Two-component Fermi Research Articles

Hydrodynamic Attractor in Ultracold Atoms.

The hydrodynamic attractor is a concept that describes universal equilibration behavior in which systems lose microscopic details before hydrodynamics becomes applicable. We propose a setup to observe hydrodynamic attractors in ultracold atomic gases, taking advantage of the fact that driving the two-body s-wave scattering length causes phenomena equivalent to isotropic fluid expansions. We specifically consider two-component fermions with contact interactions in three dimensions and discuss their dynamics under a power-law drive of the scattering length in a uniform system. By explicit computation, we derive a hydrodynamic relaxation model. We analytically solve their dynamics and find the hydrodynamic attractor solution. Our proposed method using the scattering length drive is applicable to a wide range of ultracold atomic systems, and our results establish these as a new platform for exploring hydrodynamic attractors.

Spontaneous breaking of the SO(2N) symmetry in the Gross-Neveu model

The canonical Gross-Neveu model for N two-component Dirac fermions in 2+1 dimensions suffers a continuous phase transition at a critical interaction gc1∼1/N at large N, at which its continuous symmetry SO(2N) is preserved and a discrete (Ising) symmetry becomes spontaneously broken. A recent mean-field calculation, however, points to an additional transition at a different critical gc2∼−Ngc1, at which SO(2N)→SO(N)×SO(N). To study the latter phase transition we rewrite the Gross-Neveu interaction g(ψ¯ψ)2 in terms of three different quartic terms for the single (L=1) 4N-component real (Majorana) fermion, and then extend the theory to L>1. This allows us to track the evolution of the fixed points of the renormalization group transformation starting from L≫1, where one can discern three distinct critical points which correspond to continuous phase transitions into (1) SO(2N)-singlet mass-order-parameter, (2) SO(2N)-symmetric-tensor mass-order-parameters, and (3) SO(2N)-adjoint nematic-order-parameters, down to L=1 value that is relevant to the standard Gross-Neveu model. Below the critical value of Lc(N)≈0.35N for N≫1 only the Gross-Neveu critical point (1) still implies a diverging susceptibility for its corresponding (SO(2N)-singlet) order parameter, whereas the two new critical points that existed at large L ultimately become equivalent to the Gaussian fixed point at L=1. We interpret this metamorphosis of the SO(2N)-symmetric-tensor fixed point from critical to spurious as an indication that the transition at gc2 in the original Gross-Neveu model is turned first-order by fluctuations. Published by the American Physical Society 2024

A lattice pairing-field approach to ultracold Fermi gases

We develop a pairing-field formalism for ab initio studies of non-relativistic two-component fermions on a (d+1)-dimensional spacetime lattice. More specifically, we focus on theories where the interaction between the two components can be described by the exchange of a corresponding pairing field. The introduction of a pairing field may indeed be convenient for studies of, e.g., the finite-temperature phase structure and critical behavior of, e.g., ultracold atomic Fermi gases. Moreover, such a formalism allows to directly compute the momentum and frequency dependence of the pair propagator, from which the pair-correlation function can be extracted. For a first illustration of the application of our formalism, we compute the density equation of state and the superfluid order parameter for a gas of unpolarized fermions in (0+1) dimensions by employing the complex Langevin approach to surmount the sign problem.

Scaling dimension of the 4π -flux monopole operator in four-flavor three-dimensional QED using lattice simulation

We numerically address the issue of which monopole operators are relevant under renormalization group flow in three-dimensional parity-invariant noncompact QED with four flavors of massless two-component Dirac fermion. Using lattice simulation and finite-size scaling analysis of the free energy to introduce monopole-antimonopole pairs in N=4 and N=12 flavor noncompact QED3, we estimate the infrared scaling dimensions of monopole operators that introduce 2π and 4π fluxes around them. We first show that the estimates for the monopole scaling dimensions are consistent with the large-N expectations for N=12 QED3. Applying the same procedure in N=4 QED3, we estimate the scaling dimension of 4π flux monopole operator to be 3.7(3), which allows the possibility of the operator being irrelevant. This finding offers support to the scenario in which higher-flux monopoles are irrelevant deformations to the Dirac spin liquid phase that could be realized on certain non-bipartite lattices by forbidding 2π-flux monopoles. Published by the American Physical Society 2024

Spatially random disorder in unitary fermion system in (4 − ϵ)-dimensions and effective action at finite temperature

Non-relativistic conformal field theory is significant to understand various aspects of an ultra-cold system. In this paper, we study a non-relativistic system of two-component fermions interacting with a complex boson with Yukawa-like interactions near d = 4-spatial dimensions in the presence of a quenched disorder. The homogeneous theory flows to an interacting fixed point describing a unitary fermion system. In the presence of the disorder, we find that the system has an interesting phase structure in the space of the coupling constants and exhibits an interacting disorder fixed point in ϵ-expansion. The correlation function obeys Lifshitz scaling behaviour at the disorder fixed point with the anisotropic exponent being z = 2 + γE. We also study the disorder system at finite temperature and compute the leading contribution to the 1PI effective action.

