We investigate the interaction potential of superconducting vortices at the full quantum level. We formulate the interaction potential in a constrained path integral and calculate it by the quantum Monte Carlo simulation. The vortex-vortex potential is attractive (type-I), repulsive (type-II), and flat (critical) depending on a coupling constant. The vortex-antivortex potential also depends on the coupling constant at long range but is always attractive at short range.
We consider a two-dimensional px+i py superconductor in the presence of multiple vortices, which support zero-energy Majorana fermion states in their cores. Intervortex tunnelings of the Majorana fermions lift the topological state degeneracy. Using the Bogoliubov-de Gennes equation, we calculate splitting of the zero-energy modes due to these tunneling events. We also discuss superconducting fluctuations and, in particular, their effect on the energy splitting.
The electronic spectrum of multi-vortex configurations in type-II superconductors is studied taking account of the effect of quasiparticle tunneling between the vortex cores. The tunneling is responsible for the formation of strongly coupled quasiparticle states for intervortex distances $a<a_c$, where the critical distance $a_c$ is of the order of several coherence lengths $ξ$. Analyzing the resulting spectra of vortex clusters bonded by the quasiparticle tunneling we find a transition from a set of degenerate Caroli - de Gennes - Matricon branches to anomalous branches similar to the ones in…
The standard Ginzburg-Landau model of competing-order superconductors is studied. It is observed that this model possesses two distinct species of vortex, and consequently has two distinct integer valued topological charges. A simple point particle model of long range forces between (anti)vortices of any species is developed and compared with numerical simulations of the full field theory, excellent agreement being found. Some of the results are quite counterintuitive. For example, a parameter regime exists where vortices of one species repel both vortices and antivortices of the other.
We demonstrate existence of non-pairwise interaction forces between vortices in multicomponent and layered superconducting systems. That is, in contrast to most common models, the interactions in a group of such vortices is not a universal superposition of Coulomb or Yukawa forces. Next we consider the properties of vortex clusters in Semi-Meissner state of type-1.5 two-component superconductors. We show that under certain condition non-pairwise forces can contribute to formation of very complex vortex states in type-1.5 regimes.
A systematic numerical study of non-pairwise vortex interaction forces in the Ginzburg-Landau model for single- and multicomponent superconductivity is presented. The interactions are obtained by highly accurate numerical free energy minimization. In particular a three-body interaction is defined as the difference between the total interaction and sum of pairwise interactions in a system of three vortices and such interactions are studied for single and two-component type-1, type-2, and type-1.5 superconductors. In the investigated regimes, the three-body interaction is found to be short-range…
Recently vortex coalescence was reported in superconducting Sr2RuO4 by several experimental groups for fields applied along the c-axis. We argue that Sr2RuO4 is a type-1.5 superconductor with long-range attractive, short-range repulsive intervortex interaction. The type-1.5 behavior stems from an interplay of the two orbital degrees of freedom describing this chiral superconductor together with the multiband nature of the superconductivity. These multiple degrees of freedom give rise to multiple coherence lengths, some of which are larger and some smaller than the magnetic field penetration le…
Majorana quasiparticles localized in vortex cores of a chiral p-wave superconductor hybridize with one another to form bands in a vortex lattice. We begin by solving a fully microscopic theory describing all quasiparticle bands in a chiral p-wave superconductor in magnetic field, then use this solution to build localized Wannier wavefunctions corresponding to Majorana quasiparticles. A low-energy tight-binding theory describing the intervortex hopping of these is then derived, and its topological properties---which depend crucially on the signs of the imaginary intervortex hopping parameters--…
We show that in multiband superconductors even small interband proximity effect can lead to a qualitative change in the interaction potential between superconducting vortices by producing long-range intervortex attraction. This type of vortex interaction results in unusual response to low magnetic fields leading to phase separation into domains of a two-component Meissner states and vortex droplets.
Two-dimensional low-kappa type-II superconductors are studied numerically within the Eilenberger equations of superconductivity. Depending on the Ginzburg-Landau parameter κ=λ/ξvortex-vortex interaction can be attractive or purely repulsive. The sign of interaction is manifested as a first (second) order phase transition from Meissner to the mixed state. Temperature and field dependence of the magnetic field distribution in low-kappa type-II superconductors with attractive intervortex interaction is calculated. Theoretical results are compared to the experiment.
The stress caused by vortices in tetragonal superconductors contributes to the intervortex interaction which depends on vortex orientation within the crystal, on elastic moduli, and is attractive within certain angular regions even in fields along the $c$ crystal axis. For sufficiently strong stress dependence of the critical temperature, this contribution may result in distortions of the hexagonal vortex lattice for $\bm H||\bm c$. In small fields it leads to formation of a square vortex lattice with a fixed $H$ independent spacing. This should be seen in the magnetization $M(H)$ as a discont…
We show that a moving vortex lattice, as it comes to a crystal edge, radiates into a free space the harmonics of the washboard frequency, $ω_0=2πv/a$, up to a superconducting gap, $Δ/\hbar$. Here $v$ is the velocity of the vortex lattice and $a$ is the intervortex spacing. We compute radiation power and show that this effect can be used for generation of terahertz radiation and for characterization of moving vortex lattices.
The intervortex interaction is investigated in very anisotropic layered superconductors in tilted magnetic field. In such a case, the crossing lattice of Abrikosov vortices (AVs) and Josephson vortices (JVs) appears. The interaction between pancakes vortices (PVs), forming the AVs, and JVs produces the deformation of the AV line. It is demonstrated that in the result of this deformation a long range attraction between AVs is induced. This phenomenon is responsible for the dense vortex chains formation. The vortex structure in weak perpendicular magnetic field is the vortex chain phase, while i…
We show that periodic lattice of Abrikosov vortices in chiral $p$ wave superconductor in general supports fermionic states with zero energy provided the intervortex distance is smaller than the critical one. The zero modes appear at the intersection with the Fermi level of electronic magnetic Bloch bands formed by the overlapping vortex core states. The Bloch bands are robust against lattice disorder induced by fluctuations of vortex positions and can transmit the energy flow across the lattice. The hallmark of zero modes on Bloch bands in electronic heat conductivity is discussed.
The magnetic field of moving vortices in anisotropic superconductors is considered in the framework of time-dependent London approach. It is found that at distances large relative to the core size, the field may change sign that alludes to a non-trivial intervortex interaction which depends on the crystal anisotropy and on the speed and direction of motion. These effects are caused to the electric fields and corresponding normal currents which appear due to the moving vortex magnetic structure. We find that the motion related part of the magnetic field attenuates at large distances as $1/r^3$ …
It is of interest to determine the exit angle of a vortex from a superconducting surface, since this affects the intervortex interactions and their consequences. Two ways to determine this angle are to image the vortex magnetic fields above the surface, or the vortex core shape at the surface. In this work we evaluate the field h(x, y, z) above a flat superconducting surface x, y and the currents J(x,y) at that surface for a straight vortex tilted relative to the normal to the surface, for both the isotropic and anisotropic cases. In principle, these results can be used to determine the vortex…
Superconducting materials with noncentrosymmetric lattices lacking space inversion symmetry exhibit a variety of interesting parity-breaking phenomena, including the magneto-electric effect, spin-polarized currents, helical states, and the unusual Josephson effect. We demonstrate, within a Ginzburg-Landau framework describing noncentrosymmetric superconductors with $O$ point group symmetry, that vortices can exhibit an inversion of the magnetic field at a certain distance from the vortex core. In stark contrast to conventional superconducting vortices, the magnetic-field reversal in the parity…
We discuss the unconventional magnetic response and vortex states arising in noncentrosymmetric superconductors with chiral octahedral and tetrahedral ($O$ or $T$) symmetry. We microscopically derive Ginzburg-Landau free energy. It is shown that due to spin-orbit and Zeeman coupling magnetic response of the system can change very significantly with temperature. For sufficiently strong coupling this leads to a crossover from type-1 superconductivity at elevated temperature to vortex states at lower temperature. The external magnetic field decay in such superconductors does not have the simple e…
In a single-component Ginzburg-Landau model which possesses thermodynamically stable vortex excitations, the zero-field superconducting phase transition is second order even when fluctuations are included. Beyond the mean-field approximation the transition is described in terms of proliferation of vortex loops. Here we determine the order of the superconducting transition in an effective 3D vortex-loop model for the recently proposed multiband type-1.5 superconductors. The vortex interaction is nonmonotonic, i.e., exponentially screened and attractive at large separations, and short-range repu…
