Lifshitz Scaling Research Articles

Multiferroic properties and local ferroelectricity of polycrystalline LuFeO3 thin films with triangular grains on glass substrates

Polycrystalline LuFeO3 (LFO) thin films were prepared on multilayer Pt/Ta/glass substrates. The ferroelectric hysteresis loop of the LFO thin film exhibited a remanent polarization of about 5.7 μC/cm2. The ferroelectric hysteresis loop of the LFO thin film deposited at a relatively slow rate provides valuable information about its recoverable energy density (8.8 J/cm3) and loss energy density (9.3 J/cm3), resulting in an estimated energy storage efficiency of around 49%. The LFO thin film had triangular grains with a diameter of approximately 90 nm, which well reflects the crystallinity of hexagonal LFO. From the local piezoelectric d33 hysteresis loops of a triangular grain, it was confirmed that the edge of a triangular grain had a remanent d33 value larger than the center of a triangular grain. Additionally, a mosaic domain structure of the LFO thin film was well correlated with the AFM image. By applying the Landau, Lifshitz, and Kittel (LLK) scaling law, it was confirmed that the LFO thin films have a domain wall energy lower than that of PbTiO3 thin films.

Holographic Lifshitz flows

Without Lorentz symmetry, generic fixed points of the renormalization group (RG) are labelled by their dynamical (or ‘Lifshitz’) exponent z. Hence, a rich variety of possible RG flows arises. The first example is already given by the standard non-relativistic limit, which can be viewed as the flow from a z = 1 UV fixed point to a z = 2 IR fixed point. In strongly coupled theories, there are good arguments suggesting that Lorentz invariance can emerge dynamically in the IR from a Lorentz violating UV. In this work, we perform a generic study of fixed points and the possible RG flows among them in a minimal bottom-up holographic model without Lorentz invariance, aiming to shed light on the possible options and the related phenomenology. We find: i) A minor generalization of previous models involving a massive vector field with allowed self-couplings leads to a much more efficient emergence of Lorentz invariance than in the previous attempts. Moreover, we find that generically the larger is the UV dynamical exponent zUV the faster is the recovery of Lorentz symmetry in the IR. ii) We construct explicitly a holographic model with a line of fixed points, realizing different Lifshitz scaling along the line. iii) We also confirm the monotonicity of a recently proposed a-function along all our Lorentz violating RG flows.

Massless Lifshitz field theory for arbitrary z

By using the notion of fractional derivatives, we introduce a class of massless Lifshitz scalar field theory in (1+1)-dimension with an arbitrary anisotropy index z. The Lifshitz scale invariant ground state of the theory is constructed explicitly and takes the form of Rokhsar-Kivelson (RK). We show that there is a continuous family of ground states with degeneracy parameterized by the choice of solution to the equation of motion of an auxiliary classical system. The quantum mechanical path integral establishes a 2d/1d correspondence with the equal time correlation functions of the Lifshitz scalar field theory. We study the entanglement properties of the Lifshitz theory for arbitrary z using the path integral representation. The entanglement measures are expressed in terms of certain cross ratio functions we specify, and satisfy the c-function monotonicity theorems. We also consider the holographic description of the Lifshitz theory. In order to match with the field theory result for the entanglement entropy, we propose a z-dependent radius scale for the Lifshitz background. This relation is consistent with the z-dependent scaling symmetry respected by the Lifshitz vacuum. Furthermore, the time-like entanglement entropy is determined using holography. Our result suggests that there should exist a fundamental definition of time-like entanglement other than employing analytic continuation as performed in relativistic field theory.

Finite-size versus finite-temperature effects in the critical long-range O(N) model

In this paper we consider classical and quantum versions of the critical long-range O(N) model, for which we study finite-size and finite-temperature effects, respectively, at large N. First, we consider the classical (isotropic) model, which is conformally invariant at criticality, and we introduce one compact spatial direction. We show that the finite size dynamically induces an effective mass and we compute the one-point functions for bilinear primary operators with arbitrary spin and twist. Second, we study the quantum model, mapped to a Euclidean anisotropic field theory, local in Euclidean time and long-range in space, which we dub fractional Lifshitz field theory. We show that this model admits a fixed point at zero temperature, where it displays anisotropic Lifshitz scaling, and show that at finite temperature a thermal mass is induced. We then compute the one-point functions for an infinite family of bilinear scaling operators.In both the classical and quantum model, we find that, as previously noted for the short-range O(N) model in [1], the large-N two-point function contains information about the one-point functions, not only of the bilinear operators, but also of operators that appear in the operator product expansion of two fundamental fields only at subleading order in 1/N, namely powers of the Hubbard-Stratonovich intermediate field.

Vortices in a rotating holographic superfluid with Lifshitz scaling

We have extended our previous work [1] on rotating holographic superfluids to include Lifshitz scaling. Presence of this scaling breaks relativistic invariance of the boundary superfluid system and indicates the existence of a Lifshitz fixed point [2]. We have analytically shown that we still get same vortex solutions as discovered earlier in [1]. We have recovered previous results for the case of z = 1, which restores the relativistic invariance in the holographic superfluid system. However, for z $\neq$ 1 this study indicate surprising results regarding dissipation in such a holographic superfluid. We found that higher winding number vortices increase with higher values of imaginary chemical potential for values of z in the open interval (1, 2). This result is remarkable because it asserts that dissipation in the rotating holographic superfluid increases in the presence of Lifshitz scaling.

More on entanglement properties of $$Lif_4^{(2)}\times {S}^1\times S^5$$ spacetime with string excitations

The $$Lif_{4}^{(2)} \times S^1 \times S^5$$ spacetime is an exact solution of $$F1-D2-D8$$ configuration in type IIA supergravity and can accommodate charged excitations of the fundamental string. By gauge/gravity duality, it is related to an excited state of a non-relativistic QFT with anisotropic Lifshitz scaling symmetry. We study mutual and tripartite information and entanglement wedge cross section in bulk gravity for boundary subsystems that are disjoint strips of very narrow width. Our work helps understand the nature of entanglement in the QFT excited state, which is in general a mixed one.

RG flows and symmetry enhancement in five-dimensional Lifshitz gauge theories

Lagrangian gauge theories with a z = 2 Lifshitz scaling provide a family of interacting, asymptotically free five-dimensional field theories. We examine a broad class of these theories, including some of their quantum properties, extending previous results to include matter. We present no-go theorems that, in the absence of constraints, the class of theories we consider cannot admit a spinorial supersymmetry or Galilean boost symmetry. However, we argue that there exist renormalization group flows whose fixed points can admit supersymmetry and boosts, i.e. super-Schrödinger symmetry. We also present examples of Lifshitz gauge theories with a scalar supersymmetry.

Quantum-critical electrodynamics of Luttinger fermions

We study the quantum electrodynamics of Luttinger fermions with quadratic band-crossing dispersion in three dimensions. The model can be viewed as the low-energy effective theory of a putative $U(1)$ quantum spin liquid with fermionic Luttinger spinons, or as an extension of the Luttinger-Abrikosov-Beneslavskii (LAB) model that accounts for transverse gauge fluctuations with finite photon velocity. Aided by a renormalization group analysis below four dimensions, we elucidate the presence and stability of quantum critical phenomena in this model. We find that the non-Fermi liquid LAB phase is stable against gauge fluctuations, and can thus also be viewed as a $U(1)$ spin liquid with gapless Luttinger spinons. We discover a multicritical point with Lifshitz scaling that corresponds to a time-reversal symmetry-breaking quantum phase transition from the LAB state to a chiral spin liquid with spinon Landau levels and birefringent emergent photons. This multicritical point is characterized by a finite fermion-photon coupling in the infrared and can be viewed as a fermionic analog of the Rokhsar-Kivelson point in three-dimensional quantum dimer models.

Enstrophy without boost symmetry

We construct an approximately conserved current for $2+1$ dimensional, Aristotelian (non boost invariant), fluid flow. When Aristotelian symmetry is enhanced to Galilean symmetry, this current matches the enstrophy current responsible for the inverse cascade in incompressible fluids. Other enhancements of Aristotelian symmetry discussed in this work include Lorentzian, Carrollian and Lifshitz scale symmetry.

