arXiv subjects

Igor F. Herbut

Publications and source records attributed to Igor F. Herbut.

At least 37 records · Page 2Linked to original sources

arXiv2021

Bogoliubov-Fermi surface with inversion symmetry and electron-electron interactions: relativistic analogies and lattice theory

We show that the general low-energy Bogoliubov-de Genness Hamiltonian in a multiband superconductor with broken time reversal and preserved inversion symmetry is a generator of real four-dimensional representation of $SO(4)$. In the particular representation such an effective Hamiltonian is a purely imaginary matrix, and it is proportional to the antisymmetric tensor of a fictitious electromagnetic field which one can define in the momentum space. The quantum time evolution of the low-energy quasiparticle state becomes this way closely related to the classical relativistic motion of a charged particle in the presence of the Lorentz force that would be derived from such an electromagnetic field configuration. The condition for the emergence of a Bogoliubov-Fermi surface can then be understood as orthogonality of the fictitious electric and magnetic fields, which would allow zero Lorentz force. The corresponding zero-energy eigenstates are identified as the physical timelike and the unphysical spacelike solutions of the Lorentz force equation. We study the looming instability of the inversion-symmetric Bogoliubov-Fermi surface in presence of electron-electron interaction by formulating a concrete interacting model on the Lieb lattice that features the requisite $SO(4)$ kinetic energy term together with nearest-neighbor two-body repulsion. The latter is shown to favor dynamical breaking of the inversion symmetry. The inversion symmetry in our lattice model indeed becomes spontaneously broken at zero temperature at infinitesimal repulsion, with the original Bogoliubov-Fermi surface deformed and reduced in size. General features of this symmetry breaking phenomenon are discussed and a comparison with other works in literature is presented.

cond-mat.supr-con↗

arXiv2020

Bogoliubov-Fermi Surfaces in Noncentrosymmetric Multicomponent Superconductors

We show that when the time reversal symmetry is broken in a multicomponent superconducting condensate without inversion symmetry the resulting Bogoliubov quasiparticles generically exhibit mini-Bogoliubov-Fermi (BF) surfaces, for small superconducting order parameter. The absence of inversion symmetry makes the BF surfaces stable with respect to weak perturbations. With sufficient increase of the order parameter, however, the Bogoliubov-Fermi surface may disappear through a Lifshitz transition, and the spectrum this way become fully gapped. Our demonstration is based on the computation of the effective Hamiltonian for the bands near the normal Fermi surface by the integration over high-energy states. Exceptions to the rule, and experimental consequences are briefly discussed.

cond-mat.supr-con↗

arXiv2020

Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach

Electrons on the half-filled honeycomb lattice are expected to undergo a direct continuous transition from the semimetallic into the antiferromagnetic insulating phase with increase of on-site Hubbard repulsion. We attempt to further quantify the critical behavior at this quantum phase transition by means of functional renormalization group (RG), within an effective Gross-Neveu-Yukawa theory for an SO(3) order parameter ("chiral Heisenberg universality class"). Our calculation yields an estimate of the critical exponents $ν\simeq 1.31$, $η_ϕ\simeq 1.01$, and $η_Ψ\simeq 0.08$, in reasonable agreement with the second-order expansion around the upper critical dimension. To test the validity of the present method we use the conventional Gross-Neveu-Yukawa theory with Z(2) order parameter ("chiral Ising universality class") as a benchmark system. We explicitly show that our functional RG approximation in the sharp-cutoff scheme becomes one-loop exact both near the upper as well as the lower critical dimension. Directly in 2+1 dimensions, our chiral-Ising results agree with the best available predictions from other methods within the single-digit percent range for $ν$ and $η_ϕ$ and the double-digit percent range for $η_Ψ$. While one would expect a similar performance of our approximation in the chiral Heisenberg universality class, discrepancies with the results of other calculations here are more significant. Discussion and summary of various approaches is presented.