We study superconductors with two order components and phase separation driven by intercomponent density-density interaction, focusing on the phase where only one condensate has non-zero ground-state density and a competing order parameter exists only in vortex cores. We demonstrate there, that multi-body intervortex interactions can be strongly non-pairwise, leading to some unusual vortex patterns in an external field, such as vortex pairs and vortex chains. We demonstrate that, in external magnetic field, such a system undergoes a field-driven phase transition from (broken) $U(1)$ to (broken…
At low enough temperatures and high densities, the equilibrium configuration of an ensemble of ultrasoft particles is a self-assembled, ordered, cluster-crystal. In the present work we explore the out-of-equilibrium dynamics for a two-dimensional realization, which is relevant to superconducting materials with multi-scale intervortex forces. We find that for small temperatures following a quench, the suppression of the thermally-activated particle hopping hinders the ordering. This results in a glass transition for a monodispersed ensemble, for which we derive a microscopic explanation in term…
Avalanche dynamics is found in many phenomena spanning from earthquakes to the evolution of species. It can be also found in vortex matter when a type II superconductor is externally driven, for example, by increasing the magnetic field. Vortex avalanches associated with thermal instabilities can be an undesirable effect for applications, but "dynamically driven" avalanches emerging from the competition between intervortex interactions and quenched disorder constitute an interesting scenario to test theoretical ideas related with non-equilibrium dynamics. However, differently from the equilibr…
Disorder in two-band superconductors with repulsive interband interaction induces a frustrated competition between the phase-locking preferences of the various potential and kinetic terms. This frustrated interaction can result in the formation of an $s+is$ superconducting state, that breaks the time-reversal symmetry. In this paper we study the normal modes and their associated coherence lengths in such materials. We especially focus on the consequences of the soft modes stemming from the frustration and time-reversal-symmetry breakdown. We find that two-bands superconductors with such impuri…
The distinctive features of equilibrium vortex structures in thin films of anisotropic superconductors in tilted magnetic fields are studied for the limits of moderate and strong anisotropy. The energetically favorable shape of isolated vortex lines is found in the framework of two particular models describing these limiting cases: London theory with an anisotropic mass tensor and London-type model for a stack of Josephson--decoupled superconducting layers. The increase of the field tilting is shown to result in qualitative changes in the vortex--vortex interaction potential: the balance betwe…
A gel consists of a network of particles or molecules formed for example using the sol-gel process, by which a solution transforms into a porous solid. Particles or molecules in a gel are mainly organized on a scaffold that makes up a porous system. Quantized vortices in type II superconductors mostly form spatially homogeneous ordered or amorphous solids. Here we present high-resolution imaging of the vortex lattice displaying dense vortex clusters separated by sparse or entirely vortex-free regions in $β$-Bi$_2$Pd superconductor. We find that the intervortex distance diverges upon decreasing…
We study the motion of vortices in the planar Ginzburg-Landau model with Schrodinger-Chern-Simons dynamics. We compare the moduli space approximation with the results of numerical simulations of the full field theory and find that there is agreement if the coupling constant is very close to the critical value separating Type I from Type II superconductors. However, there are significant qualitative differences even for modest deviations from the critically coupled regime. Radiation effects produce forces which are of the same order of magnitude as the intervortex force and therefore have a sig…
The recent discovery of iron pnictide superconductors has resulted in a rapidly growing interest in multiband models with more than two bands. In this work we specifically focus on the properties of three-band Ginzburg-Landau models which do not have direct counterparts in more studied two-band models. First we derive normal modes and characteristic length scales in the conventional U(1) three-band Ginzburg-Landau model as well as in its time reversal symmetry broken counterpart with $U(1)\times Z_2$ symmetry. We show that in the latter case, the normal modes are mixed phase/density collective…
It has long been a challenge to describe the origin of unconventional superconductivity. The two known examples with high Tc, based on iron and copper, have very different electronic structures, while other materials with similar electronic structure may not show superconductivity at all. In this paper, the authors show that by using high accuracy diffusion Monte Carlo calculations, the unconventional superconductors of both high Tc types form a cluster at intermediate spin-charge coupling. The spin-charge coupling may serve as a normal state marker for unconventional superconductivity, and pr…
We report the first variational Monte Carlo (VMC) study of the iron-based superconductors. We use realistic band structures, and the ordering instabilities/variational ansatzs are suggested by previous functional renormalization group calculations. We examine antiferromagnetism, superconducting pairing, normal state fermi surface distortion, and orbital order in the antiferromagnetic state.
