Quantum phase transitions from analysis of the polarization amplitude

Abstract

In the modern theory of polarization, polarization itself is given by a geometric phase. In calculations for interacting systems the polarization and its variance are obtained from the polarization amplitude. We interpret this quantity as a discretized characteristic function and derive formulas for its cumulants and moments. In the case of a non-interacting system, our scheme leads to the gauge-invariant cumulants known from polarization theory. We study the behavior of such cumulants for several interacting models. In a one-dimensional system of spinless fermions with nearest neighbor interaction the transition at which gap closure occurs can be clearly identified from the finite size scaling exponent of the variance. When next nearest neighbor interactions are turned on a model with a richer phase diagram emerges, but the finite size scaling exponent is still an effective way to identify the localization transition.

References in corpus (16)

• Berry Phase Effects on Electronic Properties
• Maximally-localized generalized Wannier functions for composite energy bands
• Maximally localized Wannier functions: Theory and applications
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• The Quantum-Mechanical Position Operator in Extended Systems
• Electron Localization in the Insulating State
• Polarization and localization in insulators: generating function approach
• Resonance-enhanced optical nonlinearity in the Weyl semimetal TaAs
• Quantum-Mechanical Position Operator and Localization in Extended Systems
• Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension
• Phase diagram of the half-filled one-dimensional t-V-V' model
• Inequivalent Berry phases for the bulk polarization
• Insulator, conductor and commensurability: a topological approach
• Scaling of polarization amplitude in quantum many-body systems in one dimension
• dc conductivity as a geometric phase
• Reconstruction of the polarization distribution of the Rice-Mele model

Cited by in corpus (19)

• Scaling and renormalization in the modern theory of polarization: application to disordered systems
• Topological invariants based on generalized position operators and application to the interacting Rice-Mele model
• Beyond the Berry Phase: Extrinsic Geometry of Quantum States
• Scaling of the bulk polarization in extended and localized phases of a quasiperiodic model
• Interaction driven polarization shift in the $t-V-V^{\prime }$ lattice fermion model at half filling: emergent Haldane phase
• Geometric cumulants associated with adiabatic cycles crossing degeneracy points: Application to finite size scaling of metal-insulator transitions in crystalline electronic systems
• A numerical study of the localization transition of Aubry-André type models
• Polarization amplitude near quantum critical points
• Calculating the polarization in bi-partite lattice models: application to an extended Su-Schrieffer-Heeger model
• Many-body-localization induced protection of symmetry-protected topological order in a XXZ spin model
• Topological indicators for systems with open boundaries: Application to the Kitaev wire
• Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field
• Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model
• Characterizing the Many Body Localization Crossover as a Metal-Insulator Transition: Localization length from Polarization and Quantum Metric
• Identification of gapless phases by a twisting operator
• Diagnosing energy gap in quantum spin liquids via polarization amplitude
• From generating functions to the geometric Binder cumulant
• Disorder averaging in random lattice models with periodic boundary conditions: Application to models with uncorrelated and correlated disorder
• Polarization-based indices in quantum many-body systems: validity and extension beyond one dimension