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arXiv:2009.06644 · Physical Review Letters

Competing Nodal d -Wave Superconductivity and Antiferromagnetism

Xiao Yan Xu, Tarun Grover

Published May 27, 2021• 31 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevlett.126.217002

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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.
Unconventional superconductors such as cuprates often host competing nodal superconductivity and antiferromagnetism. These systems are typically modeled as a repulsive Hubbard model whose unbiased simulation suffers from the fermion sign-problem at any non-zero doping. Here we will exploit the fact that neither of these phases, the nodal d-wave superconductor or the antiferromagnet, require any doping for their existence, and construct a sign-problem-free repulsive Hubbard model with an additional bosonic field which hosts both of these phases. Using Quantum Monte Carlo (QMC) simulations, supplemented with mean-field theory 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 chiral Gross-Neveu-Heisenberg theory.
One of the most challenging problems in computational condensed matter physics is the simulation of many-electron systems by unbiased numerical techniques. Quantum Monte Carlo approaches – typically the method of choice for quantum many-body systems with bosonic or spin degrees of freedom – are oftentimes limited to handle many-electron systems due to the infamous fermion-sign problem that severely limits the computational efficiency of this otherwise very potent class of algorithms. Here we report on an elegant approach to overcome the fermion-sign problem in the study of competing quantum magnetism and superconductivity in metals. This approach allows us to study the onset of spin-density wave order in such itinerant electron systems via two-dimensional lattice models amenable to numerically exact, sign-problem-free determinantal quantum Monte Carlo simulations. The finite-temperature phase diagram of these models reveal a dome-shaped d-wave superconducting phase near the magnetic quantum phase transition. The striking similarity of these numerical results to the experimentally observed phenomenology of many unconventional superconductors points a way to a microscopic understanding of such strongly coupled systems in a controlled manner.
We present a quantum Monte Carlo study of the transition between the insulating Néel state and the nodal d -wave superconductor on the square lattice at half-filling. We access a regime of frustrated magnetic order without a sign problem using a parton representation of the electron in terms of fermionic spinons and bosonic chargons. Both partons move in a background π -flux (so the electron experiences no net flux) and are coupled to a quantum fluctuating SU(2) lattice gauge field. In contrast to earlier studies directly on the electronic degrees of freedom, we find evidence for a second-order deconfined quantum phase transition at which both the Néel and d -wave superconductivity orders vanish continuously. We compute correlators of the spinon-chargon composite with the same quantum numbers as the electron: we find a gapless Dirac dispersion inside the d -wave superconductor, turning into a gapped dispersion in the antiferromagnet.
Abstract We investigate a quantum criticality of an antiferromagnetic phase transition in the Hubbard model on a square lattice with a d-wave pairing field by large-scale auxiliary-field quantum Monte Carlo simulations. Since the d-wave pairing filed induces Dirac cones in the non-interacting single-particle spectrum, the quantum criticality should correspond to the chiral Heisenberg universality class in terms of the Gross-Neveu theory, which is the same as those expected in the Hubbard model on the honeycomb lattice, despite the unit cells being different (e.g., they contain one and two sites, respectively). We show that both the two phase transitions, expected to occur on the square and on the honeycomb lattices, indeed have the same quantum criticality. We also argue that details of the models, i.e., the way of counting the total number N of fermion components and the anisotropy of the Dirac cones, do not change the critical exponents.
How superconductivity emerges in the vicinity of an antiferromagnetic insulating state is a long-standing issue of strong correlation physics. We study the transition from an antiferromagnetic insulator to a superconductor by hole doping based on a bilayer generalization of a Hubbard model. The projector quantum Monte Carlo simulations are employed, which are sign problem free both at and away from half filling. An anisotropic Ising antiferromagnetic Mott insulating phase occurs at half filling, which is weakened by hole doping. Below a critical doping value, antiferromagnetism coexists with the singlet superconductivity, which is a pairing across each rung with an extended sss-wave symmetry. As doping further increases, the antiferromagnetic order vanishes, leaving only a superconducting phase. These results provide important information on how superconductivity appears upon doping the parent Mott-insulating state.
We compute transport and thermodynamic properties of a two-band spin-fermion model describing itinerant fermions in two dimensions interacting via Z2{Z}_{2}Z2​ antiferromagnetic quantum critical fluctuations by means of a sign-problem-free quantum Monte Carlo approach. We show that the phase diagram of this model indeed contains a ddd-wave superconducting phase at low enough temperatures. However, a crucial question that arises is whether a non-Fermi-liquid metallic regime exists above Tc{T}_{c}Tc​, exhibiting hallmark strange-metal transport phenomenology. Interestingly, we find that this version of the model describes a non-Fermi-liquid metallic regime that displays an approximately TTT-linear resistivity above Tc{T}_{c}Tc​ for a strong fermion-boson interaction. Using the Nernst-Einstein relation, our QMC results also show that this strange metal phase exhibits a crossover from being characterized by a charge compressibility given approximately by ${\ensuremath{\chi}}_{c}\ensuremath{\sim}1/T$ at high temperatures to being described by a charge diffusivity consistent with the scaling ${D}_{c}\ensuremath{\sim}1/T$ at low temperatures. Therefore, our paper adds support to the view that the Z2{Z}_{2}Z2​ antiferromagnetic spin-fermion model at strong coupling can be considered a minimal model that describes both unconventional superconductivity and strange metallicity, which are fundamentally interconnected in many important strongly correlated quantum materials.