This is a "perspective" inspired by the forthcoming article, "What makes the $T_c$ of monolayer FeSe on SrTiO so high: a sign-problem free quantum Monte Carlo study," by Z-X. Li, F. Wang, H. Yao, and D-H. Lee, arXiv:1512.06179.
Phase transition between the vortex glass and the Bragg glass phases in high-$T_{\rm c}$ superconductors in $\vec{B}\parallel\vec{c}$ is studied by Monte Carlo simulations in the presence of point pins. A finite latent heat and a $δ$-function peak of the specific heat are observed, which clearly indicates that this is a thermodynamic first-order phase transition. Values of the entropy jump and the Lindemann number are consistent with those of melting transitions. A large jump of the inter-layer phase difference is consistent with the recent Josephson plasma resonance experiment of Bi$_{2}$Sr$_…
Local magnetic field distribution B(r) in the mixed state of a boride superconductor, YB6, is studied by muon spin rotation (muSR). A comparative analysis using the modified London model and Ginzburg-Landau (GL) model indicates that the GL model exhibits better agreement with muSR data at higher fields, thereby demonstrating the importance of reproducing the field profile near the vortex cores when the intervortex distance becomes closer to the GL coherence length. The temperature and field dependence of magnetic penetration depth ($λ$) does not show any hint of nonlocal effect nor of low-lyin…
We perform a systematic quantum Monte Carlo study of the pairing correlation in the $S_4$ symmetric microscopic model for iron-based superconductors. It is found that the pairing with an extensive s-wave symmetry robustly dominates over other pairings at low temperature in reasonable parameter region. The pairing susceptibility, the effective pairing interaction and the $(π,0)$antiferromagnetic correlation strongly increase as the on-site Coulomb interaction increases, indicating the importance of the effect of electron-electron correlation. Our non-biased numerical results provide a unified u…
From the perspective of thermal fluctuations, we investigate the pseudogap phenomena in underdoped high-temperature curpate superconductors. We present a local update Monte Carlo procedure based on the Green's function method to sample the fluctuating pairing field. The Chebyshev polynomial method is applied to calculate the single-particle spectral function directly and efficiently. The evolution of Fermi arcs as a function of temperature is studied by examining the spectral function at Fermi energy as well as the loss of spectral weight. Our results signify the importance of the vortex-like …
Using a combined local density functional theory (LDA-DFT) and quantum Monte Carlo (QMC) dynamic cluster approximation approach, the parameter dependence of the superconducting transition temperature Tc of several single-layer hole-doped cuprate superconductors with experimentally very different Tcmax is investigated. The parameters of two different three-band Hubbard models are obtained using the LDA and the downfolding Nth-order muffin-tin orbital technique with N=0 and 1 respectively. QMC calculations on 4-site clusters show that the d-wave transition temperature Tc depends sensitively on t…
Superconductivity is an emergent phenomena in the sense that the energy scale associated with Cooper pairing is generically much lower than the typical kinetic energy of electrons. Addressing the mechanism of Cooper pairing amounts to determine the effective interaction that operates at low energies. Deriving such an interaction from a bottom-up approach has not been possible for any superconductor, especially strongly correlated ones. Top-down approaches, where one assumes an effective interaction, is plagued with the difficulty of extracting the implied electronic instabilities without uncon…
We study the effect of a transport current on the vortex-line lattice in isotropic type-II superconductors in the presence of strong thermal fluctuations by means of 'driven-diffusion' Monte Carlo simulations of a discretized London theory with finite magnetic penetration depth. We calculate the current-voltage (I-V) characteristics for various temperatures, for transverse as well as longitudinal currents I. From these characteristics, we estimate the linear resistivities R_xx=R_yy and R_zz and compare these with equilibrium results for the vortex-lattice structure factor and the helicity modu…
We investigate the quantum phase transitions of a disordered nanowire from superconducting to metallic behavior by employing extensive Monte Carlo simulations. To this end, we map the quantum action onto a (1+1)-dimensional classical XY model with long-range interactions in imaginary time. We then analyze the finite-size scaling behavior of the order parameter susceptibility, the correlation time, the superfluid density, and the compressibility. We find strong numerical evidence for the critical behavior to be of infinite-randomness type and to belong to the random transverse-field Ising unive…
We numerically study the superconductor-insulator phase transition in a model disordered 2D superconductor as a function of applied magnetic field. The calculation involves quantum Monte Carlo calculations of the (2+1)D XY model in the presence of both disorder and magnetic field. The XY coupling is assumed to have the form -J\cos(θ_i-θ_j-A_{ij}), where A_{ij} has a mean of zero and a standard deviation ΔA_{ij}. In a real system, such a model would be approximately realized by a 2D array of small Josephson-coupled grains with slight spatial disorder and a uniform applied magnetic field. The di…