Disordered impenetrable two-component fermions in one dimension

We study the one-dimensional Hubbard model for two-component fermions with infinitely strong on-site repulsion ($t\ensuremath{-}0$ model) in the presence of disorder. Our analytical treatment demonstrates that the type of disorder drastically changes the nature of the emerging phases. The case of spin-independent disorder can be treated as a single-particle problem with Anderson localization. On the contrary, recent numerical findings show that spin-dependent disorder, which can be realized as a random magnetic field, leads to the many-body localization-delocalization transition. We find an explicit analytic expression for the matrix elements of the random magnetic field between the eigenstates of the $t\ensuremath{-}0$ model with potential disorder on a finite lattice. Analysis of the matrix elements supports the existence of the many-body localization-delocalization transition in this system and provides an extended physical picture of the random magnetic field.

Bulk viscosity of resonantly interacting fermions in the quantum virial expansion

We consider two-component fermions with a zero-range interaction both in two and three dimensions and calculate the bulk viscosity for an arbitrary scattering length in the high-temperature regime. We evaluate the Kubo formula for the bulk viscosity using an expansion with respect to the fugacity, which acts as a small parameter at high temperatures. In the zero-frequency limit of the Kubo formula, pinch singularities emerge that reduce the order of the fugacity by one. These singularities can turn higher-order vertex corrections at nonzero frequencies into the leading order at zero frequency, so that all such contributions have to be resummed. We present an exact microscopic computation for the bulk viscosity in the high-temperature regime by taking into account these pinch singularities. For negative scattering lengths, we derive the complete bulk viscosity at second order in fugacity and show that a self-consistent equation to resum the vertex corrections is identical to a linearized kinetic equation. For positive scattering lengths, a new type of pinch singularity arises for bound pairs. We show that the pinch singularity for bound pairs leads to a first-order contribution to the bulk viscosity, which is one order lower than that for negative scattering lengths, and that the vertex corrections also provide first-order contributions. We propose a new kinetic equation for bound pairs that derives from a self-consistent equation to resum the vertex corrections.

Stability of the Néel quantum critical point in the presence of Dirac fermions

We investigate the stability of the N\'eel quantum critical point of two-dimensional quantum antiferromagnets, described by a nonlinear $\ensuremath{\sigma}$ model, in the presence of a Kondo coupling to ${N}_{f}$ flavors of two-component Dirac fermion fields. The long-wavelength order parameter fluctuations are subject to Landau damping by electronic particle-hole fluctuations. Using the momentum-shell renormalization group (RG), we demonstrate that the Landau damping is weakly irrelevant at the N\'eel quantum critical point, despite the fact that the corresponding self-energy correction dominates over the quadratic gradient terms in the IR limit. In the ordered phase, the Landau damping increases under the RG, indicative of damped spin-wave excitations. Although the Kondo coupling is weakly relevant, sufficiently strong Landau damping renders the N\'eel quantum critical point quasistable for ${N}_{f}\ensuremath{\ge}4$ and thermodynamically stable for ${N}_{f}<4$. In the latter case, we identify a multicritical point which describes the transition between the N\'eel critical and Kondo runaway regimes. The symmetry breaking at this fixed point results in the opening of a gap in the Dirac fermion spectrum. Approaching the multicritical point from the disordered phase, the fermionic quasiparticle residue vanishes, giving rise to non-Fermi-liquid behavior.

