectrum. In addition to a derivation of the bulk-string decoupling criterion using classical analysis of the string zero-modes, we provide a non-perturbative derivation of the criterion, which uses supersymmetric localization techniques.

Weyl fermions in cylindrical wires

The key feature of Weyl semimetals (WSM) is the presence of topologically protected Dirac cones in a 3D material. We consider the effect of restricting geometry on the spectrum of excitations in WSM using as a model a cylindrical WSM wire. For the full manifold of hard boundary conditions, we derive the general form of the dispersion equation relating the energy of the excitations and their momentum along the wire. We show that only the special class of boundary conditions, corresponding to decoupled helicities or, equivalently, to pinned directions of the electron spin on the surface, support massless excitations. For a general boundary condition, these excitations acquire mass inversely proportional to the radius of the wire. This demonstrates that boundary phenomena may play a crucial role in formation of excitations in WSM based structures.

Entropy in Born-Infeld gravity

There is a class of higher derivative gravity theories that are in some sense natural extensions of cosmological Einstein's gravity with a unique maximally symmetric classical vacuum and only a massless spin-2 excitation about the vacuum and no other perturbative modes. These theories are of the Born-Infeld determinantal form. We show that the macroscopic dynamical entropy as defined by Wald for bifurcate Killing horizons in these theories are equivalent to the geometric Bekenstein-Hawking entropy (or more properly Gibbons-Hawking entropy for the case of de Sitter spacetime) but given with an effective gravitational constant which encodes all the information about the background spacetime and the underlying theory. We also show that the higher curvature terms increase the entropy. We carry out the computations in generic n-dimensions including the particularly interesting limits of three, four and infinite number of dimensions. We also give a preliminary discussion about the black hole entropy in generic dimensions for the BI theories.

Multiple Types of Topological Fermions in Transition Metal Silicides.

Exotic massless fermionic excitations with nonzero Berry flux, other than the Dirac and Weyl fermions, could exist in condensed matter systems under the protection of crystalline symmetries, such as spin-1 excitations with threefold degeneracy and spin-3/2 Rarita-Schwinger-Weyl fermions. Herein, by using the abinitio density functional theory, we show that these unconventional quasiparticles coexist with type-I and type-II Weyl fermions in a family of transition metal silicides, including CoSi, RhSi, RhGe, and CoGe, when spin-orbit coupling is considered. Their nontrivial topology results in a series of extensive Fermi arcs connecting projections of these bulk excitations on the side surface, which is confirmed by (001) surface electronic spectra of CoSi. In addition, these stable arc states exist within a wide energy window around the Fermi level, which makes them readily accessible in angle-resolved photoemission spectroscopy measurements.

Massless AdS2 scattering and Bethe ansatz

We first analyse the integrable scattering theory describing the massless excitations of AdS2 × S2 × T6 superstrings in the relativistic limit. The matrix part of the S-matrix is obtained in the BMN limit from the conjectured exact expression, and compared to known S-matrices with mathcal{N}=1 supersymmetry in 1 + 1 dimensions. A dressing factor, yet unknown for the complete theory, is here constructed based on relativistic crossing symmetry. We derive a Bethe-ansatz condition by employing a transfer-matrix technique based on the so-called free-fermion condition. This is known to overcome the problem of lack of a reference state. We then generalise the method to the massless non-relativistic case, and compare the resulting Bethe-ansatz condition with a simple massless limit of the one conjectured by Sorokin, Tseytlin, Wulff and Zarembo.

The Nielsen–Ninomiya theorem, -invariant non-Hermiticity and single 8-shaped Dirac cone

The Nielsen–Ninomiya theorem implies that any local, Hermitian and translationally invariant lattice action in even-dimensional spacetime possesses an equal number of left- and right-handed chiral fermions. We argue that if one sacrifices the property of Hermiticity while keeping the locality and translation invariance, and imposing invariance of the action under the space-time () reversal symmetry, then the excitation spectrum of the theory may contain a non-equal number of left- and right-handed massless fermions with real-valued dispersion. We illustrate our statement in a simple 1 + 1 dimensional lattice model which exhibits a skewed 8-figure pattern in its energy spectrum. A drawback of the model is that the symmetry of the Hamiltonian is spontaneously broken implying that the energy spectrum contains complex branches. We also demonstrate that the Dirac cone is robust against local disorder so that the massless excitations in this invariant model are not gapped by random space-dependent perturbations in the couplings.