cond-mat.str-el↗

arXiv2020

d-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals

We uncover the properties of complex tensor (d-wave) superconducting order in three-dimensional Rarita-Schwinger-Weyl semimetals that host pseudospin-3/2 fermions at a fourfold linear band crossing point. Although the general theory of d-wave order was originally developed for materials displaying quadratic band touching, it directly applies to the case of semimetals with linear dispersion, several candidate compounds of which have been discovered experimentally very recently. The spin-3/2 nature of the fermions allows for the formation of spin-2 Cooper pairs which may be described by a complex second-rank tensor order parameter. In the case of linear dispersion, for the chemical potential at the Fermi point and at strong coupling, the energetically preferred superconducting state is the uniaxial nematic state, which preserves time-reversal symmetry and provides a full (anisotropic) gap for quasiparticle excitations. In contrast, at a finite chemical potential, we find that the usual weak-coupling instability is towards the "cyclic state", well known from the studies of multicomponent Bose-Einstein condensates, which breaks time reversal symmetry maximally, has vanishing average value of angular momentum, and features 16 small Bogoliubov--Fermi surfaces. The Rarita-Schwinger-Weyl semimetals provide therefore the first example of weakly coupled, three-dimensional, isotropic d-wave superconductors where the ground state is uniquely determined by the quartic expansion of the mean-field free energy, and not afflicted by the accidental degeneracy first noticed by Mermin over 40 years ago. We discuss the appearance and stability of the Bogoliubov-Fermi surfaces in absence of inversion symmetry in the electronic Hamiltonian, as in the case at hand.

cond-mat.supr-con↗

arXiv2020

Hydrodynamic transport in the Luttinger-Abrikosov-Beneslavskii non-Fermi liquid

We determine the shear viscosity and the dc electrical conductivity of interacting three-dimensional Luttinger semimetals, which have a quadratic band touching point in the energy spectrum, in the hydrodynamic regime. It is well-known that when the chemical potential is right at the band touching point the long-range Coulomb interaction induces the Luttinger-Abrikosov-Beneslavskii (LAB) phase at T = 0, which is an interacting, scale-invariant, non-Fermi-liquid state of electrons. Upon combining the renormalization-group (RG) analysis near the upper critical spatial dimension of four with the Boltzmann kinetic equation, we determine the universal ratio of viscosity over entropy, and the electrical dc conductivity of the system at the interacting LAB fixed point of the RG flow. The projection of the Coulomb interaction on the eigenstates of the system is found to play an important quantitative role for the scattering amplitude in the collision integral, and the so-called Auger-processes make a large numerical contribution to the inverse scattering time in the transport quantities. The obtained leading order result suggests that the universal ratio of the viscosity over entropy, when extrapolated to the physical three spatial dimensions, is above, but could be rather close to, the Kovtun-Son-Starinets lower bound.

cond-mat.str-el↗

arXiv2019

Hidden role of antiunitary operators in Fierz transformation

We show that whenever the symmetry group of a field theory commutes with one or more antiunitary operators $T$, which do not have to but may represent the reversal of physical time, the number of linearly independent contact two-body (quartic) terms is determined by the number of tensors that are even, or by the number of tensors that are odd, under such $T$. The choice depends on the sign of $T^2$ and on the statistics of the fields. The theorem enables one to circumvent the usual computation of the Fierz matrix in determining the independent interaction terms. Some physical examples of current interest in many-body physics are discussed.

hep-th↗

arXiv2019

Ground state of the three-dimensional BCS d-wave superconductor

We determine the mean-field ground state of the three-dimensional rotationally symmetric d-wave ($\ell=2$) superconductor at weak coupling. It is a non-inert state, invariant under the symmetry $C_{2}$ only, which breaks time reversal symmetry almost maximally, and features a high, but again less than maximal average magnetization. The state obtained by minimization of the expanded sixth-order Ginzburg--Landau free energy is found to be an excellent approximation to the true ground state. The coupling to a parasitic s-wave component has only a minuscule quantitative and no qualitative effect on the ground state.

cond-mat.supr-con↗

arXiv2019

Abelian Higgs model at four loops, fixed-point collision and deconfined criticality

