Variational study of the interacting spinless Su-Schrieffer-Heeger model

Abstract

We study the phase diagram and the total polarization distribution of the Su-Schrieffer-Heeger model with nearest neighbor interaction in one dimension at half-filling. To obtain the ground state wave-function, we extend the Baeriswyl variational wave function to account for alternating hopping parameters. The ground state energies of the variational wave functions compare well to exact diagonalization results. For the case of uniform hopping for all bonds, where it is known that an ideal conductor to insulator transition takes place at finite interaction, we also find a transition at an interaction strength somewhat lower than the known value. The ideal conductor phase is a Fermi sea. The phase diagram in the whole parameter range shows a resemblance to the phase diagram of the Kane-Mele-Hubbard model. We also calculate the gauge invariant cumulants corresponding to the polarization (Zak phase) and use these to reconstruct the distribution of the polarization. We calculate the reconstructed polarization distribution along a path in parameter space which connects two points with opposite polarization in two ways. In one case we cross the metallic phase line, in the other, we go through only insulating states. In the former case, the average polarization changes discontinuously after passing through the metallic phase line, while in the latter the distribution "walks across" smoothly from one polarization to its opposite. This state of affairs suggests that the correlation acts to break the chiral symmetry of the Su-Schrieffer-Heeger model, in the same way as it happens when a Rice-Mele onsite potential is turned on.

References in corpus (33)

• Topological Insulators
• Berry Phase Effects on Electronic Properties
• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Experimental realisation of the topological Haldane model
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• The Quantum-Mechanical Position Operator in Extended Systems
• Electron Localization in the Insulating State
• Interacting topological insulators: a review
• Single particle Green's functions and interacting topological insulators
• Polarization and localization in insulators: generating function approach
• Topological Insulators and Mott Physics from the Hubbard Interaction
• Topological Order Parameters for Interacting Topological Insulators
• Interaction effects and quantum phase transitions in topological insulators
• Topological invariants and interacting one-dimensional fermionic systems
• Quantum-Mechanical Position Operator and Localization in Extended Systems
• Fluctuation driven topological Hund insulators
• Rashba spin orbit coupling in the Kane-Mele-Hubbard model
• Fluctuation-induced Topological Quantum Phase Transitions in Quantum Spin Hall and Quantum Anomalous Hall Insulators
• Phase diagram of the Kane-Mele-Coulomb model
• Phase diagram of the S=1/2 quantum spin chain with bond alternation
• Phase Diagram of the Kane-Mele-Hubbard model
• Charge and spin order in one-dimensional electron systems with long-range Coulomb interactions
• Reduced density matrix and order parameters of a topological insulator
• Scaling of polarization amplitude in quantum many-body systems in one dimension
• Approximate solution of variational wave functions for strongly correlated systems: Description of bound excitons in metals and insulators
• Reconstruction of the polarization distribution of the Rice-Mele model
• Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-$1/2$ Heisenberg chain
• Helical currents in metallic Rashba strips
• Quantum quench in 2D using the variational Baeriswyl wavefunction
• Gapless Phases in an s=1/2 Quantum Spin Chain with Bond Alternation
• Variational Monte Carlo method for the Baeriswyl wavefunction: application to the one-dimensional bosonic Hubbard model
• Cumulants associated with geometric phases

Cited by in corpus (13)

• The interacting Rice-Mele model: bulk and boundaries
• Exploring interacting topological insulator of extended Su-Schrieffer-Heeger model
• Topological marker approach to an interacting Su-Schrieffer-Heeger model
• