Deconfined quantum criticality of nodal $d$-wave superconductivity, Néel order, and charge order on the square lattice at half-filling

Abstract

We consider a SU(2) lattice gauge theory on the square lattice, with a single fundamental complex fermion and a single fundamental complex boson on each lattice site. Projective symmetries of the gauge-charged fermions are chosen so that they match with those of the spinons of the $\pi$-flux spin liquid. Global symmetries of all gauge-invariant observables are chosen to match with those of the particle-hole symmetric electronic Hubbard model at half-filling. Consequently, both the fundamental fermion and fundamental boson move in an average background $\pi$-flux, their gauge-invariant composite is the physical electron, and eliminating gauge fields in a strong gauge-coupling expansion yields an effective extended Hubbard model for the electrons. The SU(2) gauge theory displays several confining/Higgs phases: a nodal $d$-wave superconductor, and states with Néel, valence-bond solid, charge, or staggered current orders. There are also a number of quantum phase transitions between these phases which are very likely described by 2+1 dimensional deconfined conformal gauge theories, and we present large flavor expansions for such theories. These include the phenomenologically attractive case of a transition between a conventional insulator with a charge gap and Néel order, and a conventional $d$-wave superconductor with gapless Bogoliubov quasiparticles at 4 nodal points in the Brillouin zone. We also apply our approach to the honeycomb lattice, where we find a bicritical point at the junction of Néel, valence bond solid (Kekulé), and Dirac semi-metal phases.

arXiv comment47 pages, 20 figures

References in corpus (54)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Theory of Underdoped Cuprates
• Fractionalized Fermi liquids
• A Phenomenological Theory of The Pseudogap State
• Deconfined quantum critical points: symmetries and dualities
• Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state
• Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution
• Evolution of electronic structure of doped Mott insulators - reconstruction of poles and zeros of Green's function
• Fermi arcs and the hidden zeros of the Green's function in the pseudogap state
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Quantum criticality of U(1) gauge theories with fermionic and bosonic matter in two spatial dimensions
• Algebraic charge liquids
• Spectral functions of the Higgs mode near two-dimensional quantum critical points
• Theory of Quasi-Particles in the Underdoped High Tc Superconducting State
• High Temperature Superconductivity in a Lightly Doped Quantum Spin Liquid
• Extending Luttinger's theorem to Z(2) fractionalized phases of matter
• Imaging tunable quantum Hall broken-symmetry orders in graphene
• Effective theory of Fermi pockets in fluctuating antiferromagnets
• Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations
• SU(2) gauge theory of the Hubbard model and application to the honeycomb lattice
• From spinon band topology to the symmetry quantum numbers of monopoles in Dirac spin liquids
• Anomalies in the pseudogap phase of the cuprates: Competing ground states and the role of umklapp scattering
• Fermi surface transformation at the pseudogap critical point of a cuprate superconductor
• Hole dynamics in an antiferromagnet across a deconfined quantum critical point
• Multicritical deconfined quantum-criticality and Lifshitz point of a helical valence-bond phase
• Mott insulators with boundary zeros
• Luttinger-volume violating Fermi liquid in the pseudogap phase of the cuprate superconductors
• Breakup of the Fermi surface near the Mott transition in low-dimensional systems
• Quantum Transition between an Antiferromagnetic Mott Insulator and $d_{x^2-y^2}$ Superconductor in Two Dimensions
• From the pseudogap metal to the Fermi liquid using ancilla qubits
• The $\mathrm{SO}(5)$ Deconfined Phase Transition under the Fuzzy Sphere Microscope: Approximate Conformal Symmetry, Pseudo-Criticality, and Operator Spectrum
• Quantum Phases of the Shraiman-Siggia Model
• Fractionalized Fermi liquid with bosonic chargons as a candidate for the pseudogap metal
• Monopole Quantum Numbers in the Staggered Flux Spin Liquid
• The underdoped cuprates as fractionalized Fermi liquids: transition to superconductivity
• A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice
• Quantum phase transitions in Dirac fermion systems
• Projected wave functions for fractionalized phases of quantum spin systems
• Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula
• Competing nodal d-wave superconductivity and antiferromagnetism
• Deconfined criticality and a gapless ${\mathbb{Z}}_2$ spin liquid in the square lattice antiferromagnet
• Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet
• Geometric phases and competing orders in two dimensions
• Fermionic spinon theory of square lattice spin liquids near the Néel state
• Spin-liquid insulators can be Landau's Fermi liquids
• Superconducting valence bond fluid in lightly doped 8-leg $t$-$J$ cylinders
• Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice
• Bogoliubov Quasiparticle on the Gossamer Fermi Surface in Electron-Doped Cuprates
• Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons
• Emergence of nodal Bogoliubov quasiparticles across the transition from the pseudogap metal to the d-wave superconductor
• Anisotropic deconfined criticality in Dirac spin liquids

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• The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
• Fractionalized Fermi liquids and the cuprate phase diagram
• Vortex structure in a $d$-wave superconductor obtained by a confinement transition from the pseudogap metal
• Spin-Peierls instability of deconfined quantum critical points
• Deconfined criticality as intrinsically gapless topological state in one dimension
• Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking