Quantum-Mechanical Position Operator and Localization in Extended Systems

Abstract

We introduce a fundamental complex quantity, $z_L$, which allows us to discriminate between a conducting and non-conducting thermodynamic phase in extended quantum systems. Its phase can be related to the expectation value of the position operator, while its modulus provides an appropriate definition of a localization length. The expressions are valid for {\it any} fractional particle filling. As an illustration we use $z_L$ to characterize insulator to ``superconducting'' and Mott transitions in one-dimensional lattice models with infinite on-site Coulomb repulsion at quarter filling.

4 pages, REVTEX, 1 ps figures

References in corpus (4)

• The Quantum-Mechanical Position Operator in Extended Systems
• Electron Localization in the Insulating State
• Berry phases in superconducting transitions
• Superconductivity with s and p-symmetries in an extended Hubbard model with correlated hopping

Cited by in corpus (75)

• Polarization and localization in insulators: generating function approach
• Symmetry and Topological Order
• Many-Body Electric Multipole Operators in Extended Systems
• A Short Course on Topological Insulators: Band-structure topology and edge states in one and two dimensions
• A generalization of Bloch's theorem for arbitrary boundary conditions: Theory
• A quantum Monte Carlo study of the one-dimensional ionic Hubbard model
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension
• Electric polarization as a nonquantized topological response and boundary Luttinger theorem
• Inequivalent Berry phases for the bulk polarization
• Dielectric response of modified Hubbard models with neutral-ionic and Peierls transitions
• Filling-enforced constraint on the quantized Hall conductivity on a periodic lattice
• Phase Diagrams from Topological Transitions: The Hubbard Chain with Correlated Hopping
• Quantum Phase Diagram of the t-Jz Chain Model
• Extraction of many-body Chern number from a single wave function
• Non-local order parameters for the 1D Hubbard model
• Quantum Spin Pump in S=1/2 antiferromagnetic chains -Holonomy of phase operators in sine-Gordon theory-
• Splitting of topological charge pumping in an interacting two-component fermionic Rice-Mele Hubbard model
• Quantum phase diagram of the generalized ionic Hubbard model for AB${}_n$ chains
• Ground-state phase diagram of the one-dimensional Hubbard-model with an alternating potential
• The dimerized phase of ionic Hubbard models
• Insulator, conductor and commensurability: a topological approach
• Locality properties and Wannier functions for interacting systems
• Electron localization : band-by-band decomposition, and application to oxides
• Finite-temperature topological invariant for interacting systems
• Quantum phase diagram of the half filled Hubbard model with bond-charge interaction
• Topological invariants based on generalized position operators and application to the interacting Rice-Mele model
• Scaling of polarization amplitude in quantum many-body systems in one dimension
• Robustness of topological order against disorder
• Doped AB_2 Hubbard Chain: Spiral, Nagaoka and RVB States, Phase Separation and Luttinger Liquid Behavior
• Quantum phase transitions from analysis of the polarization amplitude
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• Interaction driven polarization shift in the $t-V-V^{\prime }$ lattice fermion model at half filling: emergent Haldane phase
• Fock space embedding theory for strongly correlated topological phases
• Ferrotoroidic Moment as a Quantum Geometric Phase
• Generalized Coherent States as Preferred States of Open Quantum Systems
• Local Chern Marker for Periodic Systems
• Variational study of the interacting spinless Su-Schrieffer-Heeger model
• Theory of Dipole Insulators
• Geometric cumulants associated with adiabatic cycles crossing degeneracy points: Application to finite size scaling of metal-insulator transitions in crystalline electronic systems
• Phase diagram of the $t-t^{\prime }-U$ chain at half filling
• Lieb Schultz Mattis-Type Theorems and Other Non-perturbative Results for Strongly Correlated Systems with Conserved Dipole Moments
• Geometric Phase and Quantum Phase Transition : Two-Band Model
• Polarization amplitude near quantum critical points
• Geometric Phases and Critical Phenomena in a Chain of Interacting Spins
• Characterization of topological insulators based on the electronic polarization with spiral boundary conditions
• Quarter-filled extended Hubbard model with alternating transfer integral: Two-dimensional Ising transition in the ground state
• Absence of topology in Gaussian mixed states of bosons
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Phase diagram of the extended Hubbard chain with charge-dipole interactions
• Two-dimensional Thouless pumping in time-space crystalline structures
• Extraction of topological information in Tomonaga-Luttinger liquids
• Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field
• Many-body position operator in lattice fermionic systems with periodic boundary conditions
• Intrinsic and extrinsic geometries of correlated many-body states
• Phase diagram of the $Cu{O}_3$ chains in $YB{a}_{2}C{u}_3{O}_{6+X}$ and $PrB{a}_{2}C{u}_3{O}_{6+X}$
• Electronic polarization in non-Bloch band theory
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Quantized polarization in a generalized Rice-Mele model at arbitrary filling
• Topological characterization of modified Kane-Mele-Rashba models via local spin Chern marker
• Eight-dimensional topological systems simulated using time-space crystalline structures
• Symmetry, topology, duality, chirality, and criticality in a spin-1/2 XXZ ladder with a four-spin interaction
• Probing entanglement dynamics and topological transitions on noisy intermediate-scale quantum computers
• Multiparticle quantum walk: a dynamical probe of topological many-body excitations
• Topologically protected quantized changes of the distance between atoms
• Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model
• Identification of gapless phases by a twisting operator
• Diagnosing energy gap in quantum spin liquids via polarization amplitude
• Absorbance marker: Detection of quantum geometry and spread of Wannier function in disordered 2D semiconductors
• Microscopic Scenario for Striped Superconductors
• Electrostatically-induced topological phase transitions in polyacetylene molecules
• Phase diagram of a spin-1/2 Heisenberg ladder with a chirality-chirality interaction
• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension
• From generating functions to the geometric Binder cumulant
• Quantized single-particle Thouless pump induced by topology transfer from a Chern insulator at finite temperature