Many features of charge-4e superconductors remain unknown because even the "mean-field Hamiltonian" describing them is an interacting model. Here we introduce an interacting model to describe a charge-4e superconductor (SC) deep in the superconducting phase, and explore its properties using quantum Monte Carlo (QMC) simulations. The QMC is sign-problem-free, but only when a Majorana representation is employed. As a function of the chemical potential we observe two sharply-distinct behaviors: a "strong" quarteting phase in which charge-4e quartets are tightly bound (like molecules) so that char…
We study the zero-temperature phase diagram of a dissipationless and disorder-free Josephson junction chain. Namely, we determine the critical Josephson energy below which the chain becomes insulating, as a function of the ratio of two capacitances: the capacitance of each Josephson junction and the capacitance between each superconducting island and the ground. We develop an imaginary-time path integral Quantum Monte-Carlo algorithm in the charge representation, which enables us to efficiently handle the electrostatic part of the chain Hamiltonian. We find that a large part of the phase diagr…
To understand the interplay between nematic fluctuation and superconductivity in iron-based superconductors, we performed a systematic study of the realistic two-orbital Hubbard model by using the constrained-path quantum Monte Carlo method. Our numerical results showed that the on-site nematic interaction induces a strong enhancement of nematic fluctuations at various momentums, especially at ($π$,$π$). Simultaneously, it was found that the on-site nematic interaction suppresses the ($π$,0)/(0,$π$) antiferromagnetic order and long-range electron pairing correlations for dominant pairing chann…
The structure function of the vortex lattice of layered superconductor is calculated to one-loop order. Based on a phenomenological melting criterion concerning the Debye-Waller factor, we calculate the melting line of the vortex lattice, and compare our results to Monte Carlo simulation and experiment. We find that our results are quantitatively in good agreement with the Monte Carlo results. Moreover, our analytic calculation of the melting line of BSCCO fits the experiment reasonably well in a temperature range not far from Tc.
We study properties of Abrikosov-Nielsen-Olesen (ANO) strings with the Coleman-Weinberg (CW) potential, which we call CW-ANO strings. While the scale-invariant scalar potential has a topologically trivial vacuum admitting no strings at the classical level, quantum correction allows topologically nontrivial vacua and stable string solutions. We find that the system of the CW potential exhibits significant difference from that of the conventional Abelian-Higgs model with the quadratic-quartic potential. While a single-winding string is qualitatively similar in both systems, and the static interv…
We study vortex lines in high-temperature superconductors with columnar defects produced by heavy ion irradiation. We reconsider scaling theory for the Bose glass transition with tilted magnetic fields, and propose, e.g., a new scaling form for the shape of the Bose glass phase boundary, which is relevant for experiments. We also consider Monte Carlo simulations for a vortex model with a screened interaction. Critical exponents are determined from scaling analysis of Monte Carlo data for current-voltage characteristics and other quantities. The dynamic critical exponent is found to be z = 4.6 …
Understanding the complex phase diagram of cuprate superconductors is a long-standing challenging problem. Recent studies have shown that orbital degrees of freedom, both Cu $e_g$ orbitals and O $p$ orbitals, are a key ingredient for a unified understanding of cuprate superconductors, including the material dependence. Here we investigate a four-band $d$-$p$ model derived from the first-principles calculations with the variational Monte Carlo method, which allows us to elucidate competing orders on an equal footing. The obtained results can consistently explain the doping dependence of superco…
We use the doped Fullerenes as an example of how realistic systems can be described by simple models. Starting from the band structure we set up a tight-binding model that describes the t_{1u} conduction band. Adding correlation terms we arrive at a generalized Hubbard Hamiltonian that we treat using quantum Monte Carlo. To address the problem of superconductivity in the doped Fullerenes, we study the screening of a point charge. We find surprisingly efficient metallic screening even for strong correlations, almost up to the Mott transition, and discuss the implications on superconductivity, i…
The vortices in a high-Tc superconductor with strong correlated pinning centers have been studied numerically using the mapping to charged bosons in two-dimensions(2D) and the Monte-Carlo algorithm. Considering the viscous dissipation of moving vortices we derived a nonlinear voltage response expression which describes different regimes and their crossover uniformly. This equation accords with experimental results.