Renormalization group in quantum critical theories with Harris-marginal disorder

We develop a renormalization group for weak Harris-marginal disorder in otherwise strongly interacting quantum critical theories, focusing on systems which have emergent conformal invariance. Using conformal perturbation theory, we argue that previously proposed random lines of fixed points with Lifshitz scaling in fact flow towards other universal fixed points, and this flow is captured by a "one-loop" analysis. Our approach appears best controlled in theories with only a few operators with low scaling dimension. In this regime, we compare our predictions for the flow of disorder to holographic models, and find complete agreement.

Entropic destruction of heavy quarkonium with hyperscaling violation * *Supported by the Innovation Fund of Key Laboratory of Quark and Lepton Physics (QLPL2020P01)

We study the entropic destruction of heavy quarkonium in strongly coupled theories with an anisotropic scaling symmetry in time and a spatial direction. We consider Lifshitz and hyperscaling violation theories, which are covariant under a generalized Lifshitz scaling symmetry with the dynamical exponent z and hyperscaling violation exponent . It is shown that the entropic force depends on the parameters of these theories. In particular, increasing z decreases the entropic force, thus reducing the quarkonium dissociation, while increasing has the opposite effect.

Entanglement entropy with Lifshitz fermions

We investigate fermions with Lifshitz scaling symmetry and study their entanglement entropy in 1+1 dimensions as a function of the scaling exponent z. Remarkably, in the ground state the entanglement entropy vanishes for even values of z, whereas for odd values it is independent of z and equal to the relativistic case with z=1. We show this using the correlation method on the lattice, and also using a holographic cMERA approach. The entanglement entropy in a thermal state is a more detailed function of z and T which we plot using the lattice correlation method. The dependence on the even- or oddness of z still shows for small temperatures, but is washed out for large temperatures or large values of z.

Effects of the hyperscaling violation and dynamical exponents on the imaginary potential and entropic force of heavy quarkonium via holography

The imaginary potential and entropic force are two important different mechanisms to characterize the dissociation of heavy quarkonia. In this paper, we calculate these two quantities in strongly coupled theories with anisotropic Lifshitz scaling and hyperscaling violation exponent using holographic methods. We study how the results are affected by the hyperscaling violation parameter theta and the dynamical exponent z at finite temperature and chemical potential. Also, we investigate the effect of the chemical potential on these quantities. As a result, we find that both mechanisms show the same results: the thermal width and the dissociation length decrease as the dynamical exponent and chemical potential increase or as the hyperscaling violating parameter decreases.

Lifshitz hydrodynamics at generic z from a moving black brane

A Lifshitz black brane at generic dynamical critical exponent z > 1, with non-zero linear momentum along the boundary, provides a holographic dual description of a non-equilibrium steady state in a quantum critical fluid, with Lifshitz scale invariance but without boost symmetry. We consider moving Lifshitz branes in Einstein-Maxwell-Dilaton gravity and obtain the non-relativistic stress tensor complex of the dual field theory via a suitable holographic renormalisation procedure. The resulting black brane hydrodynamics and thermodynamics are a concrete holographic realization of a Lifshitz perfect fluid with a generic dynamical critical exponent.

On the Rényi entropy of Lifshitz and hyperscaling violating black holes

We study Rényi entropies for geometries with Lifshitz scaling and hyperscaling violation. We calculate them for specific values of the Lifshitz parameter, and analyze the dual spectrum of the ground state. In the large d − θ limit they show that the ground state is unique in specific parameter ranges. We also calculate the Rényi entropies perturbatively around n = 1, and derive constraints using the Rényi entropy inequalities, which correspond to the thermodynamic stability of the black holes.

Bose-Einstein condensation in Hořava-Lifshitz theory

In this paper we study the corrections emergent from a Hořava-Lifshitz extension of the complex scalar sector to the Bose-Einstein condensation and to the thermodynamics parameters. We initially discussed some features of the model to only then compute the corrections to the Bose-Einstein condensation. The calculations were done by computing the generating functional, from which we extract the thermodynamics parameters. We also obtained the Lifshitz scaling correction for the critical temperature T c that sets the Bose-Einstein condensation.