Direct bandgaps, Weyl fermions, and strong light absorption ability in Janus Ti2OFCl MOene

Recently, the MXene-like MOenes provide a novel combination of mechanical, electronic, and optical properties attractive for next-generation low-dimensional quantum and optoelectronic devices. The Janus structure induced by asymmetric surfaces could bring about unique features due to the existence of a built-in electric field. In this study, Janus 2H- and 1T-Ti2OFCl monolayers are systematically scrutinized via the first-principle calculations. 2H- and 1T-Ti2OFCl monolayers are direct semiconductors with a bandgap of 0.75 and 1.12 eV, respectively. Intriguingly, biaxial strains can lead to a three-component 2D pseudospin-1 fermion and a two-component 2D double Weyl fermion during the quantum phase transitions. The effective k·p models further help to characterize these emergent fermions. In addition, the light absorbance calculations including the excitonic effect show that Ti2OFCl monolayers can be potentially applied in infrared detectors and exciton solar cells. This work would further understand the inherently chemical and physical features of the MOene family.

Unconventional exciton evolution from the pseudogap to superconducting phases in cuprates

Electron quasiparticles play a crucial role in simplifying the description of many-body physics in solids with surprising success. Conventional Landau’s Fermi-liquid and quasiparticle theories for high-temperature superconducting cuprates have, however, received skepticism from various angles. A path-breaking framework of electron fractionalization has been established to replace the Fermi-liquid theory for systems that show the fractional quantum Hall effect and the Mott insulating phenomena; whether it captures the essential physics of the pseudogap and superconducting phases of cuprates is still an open issue. Here, we show that excitonic excitation of optimally doped Bi2Sr2CaCu2O8+δ with energy far above the superconducting-gap energy scale, about 1 eV or even higher, is unusually enhanced by the onset of superconductivity. Our finding proves the involvement of such high-energy excitons in superconductivity. Therefore, the observed enhancement in the spectral weight of excitons imposes a crucial constraint on theories for the pseudogap and superconducting mechanisms. A simple two-component fermion model which embodies electron fractionalization in the pseudogap state provides a possible mechanism of this enhancement, pointing toward a novel route for understanding the electronic structure of superconducting cuprates.

Bootstrapping conformal QED3 and deconfined quantum critical point

We bootstrap the deconfined quantum critical point (DQCP) and 3D Quantum Electrodynamics (QED3) coupled to Nf flavors of two-component Dirac fermions. We show the lattice and perturbative results on the SO(5) symmetric DQCP are excluded by the bootstrap bounds with an assumption that the lowest singlet scalar is irrelevant. Remarkably, we discover a new family of kinks in the 3D SO(N) vector bootstrap bounds with N ⩾ 6. We demonstrate coincidences between SU(Nf) adjoint and textrm{SO}left({N}_f^2-1right) vector bootstrap bounds due to a novel algebraic relation between the crossing equations. By introducing gap assumptions breaking the textrm{SO}left({N}_f^2-1right) symmetry, the SU(Nf) adjoint bootstrap bounds with large Nf converge to the 1/Nf perturbative results of QED3. Our results provide strong evidence that the SO(5) DQCP is not continuous and the critical flavor number of QED3 is slightly above 2: {N}_f^{ast}in left(2,4right) . Bootstrap results near {N}_f^{ast } are well consistent with the merger and annihilation mechanism for the loss of conformality in QED3.

Role of the effective range in the density-induced BEC-BCS crossover

We elucidate the role of the effective range in the Bose-Einstein-condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) crossover regime of two-component fermions in three dimensions. In contrast to ultracold Fermi gases near the broad Feshbach resonance, where the interaction can be characterized by the contact-type interaction, the interaction range in general becomes important in the density-induced BEC-BCS crossover discussed in the context of condensed-matter and nuclear systems. By characterizing the nonlocal interaction in terms of the low-energy constants such as scattering length $a$ and effective range $r$, we show how the crossover phenomena are affected by nonzero effective ranges. In particular, we show that the superfluid order parameter is strongly suppressed in the high-density regime and the sound velocity exhibits a nonmonotonic behavior reflecting the mechanical stability of the system. Moreover, we point out that the high-momentum tail associated with the contact parameter can be visible when the magnitude of momentum $k$ is much less than $1/r$. We also discuss the relation between the high-momentum tail and the nuclear contact formalism.

Phase diagrams for two-component D-wave fermion superfluids with density imbalance

Finite-temperature phase structures for asymmetric two-component D-wave fermion superfluids in the weak coupling BCS regime are investigated. The Fulde–Ferrell–Larkin-Ovchinnikov (FFLO) state becomes non-degenerate with the orientation of Cooper pair momentum due to the anisotropic pairing gap for D-wave pairing. The new parameter θ 0, corresponding to the orientation of Cooper pair momentum, greatly enriches the phase structures. Especially, the phase separation (PS) region in the phase diagram is significantly reduced comparing to that for S-wave pairing. Theoretically, the stability condition of solutions is equivalent to the positive definite Hessian matrix of free energy in the hyperplane defined by the number density constraints in the parameter space spanned by the average chemical potential μ, relative chemical potential h, paring gap Δ, pair momentum q, and θ 0. In addition, the stability condition of the superfluid density is essentially included in the positive definite Hessian matrix. Moreover, the positiveness of imbalance number susceptibility is always equivalent to the positiveness of the smaller eigenvalue λ − of the number susceptibility matrix. While the criteria ∂2Ω/∂Δ2 and against PS in previous studies are equivalent to λ − only under the prerequisite that the solution is a local minimum in the corresponding hyperplane.