The abelian Higgs model is the textbook example for the superconducting transition and the Anderson-Higgs mechanism, and has become pivotal in the description of deconfined quantum criticality. We study the abelian Higgs model with $n$ complex scalar fields at unprecedented four-loop order in the $4-ε$ expansion and find that the annihilation of the critical and bicritical points occurs at a critical number of $n_c \approx 182.95\left(1 - 1.752ε+ 0.798 ε^2 + 0.362ε^3\right) + \mathcal{O}\left(ε^4\right)\nonumber$. Consequently, below $n_c$, the transition turns from second to first order. Resummation of the series to extract the result in three-dimensions provides strong evidence for a critical $n_c(d=3)$ which is significantly below the leading-order value, but the estimates for $n_c$ are widely spread. Conjecturing the topology of the renormalization group flow between two and four dimensions, we obtain a smooth interpolation function for $n_c(d)$ and find $n_c(3)\approx 12.2\pm 3.9$ as our best estimate in three dimensions. Finally, we discuss Miransky scaling occurring below $n_c$ and comment on implications for weakly first-order behavior of deconfined quantum transitions. We predict an emergent hierarchy of length scales between deconfined quantum transitions corresponding to different $n$.

cond-mat.str-el↗

arXiv2019

Electronic Ground State in Bilayer Graphene with Realistic Coulomb Interactions

Both insulating and conducting electronic behaviors have been experimentally seen in clean bilayer graphene samples at low temperature, and there is still no consensus on the nature of the interacting ground state at half-filling and in the absence of a magnetic field. Theoretically, several possibilities for the insulating ground states have been predicted for weak interaction strength. However, a recent renormalization-group calculation on a Hubbard model for charge-neutral bilayer graphene with short-range interactions suggests the emergence of low-energy Dirac fermions that would stabilize the metallic phase for weak interactions. Using a non-perturbative projective quantum Monte Carlo, we calculate the ground state for bilayer graphene using a realistic model for the Coulomb interaction that includes both short-range and long-range contributions. We find that a finite critical onsite interaction is needed to gap bilayer graphene, thereby confirming the Hubbard model expectations even in the presence of a long-range Coulomb potential, in agreement with our theoretical renormalization group analysis. In addition, we also find that the critical onsite interactions necessary to destabilize the metallic ground state decreases with increasing interlayer coupling.

cond-mat.str-el↗

arXiv2018

Tensor $O(N)$ model near six dimensions: fixed points and conformal windows from four loops

In search of non-trivial field theories in high dimensions, we study further the tensor representation of the $O(N)$-symmetric $ϕ^4$ field theory introduced by Herbut and Janssen (Phys. Rev. D. 93, 085005 (2016)), by using four-loop perturbation theory in two cubic interaction coupling constants near six dimensions. For infinitesimal values of the parameter $ε=(6-d)/2$ we find infrared-stable fixed point with two relevant quadratic operators for $N$ within the conformal windows $1<N<2.653$ and $2.999<N<4$, and compute critical exponents at this fixed point to the order $ε^4$. Taking the four-loop beta-functions at their face value we determine the higher-order corrections to the edges of the above conformal windows at finite $ε$, to find both intervals to shrink to zero above $ε\approx 0.15$. The disappearance of the conformal windows with the increase of $ε$ is due to the collision of the Wilson-Fisher $\mathcal{O}(ε)$ infrared fixed point with the $\mathcal{O}(1)$ mixed-stable fixed point that appears at two and persists at higher loops. The latter may be understood as a Banks-Zaks type fixed point that becomes weakly coupled near the right edge of either conformal window. The consequences and issues raised by such an evolution of the flow with dimension are discussed. It is also shown both within the perturbation theory and exactly that the tensor representation at $N=3$ and right at the $\mathcal{O}(ε)$ infrared-stable fixed point exhibits an emergent $U(3)$ symmetry. A role of this enlarged symmetry in possible protection of the infrared fixed point at $N=3$ is noted.