The critical dynamics of superconductors is studied using renormalization group and duality arguments. We show that in extreme type II superconductors the dynamic critical exponent is given exactly by $z=3/2$. This result does not rely on the widely used models of critical dynamics. Instead, it is shown that $z=3/2$ follows from the duality between the extreme type II superconductor and a model with a critically fluctuating gauge field. Our result is in agreement with Monte Carlo simulations.
Theory of melting of the vortex lattice in type II superconductors in the framework of Ginzburg - Landau approach is presented. The melting line location is determined and magnetization and specific heat jumps along it are calculated. The magnetization of liquid is larger than that of solid by 1.8% irrespective of the melting temperature, while the specific heat jump is about 6% and decreases slowly with temperature. The magnetization curves agrees with experimental results on YBCO and Monte Carlo simulations.
The stability and the critical properties of the three-dimensional vortex-glass order in random type-II superconductors with point disorder is investigated in the unscreened limit based on a lattice {\it XY} model with a uniform field. By performing equilibrium Monte Carlo simulations for the system with periodic boundary conditions, the existence of a stable vortex-glass order is established in the unscreened limit. Estimated critical exponents are compared with those of the gauge-glass model.
This paper demonstrates that the results of a Monte Carlo simulation of a diluted 2D Ising antiferromagnetic system corresponds with the phase diagram for non conventional superconductors. An energy gap of this system is defined. We also find a strange phenomenon that when the lattice size of simulation increased the crystal structure becomes more like quasi crystal at the low temperature.
A fundamental open issue in physics is whether and how the fermion sign problem in quantum Monte Carlo (QMC) simulations can be solved generically. Here, we show that Majorana-time-reversal (MTR) symmetries can provide a unifying principle to solve the fermion sign problem in interacting fermionic models. By systematically classifying Majorana-bilinear operators according to the anti-commuting MTR symmetries they respect, we rigorously proved that there are two and only two fundamental symmetry classes which are sign-problem-free and which we call the "Majorana class" and "Kramers class", resp…
Using path-integral Quantum Monte Carlo we study the low-temperature phase diagram of a two-dimensional superconductor within a phenomenological model, where vortices have a finite mass and move in a dissipative environment modeled by a Caldeira-Leggett term. The quantum vortex liquid at high magnetic fields exhibits superfluidity and thus corresponds to a {\em superinsulating} phase which is characterized by a nonlinear voltage-current law for an infinite system in the absence of pinning. This superinsulating phase is shifted to higher magnetic fields in the presence of dissipation.
Through variational Monte Carlo calculation on Gutzwiller projected wave functions, we study the quasiparticle(qp) weight for adding and removing an electron from a high temperature superconductor. We find the qp weight is particle-hole symmetric at sufficiently low energy. We propose to use the tunneling asymmetry as a tool to study the mechanism of electron incoherence in high temperature superconductors.
We study flux penetration in a disordered type II superconductor by simulations of interacting vortices, using a Monte Carlo method for vortex nucleation. Our results show that a detailed description of the nucleation process yields a correction to the scaling laws usually associated with flux front invasion. We propose a simple model to account for these corrections.
We use Monte Carlo simulations of a coarse grained three dimensional model to demonstrate that the experimentally observed approximate temperature independence of the magnetic creep rate for a broad range of temperatures may be explained in terms of record dynamics, {\it viz.} the dynamical properties of the times at which a stochastic fluctuating signal establishes records.
Recent applications of Quantum Monte Carlo (QMC) technique to Fe-based superconductors opened a way to directly verify the applicability of the itinerant scenario for these systems. Fe-based superconductors undergo various instabilities upon lowering temperature (magnetism, superconductivity, nematicity/orbital order), and one can check whether the hierarchy of instabilities obtained within the itinerant approach is the same as in unbiased QMC simulations. In a recent paper [arXiv:1512:08523] the authors considered the simplest two-band model with interaction tailored to favor orbital order. T…