New holographic Weyl superconductors in Lifshitz gravity

We build holographic p-wave conductor(insulator)/superconductor models via the numerical method with a new form of Weyl coupling in five-dimensional Lifshitz gravity, and then investigate how the Weyl coupling parameter γ and the Lifshitz scaling parameter z affect the superconductor models. In the conductor/superconductor model, an increase in the Weyl correction (Lifshitz scaling) enhances (inhibits) the superconductor phase transition. Meanwhile, both the Weyl correction (when the Lifshitz parameter is large enough and fixed) and the Lifshitz scaling suppress the growth of the real part of the conductivity. The Weyl correction used here (CB 2) shows weaker effects on the critical value than the previous Weyl correction (CF 2). In the insulator/superconductor model, larger vaules of the Weyl parameter hinder the formation of condensate. However, in increase in the Lifshitz scaling enhances the appearance of condensate. In addition, the calculation suggests that a competitive relation may exist between the Weyl correction and the Lifshitz scaling.

Lifshitz scaling in CPT-even Lorentz-violating electrodynamics and GRB time delay

In this work, we consider the Ho\v{r}ava-Lifshitz scaling to rewrite higher-order derivatives in Lorentz-violating CPT-even electrodynamics. The possibility of the Lorentz invariance violation being originally suppressed by the quantum gravity energy scale $M_{\rm QG}$, may be indeed circumvented in a scenario with anisotropy between space and time above certain intermediate energy scale $\Lambda_{\rm HL} \ll M_{\rm QG}$. To test the model, we have used observational results of a cosmological time delay between high and low energy photons from gamma ray bursts (GRB090510) event. For specific values of the Lifshitz critical exponent, we have found interesting lower bounds on the values of $M_{\rm QG}$.

Lifshitz scaling effects on the holographic p-wave superconductors coupled to nonlinear electrodynamics

We employ gauge/gravity duality to study the effects of Lifshitz scaling on the holographic p-wave superconductors in the presence of Born–Infeld nonlinear electrodynamics. By using the shooting method in the probe limit, we calculate the relation between critical temperature T_mathrm{{c}} and rho ^{z/d} numerically for different values of mass, nonlinear parameter b and Lifshitz critical exponent z in various dimensions. We observe that critical temperature decreases by increasing b, z or the mass parameter m which makes conductor/superconductor phase transition harder to form. In addition, we analyze the electrical conductivity and find the behavior of the real and the imaginary parts as a function of frequency, which depend on the model parameters. However, some universal behaviors are seen. For instance at low frequencies, the real part of conductivity shows a delta function behavior, while the imaginary part has a pole, which means that these two parts are connected to each other through the Kramers–Kronig relation. The behavior of the real part of the conductivity in the large frequency regime can be achieved by mathrm{{Re}}[sigma ]=omega ^{D-4}. Furthermore, with increasing the Lifshitz scaling z, the energy gap and the minimum values of the real and imaginary parts become unclear.

Diffusive process under Lifshitz scaling and pandemic scenarios

We here propose to model active and cumulative cases data from COVID-19 by a continuous effective model based on a modified diffusion equation under Lifshitz scaling with a dynamic diffusion coefficient. The proposed model is rich enough to capture different aspects of a complex virus diffusion as humanity has been recently facing. The model being continuous it is bound to be solved analytically and/or numerically. So, we investigate two possible models where the diffusion coefficient associated with possible types of contamination are captured by some specific profiles. The active cases curves here derived were able to successfully describe the pandemic behavior of Germany and Spain. Moreover, we also predict some scenarios for the evolution of COVID-19 in Brazil. Furthermore, we depicted the cumulative cases curves of COVID-19, reproducing the spreading of the pandemic between the cities of São Paulo and São José dos Campos, Brazil. The scenarios also unveil how the lockdown measures can flatten the contamination curves. We can find the best profile of the diffusion coefficient that better fit the real data of pandemic.