hep-th↗

arXiv2018

Critical $O(2)$ field theory near six dimensions beyond one loop

A tensorial representation of $ϕ^4$ field theory introduced in Phys. Rev. D. 93, 085005 (2016) is studied close to six dimensions, with an eye towards a possible realization of an interacting conformal field theory in five dimensions. We employ the two-loop $ε$-expansion, two-loop fixed-dimension renormalization group, and non-perturbative functional renormalization group. An interacting, real, infrared-stable fixed point is found near six dimensions, and the corresponding anomalous dimensions are computed to the second order in small parameter $ε=6-d$. Two-loop epsilon-expansion indicates, however, that the second-order corrections may destabilize the fixed point at some critical $ε_c <1$. A more detailed analysis within all three computational schemes suggests that the interacting, infrared-stable fixed point found previously collides with another fixed point and becomes complex when the dimension is lowered from six towards five. Such a result would conform to the expectation of triviality of $O(2)$ field theories above four dimensions.

hep-th↗

arXiv2018

Dirac cones and mass terms in bosonic spectra

The notion of Dirac cones, wherein two or more bands become degenerate at a certain momentum, is the starting point for the study of topological phases. Dirac cones have been thoroughly explored in fermionic systems such as graphene, Weyl semimetals, etc. The underlying mathematical structure in these systems is a Clifford algebra -- a rule for identifying sets of matrices that span the Hamiltonian. This structure allows for the identification of suitable `mass' terms to open band gaps. In this article, we extend these ideas to bosonic systems. Due to the pseudo-orthogonal nature of eigenvectors, the algebra of matrices takes a very different form. Taking the honeycomb XY ferromagnet as a prototype, we show that a Dirac cone emerges in the magnon spectrum. A gap can be opened by a suitable mass term involving next-nearest neighbour interactions. We next construct a one-dimensional ladder model with triplon excitations. Using the new Clifford algebra, we define winding number as a topological invariant. In analogy with the Su-Schrieffer-Heeger model, topological transitions occur when the band gap closes, leading to the appearance (or disappearance) of protected edge states. Our results suggest a new route to studying band touching and band topology in bosonic systems.

cond-mat.mes-hall↗

arXiv2018

Critical phenomena at the complex tensor ordering phase transition

We investigate the critical properties of the phase transition towards complex tensor order that has been proposed to occur in spin-orbit coupled superconductors. For this purpose we formulate the bosonic field theory for fluctuations of the complex irreducible second-rank tensor order parameter close to the transition. We then determine the scale dependence of the couplings of the theory by means of the perturbative Renormalization Group (RG). For the isotropic system we generically detect a fluctuation-induced first-order phase transition. The initial values for the running couplings are determined by the underlying microscopic model for the tensorial order. As an example we study three-dimensional Luttinger semimetals with electrons at a quadratic band touching point. Whereas the strong-coupling transition of the model receives substantial fluctuation corrections, the weak-coupling transition at low temperatures is rendered only weakly first-order due to the presence of a fixed point in the vicinity of the RG trajectory. If the number of fluctuating complex components of the order parameter is reduced by cubic anisotropy, the theory maps onto the field theory for frustrated magnetism.

cond-mat.str-el↗

arXiv2018

Unconventional Superconductivity in Luttinger Semimetals: Theory of Complex Tensor Order and the Emergence of the Uniaxial Nematic State

We investigate unconventional superconductivity in three-dimensional electronic systems with the chemical potential close to a quadratic band touching point in the band dispersion. Short-range interactions can lead to d-wave superconductivity, described by a complex tensor order parameter. We elucidate the general structure of the corresponding Ginzburg--Landau free energy and apply these concepts to the case of an isotropic band touching point. For vanishing chemical potential, the ground state of the system is given by the superconductor analogue of the uniaxial nematic state, which features line nodes in the excitation spectrum of quasiparticles. In contrast to the theory of real tensor order in liquid crystals, however, the ground state is selected here by the sextic terms in the free energy. At finite chemical potential, the nematic state has an additional instability at weak coupling and low temperatures. In particular, the one-loop coefficients in the free energy indicate that at weak coupling genuinely complex orders, which break time-reversal symmetry, are energetically favored. We relate our analysis to recent measurements in the half-Heusler compound YPtBi and discuss the role of the cubic crystal symmetry.