Anomalous Dimensions of Monopole Operators at the Transitions between Dirac and Topological Spin Liquids

Monopole operators are studied in a large family of quantum critical points between Dirac and topological quantum spin liquids (QSLs): chiral and Z$_{2}$ QSLs. These quantum phase transitions are described by conformal field theories (CFTs): quantum electrodynamics in 2+1 dimensions with 2N flavors of two-component massless Dirac fermions and a four-fermion interaction. For the transition to a chiral spin liquid, it is the Gross-Neveu interaction (QED$_{3}$-GN), while for the transitions to Z$_{2}$ QSLs it is a superconducting pairing term with general spin/valley structure (generalized QED$_{3}$-Z$_{2}$GN). Using the state-operator correspondence, we obtain monopole scaling dimensions to sub-leading order in 1/N. For monopoles with a minimal topological charge q=1/2, the scaling dimension is 2N*0.26510 at leading-order, with the quantum correction being 0.118911(7) for the chiral spin liquid, and 0.102846(9) for the simplest Z$_{2}$ case (the expression is also given for a general pairing term). Although these two anomalous dimensions are nearly equal, the underlying quantum fluctuations possess distinct origins. The analogous result in QED$_{3}$ is also obtained and we find a sub-leading contribution of -0.038138(5), which differs slightly from the value first obtained in the literature. The scaling dimension of a QED$_{3}$-GN monopole with minimal charge is very close to the scaling dimensions of other operators predicted to be equal by a conjectured duality between QED$_{3}$-GN with 2N=2 flavors and the CP$^{1}$ model. Additionally, non-minimally charged monopoles on both sides of the duality have similar scaling dimensions. By studying the large-q asymptotics of the scaling dimensions in QED$_{3}$, QED$_{3}$-GN, and QED$_{3}$-Z$_{2}$GN we verify that the constant O(q$^{0}$) coefficient precisely matches the universal non-perturbative prediction for CFTs with a global U(1) symmetry.

Many-body localization of 1D disordered impenetrable two-component fermions

We study effects of disorder on eigenstates of 1D two-component fermions with infinitely strong Hubbard repulsion. We demonstrate that the spin-independent (potential) disorder reduces the problem to the one-particle Anderson localization taking place at arbitrarily weak disorder. In contrast, a random magnetic field can cause reentrant many-body localization–delocalization transitions. Surprisingly weak magnetic field destroys one-particle localization caused by not too strong potential disorder, whereas at much stronger fields the states are many-body localized. We present numerical support of these conclusions.

Conformality and self-duality of Nf = 2 QED3

We study the IR phase of three dimensional quantum electrodynamics (QED3) coupled to Nf=2 flavors of two-component Dirac fermions, which has been controversial for decades. This theory has been proposed to be self-dual with symmetry enhancement (SU(2)f×U(1)t)/Z2→O(4) at the IR fixed point. We focus on the four-point correlator of monopole operators with unit topological charge of U(1)t. We illustrate the O(4)→SU(2)f×U(1)t branching rules based on an O(4) symmetric positive structure in the monopole four-point crossing equations. We use conformal bootstrap method to derive nonperturbative constraints on the CFT data and test the conformality and self-duality of Nf=2 QED3. In particular we find the CFT data obtained from previous lattice simulations can be ruled out by introducing irrelevant assumptions in the spectrum, indicating the IR phase of Nf=2 QED3 is not conformal.

Bootstrapping Nf=4 conformal QED3

We present the results of a conformal bootstrap study of the presumed unitary IR fixed point of quantum electrodynamics in three dimensions (${\mathrm{QED}}_{3}$) coupled to ${N}_{f}=4$ two-component Dirac fermions. Specifically, we study the four-point correlators of the $SU(4)$ adjoint fermion bilinear $r$ and the monopole of lowest topological charge ${\mathcal{M}}_{1/2}$. Most notably, the scaling dimensions of the fermion bilinear $r$ and the monopole ${\mathcal{M}}_{1/2}$ are found to be constrained into a closed island with a combination of spectrum assumptions inspired by the $1/{N}_{f}$ perturbative results as well as a novel interval positivity constraint on the next-lowest-charge monopole ${\mathcal{M}}_{1}$. Bounds in this island on the $SU(4)$ and topological $U(1{)}_{t}$ conserved current central charges ${c}_{J}$, ${c}_{J}^{t}$, as well as on the stress tensor central charge ${c}_{T}$, are comfortably consistent with the perturbative results. Together with the scaling dimensions, this suggests that a part of estimates from the $1/{N}_{f}$ expansion---even at ${N}_{f}=4$---provide a self-consistent solution to the bootstrap crossing equations, despite some of our assumptions not being strictly justified.

Cosmological Evolution of a Statistical System of Degenerate Scalarly Charged Fermions with an Asymmetric Scalar Doublet. II. One-Component System of Doubly Charged Fermions$${}^{a}$$

Based on the previously formulated mathematical model of a statistical system with scalar interaction of fermions, a cosmological model based on a one-component statistical system of doubly scalar charged degenerate fermions interacting with an asymmetric scalar doublet-canonical and phantom scalar fields-is studied. The connection of the presented model with previously studied models based on one-component and two-component fermion systems is investigated. The asymptotic and limiting properties of the cosmological model are investigated, it is shown that among all models there is a class of models with a finite lifetime. The asymptotic behavior of models near the corresponding singularities is investigated, a qualitative analysis of the corresponding dynamical system is carried out, and numerical implementations of such models are constructed. Based on numerical integration, it is shown that in the presented model there can be transitions from a stable asymptotically vacuum state with a zero canonical field and a constant phantom field corresponding to the phase of cosmological compression to a symmetric state corresponding to the expansion phase. The time interval of the transition between phases is accompanied by oscillations of the canonical scalar field.

Topological quantum critical points in strong coupling limits: Global symmetries and strongly interacting Majorana fermions

In this paper, we discuss strong coupling limits of topological quantum critical points (TQCPs) where quantum phase transitions between two topological distinct superconducting states take place. We illustrate that while superconducting phases on both sides of TQCPs spontaneously break the same symmetries, universality classes of critical states can be identified only when global symmetries in topological states are further specified. In dimensions $d=2\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}3$, we find that continuous $(d+1)\mathrm{th}$-order transitions at weakly interacting TQCPs that were pointed out previously in the presence of the emergent Lorentz symmetry can be terminated by strongly interacting fixed points of Majorana fields. For $2d$ time reversal symmetry breaking TQCPs, termination points are supersymmetric with $\mathcal{N}=4{N}_{f}=1$ (where ${N}_{f}$ is the number of four-component Dirac fermions and $\mathcal{N}$ is the number of two-component real fermions) beyond which transitions are discontinuous first-order ones. For $2d$ time reversal symmetric TQCPs without other global symmetries, termination points of $(d+1)\mathrm{th}$-order continuous transition lines are generically conformal invariant without supersymmetry. Beyond these strong coupling fixed points, there are first-order discontinuous transitions as far as the protecting symmetry is not spontaneously broken but no direct transitions if the protecting symmetry is spontaneously broken in the presence of strong interactions. In this case, termination points can become supersymmetric with $\mathcal{N}=4{N}_{f}=2$ only when interacting Majorana fermions further display an emergent global $\text{U}(1)$ symmetry. In $3d$, strong coupling termination points can be further effectively represented by new emergent gapless real bosons weakly coupled with free gapless Majorana fermions. However, in $1d$, time reversal symmetric $(d+1)\mathrm{th}$ continuous transition lines of TQCPs are terminated by simple free Majorana fermion fixed points.

Tan's adiabatic sweep theorem from the variational theorem for the scattering length

It is shown that variation of the one-particle dispersion in a universal many-body system enables us to obtain Tan's adiabatic sweep theorem and its generalization. The derivation is based on the Hellmann-Feynman theorem and the variational theorem for the scattering length suggested in our previous paper [Cherny and Shanenko, Phys. Rev. E 62, 1646 (2000)]. As an example, the universal effects in the system of spinless bosons are considered. With the help of the variational theorem, we obtain the mean kinetic and interaction energies and derive the virial theorem for the homogeneous and trapped bosons. The results can easily be generalized to the two-component fermions with interactions between opposite spins.