$Z_2$-gauge theory description of the Mott transition in infinite dimensions

Abstract

The infinite dimensional half-filled Hubbard model can be mapped exactly with no additional constraint onto a model of free fermions coupled in a $Z_2$ gauge-invariant manner to auxiliary Ising spins in a transverse field. In this slave-spin representation, the zero-temperature insulator-to-metal transition translates into spontaneous breaking of the local $Z_2$ gauge symmetry, which is not forbidden in infinite dimensions, thus endowing the Mott transition of an order parameter that is otherwise elusive in the original fermion representation. We demonstrate this interesting scenario by exactly solving the effective spin-fermion model by dynamical mean-field theory both at zero and at finite temperature.

10 pages, 8 figures

References in corpus (9)

• The numerical renormalization group method for quantum impurity systems
• Sum-rule Conserving Spectral Functions from the Numerical Renormalization Group
• Cluster Dynamical Mean Field Theory of the Mott Transition
• A Numerical Renormalization Group approach to Green's Functions for Quantum Impurity Models
• Orbital selective Mott transition in multi-band systems: slave-spin representation and dynamical mean-field theory
• Time-Dependent Mean Field Theory for Quench Dynamics in correlated electron systems
• Gutzwiller description of non-magnetic Mott insulators: a dimer lattice model
• Dynamically Generated Double Occupancy as a Probe of Cold Atom Systems
• Spin-charge separation and simultaneous spin and charge Kondo effect

Cited by in corpus (19)

• Disorder-Free Localization
• Dynamical Localization in ${\mathbb{Z}}_2$ Lattice Gauge Theories
• Simple ${\mathbb{Z}}_2$ lattice gauge theories at finite fermion density
• Two-particle Fermi liquid parameters at the Mott transition: Vertex divergences, Landau parameters, and incoherent response in dynamical mean-field theory
• Logarithmic spreading of out-of-time-ordered correlators without many-body localization
• Fractionalized Metal in a Falicov-Kimball Model
• Analytical slave-spin mean-field approach to orbital selective Mott insulators
• Non-equilibrium and non-homogeneous phenomena around a first-order quantum phase transition
• Nonequilibrium self-energy functional approach to the dynamical Mott transition
• Renormalized dispersing multiplets in the spectrum of nearly Mott localized systems
• Interplay of charge and spin dynamics after an interaction quench in the Hubbard model
• Orthogonal metal in the Hubbard model with liberated slave spins
• Dynamic charge Kondo effect and a slave fermion approach to the Mott transition
• Dynamics of a Lattice Gauge Theory with Fermionic Matter -- Minimal Quantum Simulator with Time-Dependent Impurities in Ultracold Gases
• Emergent statistical bubble localization in a Z2 lattice gauge theory
• Manumitting slave-spins in the Anderson impurity model
• Exactly solvable Majorana-Anderson impurity models
• Semiconductor of spinons: from Ising band insulator to orthogonal band insulator
• Slave-spin approach to the Anderson-Josephson quantum dot