Emergent gravity of fractons: Mach’s principle revisited

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 arises from the principles of locality and conservation of center of mass. This interaction between fractons is always attractive and can be recast in geometric language, with a geodesic-like formulation, thereby satisfying the expected properties of a gravitational force. This force will generically be short-ranged, but we discuss how the power-law behavior of Newtonian gravity can arise under certain conditions. We then show that, while an isolated fracton is immobile, fractons are endowed with finite inertia by the presence of a large-scale distribution of other fractons, in a concrete manifestation of Mach's principle. Our formalism provides suggestive hints that matter plays a fundamental role, not only in perturbing, but in creating the background space in which it propagates.

Local particle-hole pair excitations by SU(2) symmetry fluctuations

Understanding the pseudo-gap phase which opens in the under-doped regime of cuprate superconductors is one of the most enduring challenges of the physics of these compounds. A depletion in the electronic density of states is observed, which is gapping out part of the Fermi surface, leading to the formation of mysterious lines of massless excitations- the Fermi arcs. Here we give a new theoretical account of the physics of the pseudo-gap phase in terms of the emergence of local patches of particle-hole pairs generated by SU(2) symmetry fluctuations. The proliferation of these local patches accounts naturally for the robustness of the pseudo-gap phase to disturbances like disorder or magnetic field and is shown to gap out part of the Fermi surface, leading to the formation of the Fermi arcs. Most noticeably, we show that these patches induce a modulated charge distribution on the Oxygen atoms, in remarkable agreement with recent X-ray and STM observations.

Topological Quantum Phase Transition and Local Topological Order in a Strongly Interacting Light-Matter System

An attempt is made to understand the topological quantum phase transition, emergence of relativistic modes and local topological order of light in a strongly interacting light-matter system. We study this system, in a one dimensional array of nonlinear cavities. Topological quantum phase transition occurs with massless excitation only for the finite detuning process. We present a few results based on the exact analytical calculations along with the physical explanations. We observe the emergence of massive Majorana fermion mode at the topological state, massless Majorana-Weyl fermion mode during the topological quantum phase transition and Dirac fermion mode for the non-topological state. Finally, we study the quantized Berry phase (topological order) and its connection to the topological number (winding number).

Three-dimensional topological insulators and bosonization

Massless excitations at the surface of three-dimensional time-reversal invariant topological insulators possess both fermionic and bosonic descriptions, originating from band theory and hydrodynamic BF theory, respectively. We analyze the corresponding field theories of the Dirac fermion and compactified boson and compute their partition functions on the three-dimensional torus geometry. We then find some non-dynamic exact properties of bosonization in (2+1) dimensions, regarding fermion parity and spin sectors. Using these results, we extend the Fu-Kane-Mele stability argument to fractional topological insulators in three dimensions.

Schwinger mechanism in linear covariant gauges

In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully-dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modelled by means of certain physically motivated Ans\"atze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ans\"atze are compatible with the existence of nontrivial solutions. When such Ans\"atze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic "zero crossing", while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed.

Coexistence of topological Dirac fermions on the surface and three-dimensional Dirac cone state in the bulk of ZrTe5 single crystal

Although, the long-standing debate on the resistivity anomaly in ZrTe5 somewhat comes to an end, the exact topological nature of the electronic band structure remains elusive till today. Theoretical calculations predicted that bulk ZrTe5 to be either a weak or a strong three-dimensional (3D) topological insulator. However, the angle resolved photoemission spectroscopy and transport measurements clearly demonstrate 3D Dirac cone state with a small mass gap between the valence band and conduction band in the bulk. From the magnetization and magneto-transport measurements on ZrTe5 single crystal, we have detected both the signature of helical spin texture from topological surface state and chiral anomaly associated with the 3D Dirac cone state in the bulk. This implies that ZrTe5 hosts a novel electronic phase of material, having massless Dirac fermionic excitation in its bulk gap state, unlike earlier reported 3D topological insulators. Apart from the band topology, it is also apparent from the resistivity and Hall measurements that the anomalous peak in the resistivity can be shifted to a much lower temperature (T < 2 K) by controlling impurity and defects.

