Non-Hertz-Millis scaling of the antiferromagnetic quantum critical metal via scalable Hybrid Monte Carlo

A key component of the phase diagram of many iron-based superconductors and electron-doped cuprates is believed to be a quantum critical point (QCP), delineating the onset of antiferromagnetic spin-density wave order in a quasi-two-dimensional metal. The universality class of this QCP is believed to play a fundamental role in the description of the proximate non-Fermi liquid behavior and superconducting phase. A minimal model for this transition is the O(3) spin-fermion model. Despite many efforts, a definitive characterization of its universal properties is still lacking. Here, we numerically study the O(3) spin-fermion model and extract the scaling exponents and functional form of the static and zero-momentum dynamical spin susceptibility. We do this using a Hybrid Monte Carlo (HMC) algorithm with a novel auto-tuning procedure, which allows us to study unprecedentedly large systems of 80 × 80 sites. We find a strong violation of the Hertz-Millis form, contrary to all previous numerical results. Furthermore, the form that we do observe provides good evidence that the universal scaling is actually governed by the analytically tractable fixed point discovered near perfect "hot-spot'" nesting, even for a larger nesting window. Our predictions can be directly tested with neutron scattering. Additionally, the HMC method we introduce is generic and can be used to study other fermionic models of quantum criticality, where there is a strong need to simulate large systems.

Fast and scalable quantum Monte Carlo simulations of electron-phonon models

We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and we report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but it incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat "stiffness" arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. These methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.

Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations

The origin of the pseudogap behavior, found in many high-T_c superconductors, remains one of the greatest puzzles in condensed matter physics. One possible mechanism is fermionic incoherence, which near a quantum critical point allows pair formation but suppresses superconductivity. Employing quantum Monte Carlo simulations of a model of itinerant fermions coupled to ferromagnetic spin fluctuations, represented by a quantum rotor, we report numerical evidence of pseudogap behavior, emerging from pairing fluctuations in a quantum-critical non-Fermi liquid. Specifically, we observe enhanced pairing fluctuations and a partial gap opening in the fermionic spectrum. However, the system remains non-superconducting until reaching a much lower temperature. In the pseudogap regime the system displays a “gap-filling" rather than “gap-closing" behavior, similar to the one observed in cuprate superconductors. Our results present direct evidence of the pseudogap state, driven by superconducting fluctuations.

The origin of pseudogap in high-T_c superconductors remains a big puzzle. Here, the authors report numerical evidence of pseudogap behavior employing Quantum Monte Carlo algorithm emerging from pairing fluctuations in a quantum-critical non-Fermi liquid, similar to the pseudogap phase observed in cuprate superconductors.

Quantum critical points and the sign problem

The "sign problem" (SP) is a fundamental limitation to simulations of strongly correlated matter. It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians because its behavior can be influenced by the choice of algorithm. By contrast, we show that the SP in determinant quantum Monte Carlo (QMC) is quantitatively linked to quantum critical behavior. We demonstrate this through simulations of several models with critical properties that are relatively well understood. We propose a reinterpretation of the low average sign for the Hubbard model on the square lattice away from half filling in terms of the onset of pseudogap behavior and exotic superconductivity. Our study charts a path for exploiting the average sign in QMC simulations to understand quantum critical behavior.

Antiferromagnetism Induced by Bond Su-Schrieffer-Heeger Electron-Phonon Coupling: A Quantum Monte Carlo Study

Antiferromagnetism (AFM) such as Néel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Néel AFM ordering in two dimensions can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that bond Su-Schrieffer-Heeger (SSH) phonons with frequency ω and EPC constant λ can induce AFM ordering for a wide range of phonon frequency ω>ω_{c}. For ω<ω_{c}, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AFM phases at ω_{c}. The phonon mechanism of the AFM ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AFM spin exchange. Our results shall shed new light on understanding AFM ordering in correlated quantum materials.

