Mott Insulators Atomic Limit - View Electrons in Real Space

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Mott insulators Atomic limit - view electrons in real space Virtual system: lattice of H-Atoms: aB << d 2aB d H Mott insulators Atomic limit - view electrons in real space lattice of H-Atoms: Virtual system: aB << d 2aB d hopping - electron transfer - H H + -t ionization energy H delocalization localization kinetic energy charge excitation energy metal Mott insulator Mott insulators Atomic limit - view electrons in real space lattice of H-Atoms: Virtual system: aB << d 2aB d hopping - electron transfer ionization energy H -t S = 1/2 Mott isolator effective low-energy model low-energy physics no charge fluctuation only spin fluctuation Mott insulators Metal-insulator transition from the insulating side Hubbard-model: n.n. hopping onsite repulsion density: n=1 „ground state“ t = 0 E charge excitation U h d Mott insulators Metal-insulator transition from the insulating side Hubbard-model: n.n. hopping onsite repulsion density: n=1 t > 0 „ground state“ E W = 4d t U charge excitation h d metal-insulator transition: Uc = 4dt Mott insulators Metal-insulator transition from the metallic side h d tight-binding model density empty sites h = 1/4 doubly occupied sites d = 1/4 half-filled singly occupied sites s = 1/2 conduction band reducing mobility Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side Gutzwiller-approach: variational diminish double-occupancy uncorrelated state variational groundstate density of doubly occupied sites renormalized hopping Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side densities: 1 electron density density of singly occupied sites with spin density of singly occupied sites with spin d density of doubly occupied sites h density of empty sites no spin polarization half-filling sum rule Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side hopping probability: sector of fixed d correlated renormalization uncorrelated factor analogous with same gt d changed, not in sector Mott insulators Gutzwiller approximation Metal-insulator transition from the metallic side correlated renormalization uncorrelated factor minimize w.r.t. d per site Brinkmann-Rice (1970) Mott insulators Gutzwiller approximation optical conductivity: Drude weight single particle spectral function coherent A quasiparticles metallic quasiparticle weight: variational lower upper E at MIT Hubbard band Hubbard band A insulating renormalizedµ hoppingE Mott insulators Gutzwiller approximation Fermi liquid properties within Gutzwiller approximation: n n k renormalized k Gutzwiller momentum Z nin Z distribution k nout k kF kF half-filling renormalized hopping particle-hole symmetry Mott insulators Gutzwiller approximation Fermi liquid properties within Gutzwiller approximation: n n k renormalized k Gutzwiller momentum Z nin Z distribution k nout k kF kF quasiparticle weight compressibility half-filling half-filling renormalized hopping renormalized hopping particle-hole symmetry particle-hole symmetry.

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9 Quantum Phases and Phase Transitions of Mott Insulators
9 Quantum Phases and Phase Transitions of Mott Insulators Subir Sachdev Department of Physics, Yale University, P.O. Box 208120, New Haven CT 06520-8120, USA, [email protected] Abstract. This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. Mott insulators in the simplest class have an even number of S =1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic ﬁeld. The case of an odd number of S =1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S =1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-Ginzburg-Wilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations. 9.1 Introduction The physics of Mott insulators in two and higher dimensions has enjoyed much attention since the discovery of cuprate superconductors. While a quan- titative synthesis of theory and experiment in the superconducting materials remains elusive, much progress has been made in describing a number of antiferromagnetic Mott insulators.
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Structural Superfluid-Mott Insulator Transition for a Bose Gas in Multi
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Arxiv:2002.00554V2 [Cond-Mat.Str-El] 28 Jul 2020
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