Charges and Electromagnetic Radiation as Topological Excitations

We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number.

Exact results for the behavior of the thermodynamic Casimir force in a model with a strong adsorption

When massless excitations are limited or modified by the presence of material bodies one observes a force acting between them generally called Casimir force. Such excitations are present in any fluid system close to its true bulk critical point. We derive exact analytical results for both the temperature and external ordering field behavior of the thermodynamic Casimir force within the mean-field Ginzburg–Landau Ising type model of a simple fluid or binary liquid mixture. We investigate the case when under a film geometry the boundaries of the system exhibit strong adsorption onto one of the phases (components) of the system. We present analytical and numerical results for the (temperature-field) relief map of the force in both the critical region of the film close to its finite-size or bulk critical points as well as in the capillary condensation regime below but close to the finite-size critical point.

Competing Orders and Anomalies.

A conservation law is one of the most fundamental properties in nature, but a certain class of conservation “laws” could be spoiled by intrinsic quantum mechanical effects, so-called quantum anomalies. Profound properties of the anomalies have deepened our understanding in quantum many body systems. Here, we investigate quantum anomaly effects in quantum phase transitions between competing orders and striking consequences of their presence. We explicitly calculate topological nature of anomalies of non-linear sigma models (NLSMs) with the Wess-Zumino-Witten (WZW) terms. The non-perturbative nature is directly related with the ’t Hooft anomaly matching condition: anomalies are conserved in renormalization group flow. By applying the matching condition, we show massless excitations are enforced by the anomalies in a whole phase diagram in sharp contrast to the case of the Landau-Ginzburg-Wilson theory which only has massive excitations in symmetric phases. Furthermore, we find non-perturbative criteria to characterize quantum phase transitions between competing orders. For example, in 4D, we show the two competing order parameter theories, CP(1) and the NLSM with WZW, describe different universality class. Physical realizations and experimental implication of the anomalies are also discussed.

A statistical representation of the cosmological constant from finite size effects at the apparent horizon

In this paper we present a statistical description of the cosmological constant in terms of massless bosons (gravitons). To this purpose, we use our recent results implying a non vanishing temperature ${T_{\Lambda}}$ for the cosmological constant. In particular, we found that a non vanishing $T_{\Lambda}$ allows us to depict the cosmological constant $\Lambda$ as composed of elementary oscillations of massless bosons of energy $\hbar\omega$ by means of the Bose-Einstein distribution. In this context, as happens for photons in a medium, the effective phase velocity $v_g$ of these massless excitations is not given by the speed of light $c$ but it is suppressed by a factor depending on the number of quanta present in the universe at the apparent horizon. We found interesting formulas relating the cosmological constant, the number of quanta $N$ and the mean value $\overline{\lambda}$ of the wavelength of the gravitons. In this context, we study the possibility to look to the gravitons system so obtained as being very near to be a Bose-Einstein condensate. Finally, an attempt is done to write down the Friedmann flat equations in terms of $N$ and $\overline{\lambda}$.

