SU(2) gauge theory of the pseudogap phase in the two-dimensional Hubbard model

Abstract

We present a SU(2) gauge theory of fluctuating magnetic order in the two-dimensional Hubbard model. The theory is based on a fractionalization of electrons in fermionic chargons and bosonic spinons. The chargons undergo Néel or spiral magnetic order below a density dependent transition temperature $T^{\ast }$. Fluctuations of the spin orientation are described by a non-linear sigma model obtained from a gradient expansion of the spinon action. The spin stiffnesses are computed from a renormalization group improved random phase approximation. Our approximations are applicable for a weak or moderate Hubbard interaction. The spinon fluctuations prevent magnetic long-range order of the electrons at any finite temperature. The phase with magnetic chargon order exhibits many features characterizing the pseudogap regime in high-$T_c$ cuprates: a strong reduction of charge carrier density, a spin gap, Fermi arcs, and electronic nematicity.

arXiv comment17 pages, 7 figures

References in corpus (45)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Functional renormalization group approach to correlated fermion systems
• The nonperturbative functional renormalization group and its applications
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Theory of Underdoped Cuprates
• The remarkable underlying ground states of cuprate superconductors
• Topological order, emergent gauge fields, and Fermi surface reconstruction
• Efficient Parametrization of the Vertex Function, $\Omega$-Scheme, and the (t,t')-Hubbard Model at Van Hove Filling
• The temperature-flow renormalization group and the competition between superconductivity and ferromagnetism
• Fluctuation diagnostics of the electron self-energy: Origin of the pseudogap physics
• Crossover and scaling in a nearly antiferromagnetic Fermi liquid in two dimensions
• Universal Magnetic Properties of Frustrated Quantum Antiferromagnets in Two Dimensions
• Quantum Phase Transition in Frustrated Two-Dimensional Antiferromagnets
• Incommensurate magnetic order and phase separation in the two-dimensional Hubbard model with nearest and next-nearest neighbor hopping
• Topological order in the pseudogap metal
• Pseudogap and Fermi surface topology in the two-dimensional Hubbard model
• High-performance functional renormalization group calculations for interacting fermions
• Theory of single-particle properties of the Hubbard model
• Fluctuating spin density waves in metals
• Gauge theory for the cuprates near optimal doping
• Antiferromagnetism and single-particle properties in the two-dimensional half-filled Hubbard model: a non-linear sigma model approach
• A Renormalization Group Study of Helimagnets in D=2+EPSILON Dimensions
• Magnetic Phases of the 2D Hubbard Model at Low Doping
• Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group
• Coexistence of incommensurate magnetism and superconductivity in the two-dimensional Hubbard model
• Frequency Dependent Vertex Functions of the (t,t')-Hubbard Model at Weak Coupling
• Fermi surface reconstruction and drop of Hall number due to spiral antiferromagnetism in high-$T_c$ cuprates
• Hall effect and Fermi surface reconstruction via electron pockets in the high-$T_c$ cuprates
• Competing order in correlated electron systems made simple: Consistent fusion of functional renormalization and mean-field theory
• Non-separable frequency dependence of two-particle vertex in interacting fermion systems
• The novel metallic states of the cuprates: Fermi liquids with topological order, and strange metals
• Intertwining topological order and broken symmetry in a theory of fluctuating spin density waves
• Dynamical functional renormalization group computation of order parameters and critical temperatures in the two-dimensional Hubbard model
• The massive $C{P}^{N-1}$ model for frustrated spin systems
• Phenomenological theories of the low-temperature pseudogap: Hall number, specific heat and Seebeck coefficient
• Longitudinal conductivity and Hall coefficient in two-dimensional metals with spiral magnetic order
• Charge carrier drop at the onset of pseudogap behavior in the two-dimensional Hubbard model
• Thermal and electrical transport in metals and superconductors across antiferromagnetic and topological quantum transitions
• Spin fluctuations and pseudogap in the two-dimensional half-filled Hubbard model at weak coupling
• Accessing the ordered phase of correlated Fermi systems: vertex bosonization and mean-field theory within the functional renormalization group
• Dynamically enhanced magnetic incommensurability: Effects of local dynamics on non-local spin-correlations in a strongly correlated metal
• Hall effect in cuprates with incommensurate spin-density wave
• SO(3) nonlinear $\sigma$ model for a doped quantum helimagnet
• Local Ward identities for collective excitations in fermionic systems with spontaneously broken symmetries
• Simultaneous drop in mean free path and carrier density at the pseudogap onset in high-$T_c$ cuprates

Cited by in corpus (21)

• A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice
• Comprehensive mean-field analysis of magnetic and charge orders in the two-dimensional Hubbard model
• Mott transition and pseudogap of the square-lattice Hubbard model: results from center-focused cellular dynamical mean-field theory
• Spin density wave, Fermi liquid, and fractionalized phases in a theory of antiferromagnetic metals using paramagnons and bosonic spinons
• Strange metals and black holes: insights from the Sachdev-Ye-Kitaev model
• Commensurate and incommensurate magnetic order in the doped two-dimensional Hubbard model: dynamical mean-field theory analysis
• The foot, the fan, and the cuprate phase diagram: Fermi-volume-changing quantum phase transitions
• Spiral to stripe transition in the two-dimensional Hubbard model
• Quantum oscillations in the hole-doped cuprates and the confinement of spinons
• Antiferromagnetic and spin spiral correlations in the doped two-dimensional Hubbard model: gauge symmetry, Ward identities, and dynamical mean-field theory analysis
• Electrons interacting with Goldstone modes and the rotating frame
• Fractionalized Fermi liquids and the cuprate phase diagram
• Non-Perturbative Feats in the Physics of Correlated Antiferromagnets
• Geometric orthogonal metals: Hidden antiferromagnetism and pseudogap from fluctuating stripes
• Canted magnetism and ${\mathbb{Z}}_2$ fractionalization in metallic states of the Lieb lattice Hubbard model near quarter filling
• Mean-field analysis of a Hubbard interaction on Bernal Bilayer Graphene
• Thermopower across Fermi-volume-changing quantum phase transitions without translational symmetry breaking
• Spin susceptibility in a pseudogap state with fluctuating spiral magnetic order
• Yamaji effect in models of underdoped cuprates
• Frequency dependence of temporal spin stiffness and short-range magnetic order in the doped two-dimensional Hubbard model
• Non-Fermi Liquid Behavior of the $t$-$J$ Model in the Strange Metal Phase: $U(1)$ Gauge Theory Consistent with Local Constraints