Amelioration for the Sign Problem: An Adiabatic Quantum Monte Carlo Algorithm

We introduce the adiabatic quantum Monte Carlo (AQMC) method, where we gradually crank up the interaction strength, as an amelioration of the sign problem. It is motivated by the adiabatic theorem and will approach the true ground state if the evolution time is long enough. We demonstrate that the AQMC algorithm enhances the average sign exponentially such that low enough temperatures can be accessed and ground-state properties probed. It is a controlled approximation that satisfies the variational theorem and provides an upper bound for the ground-state energy. We first benchmark the AQMC algorithm vis-à-vis the undoped Hubbard model on the square lattice which is known to be sign-problem-free within the conventional quantum Monte Carlo formalism. Next, we test the AQMC algorithm against the density-matrix-renormalization-group approach for the doped four-leg ladder Hubbard model and demonstrate its remarkable accuracy. As a nontrivial example, we apply our method to the Hubbard model at p=1/8 doping for a 16×8 system and discuss its ground-state properties. We finally utilize our method and demonstrate the emergence of U(1)_{2}∼SU(2)_{1} topological order in a strongly correlated Chern insulator.

Identification of Non-Fermi Liquid Physics in a Quantum Critical Metal via Quantum Loop Topography

Non-Fermi liquid physics is ubiquitous in strongly correlated metals, manifesting itself in anomalous transport properties, such as a T-linear resistivity in experiments. However, its theoretical understanding in terms of microscopic models is lacking, despite decades of conceptual work and attempted numerical simulations. Here we demonstrate that a combination of sign-problem-free quantum Monte Carlo sampling and quantum loop topography, a physics-inspired machine-learning approach, can map out the emergence of non-Fermi liquid physics in the vicinity of a quantum critical point (QCP) with little prior knowledge. Using only three parameter points for training the underlying neural network, we are able to robustly identify a stable non-Fermi liquid regime tracing the fans of metallic QCPs at the onset of both spin-density wave and nematic order. In particular, we establish for the first time that a spin-density wave QCP commands a wide fan of non-Fermi liquid region that funnels into the quantum critical point. Our study thereby provides an important proof-of-principle example that new physics can be detected via unbiased machine-learning approaches.

Specific Heat of a Quantum Critical Metal

We investigate the specific heat c, near an Ising nematic quantum critical point (QCP), using sign problem-free quantum Monte Carlo simulations. Cooling towards the QCP, we find a broad regime of temperature where c/T is close to the value expected from the noninteracting band structure, even for a moderately large coupling strength. At lower temperature, we observe a rapid rise of c/T, followed by a drop to zero as the system becomes superconducting. The spin susceptibility begins to drop at roughly the same temperature where the enhancement of c/T onsets, most likely due to the opening of a gap associated with superconducting fluctuations. These findings suggest that superconductivity and non-Fermi liquid behavior (manifested in an enhancement of the effective mass) onset at comparable energy scales. We support these conclusions with an analytical perturbative calculation.

Competing Nodal d-Wave Superconductivity and Antiferromagnetism

Competing unconventional superconductivity and antiferromagnetism widely exist in several strongly correlated quantum materials whose direct simulation generally suffers from fermion sign problem. Here, we report unbiased quantum Monte Carlo (QMC) simulations on a sign-problem-free repulsive toy model with same on site symmetries as the standard Hubbard model on a 2D square lattice. Using QMC simulations, supplemented with mean-field and continuum field-theory arguments, we find that it hosts three distinct phases: a nodal d-wave phase, an antiferromagnet, and an intervening phase which hosts coexisting antiferromagnetism and nodeless d-wave superconductivity. The transition from the coexisting phase to the antiferromagnet is described by the 2+1-D XY universality class, while the one from the coexisting phase to the nodal d-wave phase is described by the Heisenberg-Gross-Neveu theory. The topology of our phase diagram resembles that of layered organic materials which host pressure tuned Mott transition from antiferromagnet to unconventional superconductor at half-filling.

Modeling Unconventional Superconductivity at the Crossover between Strong and Weak Electronic Interactions

High-temperature superconductivity emerges in many different quantum materials, often in regions of the phase diagram where the electronic kinetic energy is comparable to the electron-electron repulsion. Describing such intermediate-coupling regimes has proven challenging as standard perturbative approaches are inapplicable. Here, we employ quantum Monte Carlo methods to solve a multiband Hubbard model that does not suffer from the sign problem and in which only repulsive interband interactions are present. In contrast to previous sign-problem-free studies, we treat magnetic, superconducting, and charge degrees of freedom on an equal footing. We find an antiferromagnetic dome accompanied by a metal-to-insulator crossover line in the intermediate-coupling regime, with a smaller superconducting dome appearing in the metallic region. Across the antiferromagnetic dome, the magnetic fluctuations change from overdamped in the metallic region to propagating in the insulating region. Our findings shed new light on the intertwining between superconductivity, magnetism, and charge correlations in quantum materials.

Biexciton Condensation in Electron-Hole-Doped Hubbard Bilayers: A Sign-Problem-Free Quantum Monte Carlo Study

The bilayer Hubbard model with electron-hole doping is an ideal platform to study excitonic orders due to suppressed recombination via spatial separation of electrons and holes. However, suffering from the sign problem, previous quantum Monte Carlo studies could not arrive at an unequivocal conclusion regarding the presence of phases with clear signatures of excitonic condensation in bilayer Hubbard models. Here, we develop a determinant quantum Monte Carlo algorithm for the bilayer Hubbard model that is sign-problem-free for equal and opposite doping in the two layers and study excitonic order and charge and spin density modulations as a function of chemical potential difference between the two layers, on-site Coulomb repulsion, and interlayer interaction. In the intermediate coupling regime and in proximity to the SU(4)-symmetric point, we find a biexcitonic condensate phase at finite electron-hole doping, as well as a competing (π,π) charge density wave state. We extract the Berezinskii-Kosterlitz-Thouless transition temperature from superfluid density and a finite-size scaling analysis of the correlation functions and explain our results in terms of an effective biexcitonic hard-core boson model.

Revealing fermionic quantum criticality from new Monte Carlo techniques

This review summarizes recent developments in the study of fermionic quantum criticality, focusing on new progress in numerical methodologies, especially quantum Monte Carlo methods, and insights that emerged from recently large-scale numerical simulations. Quantum critical phenomena in fermionic systems have attracted decades of extensive research efforts, partially lured by their exotic properties and potential technology applications, and partially awakened by the profound and universal fundamental principles that govern these quantum critical systems. Due to the complex and non-perturbative nature, these systems face the most difficult and challenging problems in the study of modern condensed matter physics, and many important fundamental problems remain open. Recently, new developments in model design and algorithm improvements enabled unbiased large-scale numerical solutions to be achieved in the close vicinity of these quantum critical points, which paves a new pathway towards achieving controlled conclusions through combined efforts of theoretical and numerical studies, as well as possible theoretical guidance for experiments in heavy-fermion compounds, Cu-based and Fe-based superconductors, ultra-cold fermionic atomic gas, twisted graphene layers, etc, where signatures of fermionic quantum criticality exist.

Itinerant quantum critical point with fermion pockets and hotspots

The present work summarizes major progress in research on the itinerant quantum critical point (QCP). The authors designed a model and developed quantum Monte Carlo simulation to examine itinerant QCPs generated by antiferromagnetic fluctuations. The model has immediate relevance to a wide range of strongly correlated systems, such as cuprate superconductors. Large system size and low temperature are comfortably accessed and quantum critical scaling relations are revealed with high accuracy. At the QCP, a finite anomalous dimension is observed, and fermions at hotspots evolve into a non-Fermi liquid. These results are being observed in an unbiased manner and they could bridge future developments both in analytical theory and in numerical simulation of itinerant QCPs.

Metallic quantum criticality is among the central themes in the understanding of correlated electronic systems, and converging results between analytical and numerical approaches are still under review. In this work, we develop a state-of-the-art large-scale quantum Monte Carlo simulation technique and systematically investigate the itinerant quantum critical point on a 2D square lattice with antiferromagnetic spin fluctuations at wavevector Q=(π,π)—a problem that resembles the Fermi surface setup and low-energy antiferromagnetic fluctuations in high-Tc cuprates and other critical metals, which might be relevant to their non–Fermi-liquid behaviors. System sizes of 60×60×320 (L×L×Lτ) are comfortably accessed, and the quantum critical scaling behaviors are revealed with unprecedented high precision. We found that the antiferromagnetic spin fluctuations introduce effective interactions among fermions and the fermions in return render the bare bosonic critical point into a different universality, different from both the bare Ising universality class and the Hertz–Mills–Moriya RPA prediction. At the quantum critical point, a finite anomalous dimension η∼0.125 is observed in the bosonic propagator, and fermions at hotspots evolve into a non-Fermi liquid. In the antiferromagnetically ordered metallic phase, fermion pockets are observed as the energy gap opens up at the hotspots. These results bridge the recent theoretical and numerical developments in metallic quantum criticality and can serve as the stepping stone toward final understanding of the 2D correlated fermions interacting with gapless critical excitations.

Superconductivity from the condensation of topological defects in a quantum spin-Hall insulator

The discovery of quantum spin-Hall (QSH) insulators has brought topology to the forefront of condensed matter physics. While a QSH state from spin-orbit coupling can be fully understood in terms of band theory, fascinating many-body effects are expected if it instead results from spontaneous symmetry breaking. Here, we introduce a model of interacting Dirac fermions where a QSH state is dynamically generated. Our tuning parameter further allows us to destabilize the QSH state in favour of a superconducting state through proliferation of charge-2e topological defects. This route to superconductivity put forward by Grover and Senthil is an instance of a deconfined quantum critical point (DQCP). Our model offers the possibility to study DQCPs without a second length scale associated with the reduced symmetry between field theory and lattice realization and, by construction, is amenable to large-scale fermion quantum Monte Carlo simulations.

Benchmark of correlation matrix renormalization method in molecule calculations

We report benchmark calculations of the correlation matrix renormalization (CMR) approach for 23 molecules in the well-established G2 molecule set. This subset represents molecules with spin-singlet ground state in a variety of chemical bonding and coordination environments. The QUAsi-atomic minimal basis-set orbitals (QUAMBOs) are used as local orbitals in both CMR and full configuration interaction (FCI) calculations for comparison. The results obtained from the calculations are also compared with available experimental data. It is shown that the CMR method produces binding and dissociation energy curves in good agreement with the QUAMBO-FCI calculations as well as experimental results. The CMR benchmark calculations yield a standard deviation of 0.09 Å for the equilibrium bond length and 0.018 Hartree/atom for the formation energy, with a gain of great computational efficiency which scales like Hartree-Fock method.

Numerical observation of emergent spacetime supersymmetry at quantum criticality

No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. Moreover, the question of whether spacetime SUSY in 2 + 1 and higher dimensions can emerge in generic lattice microscopic models remains open. Here, we introduce a lattice realization of a single Dirac fermion in 2 + 1 dimensions with attractive interactions that preserves both time-reversal and chiral symmetries. By performing sign problem-free determinant quantum Monte Carlo simulations, we show that an interacting single Dirac fermion in 2 + 1 dimensions features a superconducting quantum critical point (QCP). We demonstrate that the N = 2 spacetime SUSY in 2 + 1 dimensions emerges at the superconducting QCP by showing that the fermions and bosons have identical anomalous dimensions 1/3, a hallmark of the emergent SUSY. We further show some experimental signatures that may be measured to test such emergent SUSY in candidate systems.

Fragility of Charge Order Near an Antiferromagnetic Quantum Critical Point

We investigate the interplay between charge order and superconductivity near an antiferromagnetic quantum critical point using sign-problem-free Quantum Monte Carlo simulations. We establish that, when the electronic dispersion is particle-hole symmetric, the system has an emergent SU(2) symmetry that implies a degeneracy between d-wave superconductivity and charge order with d-wave form factor. Deviations from particle-hole symmetry, however, rapidly lift this degeneracy, despite the fact that the SU(2) symmetry is preserved at low energies. As a result, we find a strong suppression of charge order caused by the competing, leading superconducting instability. Across the antiferromagnetic phase transition, we also observe a shift in the charge order wave vector from diagonal to axial. We discuss the implications of our results to the universal phase diagram of antiferromagnetic quantum-critical metals and to the elucidation of the charge order experimentally observed in the cuprates.