cond-mat.str-el↗

arXiv2018

Fermion-induced quantum criticality with two length scales in Dirac systems

The quantum phase transition to a $\mathbb{Z}_3$-ordered Kekulé valence bond solid in two-dimensional Dirac semimetals is governed by a fermion-induced quantum critical point, which renders the putatively discontinuous transition continuous. We study the resulting universal critical behavior in terms of a functional RG approach, which gives access to the scaling behavior on the symmetry-broken side of the phase transition, for general dimension and number of Dirac fermions. In particular, we investigate the emergence of the fermion-induced quantum critical point for space-time dimensions $2<d<4$. We determine the integrated RG flow from the Dirac semi-metal to the symmetry-broken regime and analyze the underlying fixed point structure. We show that the fermion-induced criticality leads to a scaling form with two divergent length scales, due to the breaking of the discrete $\mathbb{Z}_3$ symmetry. This provides another source of scaling corrections, besides the one stemming from being in the proximity to the first order transition.

cond-mat.str-el↗

arXiv2018

Compatible orders and fermion-induced emergent symmetry in Dirac systems

We study the quantum multicritical point in a (2+1)-dimensional Dirac system between the semimetallic phase and two ordered phases that are characterized by anticommuting mass terms with $O(N_1)$ and $O(N_2)$ symmetry, respectively. Using $ε$ expansion around the upper critical space-time dimension of four, we demonstrate the existence of a stable renormalization-group fixed point, enabling a direct and continuous transition between the two ordered phases directly at the multicritical point. This point is found to be characterized by an emergent $O(N_1+N_2)$ symmetry for arbitrary values of $N_1$ and $N_2$ and fermion flavor numbers $N_f$, as long as the corresponding representation of the Clifford algebra exists. Small $O(N)$-breaking perturbations near the chiral $O(N)$ fixed point are therefore irrelevant. This result can be traced back to the presence of gapless Dirac degrees of freedom at criticality, and it is in clear contrast to the purely bosonic $O(N)$ fixed point, which is stable only when $N < 3$. As a by-product, we obtain predictions for the critical behavior of the chiral $O(N)$ universality classes for arbitrary $N$ and fermion flavor number $N_f$. Implications for critical Weyl and Dirac systems in 3+1 dimensions are also briefly discussed.

cond-mat.str-el↗

arXiv2017

Fermion-induced quantum criticality in two-dimensional Dirac semimetals: Non-perturbative flow equations, fixed points and critical exponents

We establish a scenario where fluctuations of new degrees of freedom at a quantum phase transition change the nature of a transition beyond the standard Landau-Ginzburg paradigm. To this end we study the quantum phase transition of gapless Dirac fermions coupled to a $\mathbb{Z}_3$ symmetric order parameter within a Gross-Neveu-Yukawa model in 2+1 dimensions, appropriate for the Kekulé transition in honeycomb lattice materials. For this model the standard Landau-Ginzburg approach suggests a first order transition due to the symmetry-allowed cubic terms in the action. At zero temperature, however, quantum fluctuations of the massless Dirac fermions have to be included. We show that they reduce the putative first-order character of the transition and can even render it continuous, depending on the number of Dirac fermions $N_f$. A non-perturbative functional renormalization group approach is employed to investigate the phase transition for a wide range of fermion numbers. For the first time we obtain the critical $N_f$, where the nature of the transition changes. Furthermore, it is shown that for large $N_f$ the change from the first to second order of the transition as a function of dimension occurs exactly in the physical 2+1 dimensions. We compute the critical exponents and predict sizable corrections to scaling for $N_f =2$.

cond-mat.str-el↗

arXiv2017

Four-loop critical exponents for the Gross-Neveu-Yukawa models

We study the chiral Ising, the chiral XY and the chiral Heisenberg models at four-loop order with the perturbative renormalization group in $4-ε$ dimensions and compute critical exponents for the Gross-Neveu-Yukawa fixed points to order $\mathcal{O}(ε^4)$. Further, we provide Padé estimates for the correlation length exponent, the boson and fermion anomalous dimension as well as the leading correction to scaling exponent in 2+1 dimensions. We also confirm the emergence of supersymmetric field theories at four loops for the chiral Ising and the chiral XY models with $N=1/4$ and $N=1/2$ fermions, respectively. Furthermore, applications of our results relevant to various quantum transitions in the context of Dirac and Weyl semimetals are discussed, including interaction-induced transitions in graphene and surface states of topological insulators.

hep-th↗