Dual field theories of quantum computation

Given two quantum states of N q-bits we are interested to find the shortest quantum circuit consisting of only one- and two- q-bit gates that would transfer one state into another. We call it the quantum maze problem for the reasons described in the paper. We argue that in a large N limit the quantum maze problem is equivalent to the problem of finding a semiclassical trajectory of some lattice field theory (the dual theory) on an N+1 dimensional space-time with geometrically flat, but topologically compact spatial slices. The spatial fundamental domain is an N dimensional hyper-rhombohedron, and the temporal direction describes transitions from an arbitrary initial state to an arbitrary target state. We first consider a complex Klein-Gordon field theory and argue that it can only be used to study the shortest quantum circuits which do not involve generators composed of tensor products of multiple Pauli Z matrices. Since such situation is not generic we call it the Z-problem. On the dual field theory side the Z-problem corresponds to massless excitations of the phase (Goldstone modes) that we attempt to fix using Higgs mechanism. The simplest dual theory which does not suffer from the massless excitation (or from the Z-problem) is the Abelian-Higgs model which we argue can be used for finding the shortest quantum circuits. Since every trajectory of the field theory is mapped directly to a quantum circuit, the shortest quantum circuits are identified with semiclassical trajectories. We also discuss the complexity of an actual algorithm that uses a dual theory prospective for solving the quantum maze problem and compare it with a geometric approach. We argue that it might be possible to solve the problem in sub-exponential time in 2^N, but for that we must consider the Klein-Gordon theory on curved spatial geometry and/or more complicated (than N-torus) topology.

Higher rank antisymmetric tensor fields in Klebanov-Strassler geometry

In string theory, higher rank antisymmetric tensor fields appear as massless excitations of closed strings. Till date there is no experimental support in favour of their existence. In a stringy framework, starting from a warped throat-like Klebanov-Strassler geometry, we show that all the massless higher rank antisymmetric tensor fields are heavily suppressed due to the background fluxes leading to their invisibility in our Universe.

Dirac electrons in the presence of a matrix potential barrier: application to graphene and topological insulators

Scattering of 2D Dirac electrons on a rectangular matrix potential barrier is considered using the formalism of spinor transfer matrices. It is shown, in particular, that in the absence of the mass term, the Klein tunneling is not necessarily suppressed but occurs at oblique incidence. The formalism is applied to studying waveguiding modes of the barrier, which are supported by the edge and bulk states. The condition of the existence of the uni-directionality property is found. We show that the band of edge states is always finite with massless excitations, while the spectrum of the bulk states, depending on the parameters of the barrier, may consist of the infinite or finite band with both, massive and massless, low-energy excitations. The effect of the Zeeman term is considered and the condition of the appearance of two distinct energy-dependent directions corresponding to the Klein tunneling is found.

Exploring dynamical gluon mass generation in three dimensions

In the d=3 gluon mass problem in pure-glue non-Abelian $SU(N)$ gauge theory we pay particular attention to the observed (in Landau gauge) violation of positivity for the spectral function of the gluon propagator. This causes a large bulge in the propagator at small momentum. Mass is defined through $m^{-2}=\Delta (p=0)$, where $\Delta(p)$ is the scalar function for the gluon propagator in some chosen gauge, it is not a pole mass and is generally gauge-dependent, except in the gauge-invariant Pinch Technique (PT). We truncate the PT equations with a new method called the vertex paradigm that automatically satisfies the QED-like Ward identity relating the 3-gluon PT vertex function with the PT propagator. The mass is determined by a homogeneous Bethe-Salpeter equation involving this vertex and propagator. This gap equation also encapsulates the Bethe-Salpeter equation for the massless scalar excitations, essentially Nambu-Goldstone fields, that necessarily accompany gauge-invariant gluon mass. The problem is to find a good approximate value for $m$ and at the same time explain the bulge, which by itself leads, in the gap equation for the gluon mass, to excessively large values for the mass. Our point is not to give a high-accuracy determination of $m$ but to clarify the way in which the propagator bulge and a fairly accurate estimate of $m$ can co-exist, and we use various approximations that illustrate the underlying mechanisms. The most critical point is to satisfy the Ward identity. In the PT we estimate a gauge-invariant dynamical gluon mass of $m \approx Ng^2/(2.48 \pi)$. We translate these results to the Landau gauge using a background-quantum identity involving a dynamical quantity $\kappa$ such that $m=\kappa m_L$, where $m_L^{-2}\equiv \Delta_L(p=0)$. Given our estimates for $m,\kappa$ the relation is fortuitously well-satisfied for $SU(2)$ lattice data.