Resilient Nodeless d-Wave Superconductivity in Monolayer FeSe

Monolayer FeSe exhibits the highest transition temperature among the iron based superconductors and appears to be fully gapped, seemingly consistent with s-wave superconductivity. Here, we develop a theory for the superconductivity based on coupling to fluctuations of checkerboard magnetic order (which has the same translation symmetry as the lattice). The electronic states are described by a symmetry based k·p-like theory and naturally account for the states observed by angle resolved photoemission spectroscopy. We show that a prediction of this theory is that the resultant superconducting state is a fully gapped, nodeless, d-wave state. This state, which would usually have nodes, stays nodeless because, as seen experimentally, the relevant spin-orbit coupling has an energy scale smaller than the superconducting gap.

Edge Quantum Criticality and Emergent Supersymmetry in Topological Phases

Proposed as a fundamental symmetry describing our Universe, spacetime supersymmetry (SUSY) has not been discovered yet in nature. Nonetheless, it has been predicted that SUSY may emerge in low-energy physics of quantum materials such as topological superconductors and Weyl semimetals. Here, by performing state-of-the-art sign-problem-free quantum Monte Carlo simulations of an interacting two-dimensional topological superconductor, we show convincing evidence that the N=1 SUSY emerges at its edge quantum critical point (EQCP) while its bulk remains gapped and topologically nontrivial. Remarkably, near the EQCP, we find that the edge Majorana fermion acquires a mass that is identical with that of its bosonic superpartner. To the best of our knowledge, this is the first observation that fermions and bosons have equal dynamically generated masses, a hallmark of emergent SUSY. We further discuss experimental signatures of such EQCP and associated SUSY.

Fermion-induced quantum critical points

A unified theory of quantum critical points beyond the conventional Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic criterion, phase transitions should be first-order when cubic terms of order parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here, from renormalization group analysis, we show that second-order quantum phase transitions can occur at such putatively first-order transitions in interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden quantum critical points are induced by gapless fermions, we call them fermion-induced quantum critical points. We further introduce a microscopic model of SU(N) fermions on the honeycomb lattice featuring a transition between Dirac semimetals and Kekule valence bond solids. Remarkably, our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show convincing evidences of a fermion-induced quantum critical points for N = 2, 3, 4, 5 and 6, consistent with the renormalization group analysis. We finally discuss possible experimental realizations of the fermion-induced quantum critical points in graphene and graphene-like materials.Quantum phase transitions are governed by Landau-Ginzburg theory and the exceptions are rare. Here, Li et al. propose a type of Landau-forbidden quantum critical points induced by gapless fermions in two-dimensional Dirac semimetals.

Majorana-Time-Reversal Symmetries: A Fundamental Principle for Sign-Problem-Free Quantum Monte Carlo Simulations

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 anticommuting MTR symmetries they respect, we rigorously prove 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," respectively. Novel sign-problem-free models in the Majorana class include interacting topological superconductors and interacting models of charge-4e superconductors. We believe that our MTR unifying principle could shed new light on sign-problem-free QMC simulation on strongly correlated systems and interacting topological matters.

Numerical stabilization of entanglement computation in auxiliary-field quantum Monte Carlo simulations of interacting many-fermion systems

In the absence of a fermion sign problem, auxiliary-field (or determinantal) quantum Monte Carlo (DQMC) approaches have long been the numerical method of choice for unbiased, large-scale simulations of interacting many-fermion systems. More recently, the conceptual scope of this approach has been expanded by introducing ingenious schemes to compute entanglement entropies within its framework. On a practical level, these approaches, however, suffer from a variety of numerical instabilities that have largely impeded their applicability. Here we report on a number of algorithmic advances to overcome many of these numerical instabilities and significantly improve the calculation of entanglement measures in the zero-temperature projective DQMC approach, ultimately allowing us to reach similar system sizes as for the computation of conventional observables. We demonstrate the applicability of this improved DQMC approach by providing an entanglement perspective on the quantum phase transition from a magnetically ordered Mott insulator to a band insulator in the bilayer square lattice Hubbard model at half filling.

Sign-Problem-Free Monte Carlo Simulation of Certain Frustrated Quantum Magnets

We introduce a quantum Monte Carlo (QMC) method for efficient sign-problem-free simulations of a broad class of frustrated S=1/2 antiferromagnets using the basis of spin eigenstates of clusters to avoid the severe sign problem faced by other QMC methods. We demonstrate the utility of the method in several cases with competing exchange interactions and flag important limitations as well as possible extensions of the method.

Competing Orders in a Nearly Antiferromagnetic Metal

We study the onset of spin-density wave order in itinerant electron systems via a two-dimensional lattice model amenable to numerically exact, sign-problem-free determinantal quantum Monte Carlo simulations. The finite-temperature phase diagram of the model reveals a dome-shaped d-wave superconducting phase near the magnetic quantum phase transition. Above the critical superconducting temperature, an extended fluctuation regime manifests itself in the opening of a gap in the electronic density of states and an enhanced diamagnetic response. While charge density wave fluctuations are moderately enhanced in the proximity of the magnetic quantum phase transition, they remain short ranged. The striking similarity of our results to the phenomenology of many unconventional superconductors points a way to a microscopic understanding of such strongly coupled systems in a controlled manner.

Majorana Positivity and the Fermion Sign Problem of Quantum Monte Carlo Simulations

The sign problem is a major obstacle in quantum Monte Carlo simulations for many-body fermion systems. We examine this problem with a new perspective based on the Majorana reflection positivity and Majorana Kramers positivity. Two sufficient conditions are proven for the absence of the fermion sign problem. Our proof provides a unified description for all the interacting lattice fermion models previously known to be free of the sign problem based on the auxiliary field quantum Monte Carlo method. It also allows us to identify a number of new sign-problem-free interacting fermion models including, but not limited to, lattice fermion models with repulsive interactions but without particle-hole symmetry, and interacting topological insulators with spin-flip terms.

What makes the Tc of monolayer FeSe on SrTiO3 so high: a sign-problem-free quantum Monte Carlo study

Monolayer FeSe films grown on SrTiO₃ (STO) substrate show superconducting gap-opening temperatures (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}}$$\end{document}Tc) which are almost an order of magnitude higher than those of the bulk FeSe and are highest among all known Fe-based superconductors. Angle-resolved photoemission spectroscopy observed “replica bands” suggesting the importance of the interaction between FeSe electrons and STO phonons. These facts rejuvenated the quest for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{{\mathrm{c}}}$$\end{document}Tc enhancement mechanisms in iron-based, especially iron-chalcogenide, superconductors. Here, we perform the first numerically-exact sign-problem-free quantum Monte Carlo simulations to iron-based superconductors. We (1) study the electronic pairing mechanism intrinsic to heavily electron doped FeSe films, and (2) examine the effects of electron–phonon interaction between FeSe and STO as well as nematic fluctuations on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{{\mathrm{c}}}$$\end{document}Tc. Armed with these results, we return to the question “what makes the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{{\mathrm{c}}}$$\end{document}Tc of monolayer FeSe on SrTiO₃ so high?” in the conclusion and discussions.

Split Orthogonal Group: A Guiding Principle for Sign-Problem-Free Fermionic Simulations

We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving matrices that lie in the split orthogonal group provide a guideline for sign-free simulations of fermionic models on bipartite lattices. This guiding principle not only unifies the recent solutions of the sign problem based on the continuous-time quantum Monte Carlo methods and the Majorana representation, but also suggests new efficient algorithms to simulate physical systems that were previously prohibitive because of the sign problem.

The ionothermal synthesis, structure, and magnetism-structure relationship of two biphenyl tetracarboxylic acid-based metal-organic frameworks

Two new metal-organic frameworks (1-2) were ionothermally obtained by the reaction of a biphenyltetracarboxylic sodium (Na4BPTC) ligand and M(OOCCH3)2 (M = Co(1) and Mn(2)). Crystal structure analysis reveals that 1 is a Co3Na6 unit-based three dimensional heterometallic MOF, while 2 exhibits a {Mn(COO)n} chain-based three-dimensional framework. Furthermore, the magnetic measurement shows that both of them have anti-ferromagnetic properties. A combination of Density Functional Theory (DFT) and Quantum Monte Carlo (QMC) simulation uncovers that in 2 the coupling parameters between two adjacent Mn(II) ions are J1 = -2.0 cm(-1) and J2 = -1.6 cm(-1), and the magnetism mainly originates from the propagation of Mn(II) ions by the super-exchange of carboxylates. Interestingly, the superexchange modes of J1 and J2 are different. Two spin nets of -/+/- dominate in the coupling for J1, while for J2 there are two spin nets of -/+/- and one spin net of +/-/+.

Enhancement of superconductivity near a nematic quantum critical point

We consider a low T_{c} metallic superconductor weakly coupled to the soft fluctuations associated with proximity to a nematic quantum critical point (NQCP). We show that (1) a BCS-Eliashberg treatment remains valid outside of a parametrically narrow interval about the NQCP, (2) the symmetry of the superconducting state (d wave, s wave, p wave) is typically determined by the noncritical interactions, but T_{c} is enhanced by the nematic fluctuations in all channels, and (3) in 2D, this enhancement grows upon approach to criticality up to the point at which the weak coupling approach breaks down, but in 3D, the enhancement is much weaker.

Singularity of the London penetration depth at quantum critical points in superconductors

We present a general theory of the singularity in the London penetration depth at symmetry-breaking and topological quantum critical points within a superconducting phase. While the critical exponents and ratios of amplitudes on the two sides of the transition are universal, an overall sign depends upon the interplay between the critical theory and the underlying Fermi surface. We determine these features for critical points to spin density wave and nematic ordering, and for a topological transition between a superconductor with Z2 fractionalization and a conventional superconductor. We note implications for recent measurements of the London penetration depth in BaFe2(As(1-x)P(x))2 [K. Hashimoto et al., Science 336, 1554 (2012)].

Entanglement of interacting fermions in quantum Monte Carlo calculations

Given a specific interacting quantum Hamiltonian in a general spatial dimension, can one access its entanglement properties, such as the entanglement entropy corresponding to the ground state wave function? Even though progress has been made in addressing this question for interacting bosons and quantum spins, as yet there exist no corresponding methods for interacting fermions. Here we show that the entanglement structure of interacting fermionic Hamiltonians has a particularly simple form-the interacting reduced density matrix can be written as a sum of operators that describe free fermions. This decomposition allows one to calculate the Renyi entropies for Hamiltonians which can be simulated via determinantal quantum Monte Carlo calculations, while employing the efficient techniques hitherto available only for free fermions. The method presented works for the ground state, as well as for the thermally averaged reduced density matrix.

Superconductivity at the onset of spin-density-wave order in a metal

We revisit the issue of superconductivity at the quantum-critical point (QCP) between a 2D paramagnet and a spin-density-wave metal with ordering momentum (π, π). This problem is highly nontrivial because the system at criticality displays a non-Fermi-liquid behavior and because the effective coupling constant λ for the pairing is generally of order one, even when the actual interaction is smaller than fermionic bandwidth. Previous study [M. A. Metlitski and S. Sachdev, Phys. Rev. B 82, 075128 (2010)] has found that the renormalizations of the pairing vertex are stronger than in BCS theory and hold in powers of log(2)(1/T). We analyze the full gap equation and argue that summing up of the leading logarithms does not lead to a pairing instability. Yet, we show that superconductivity has no threshold and appears even if λ is set to be small, because subleading logarithmical renormalizations diverge and give rise to a BCS-like result log1/T(c) ∝ 1/λ. We argue that the analogy with BCS is not accidental as at small λ superconductivity at a QCP predominantly comes from fermions that retain Fermi-liquid behavior at criticality. We compute T(c) for the actual λ ∼ O(1), and find that both Fermi-liquid and non-Fermi-liquid fermions contribute to the pairing.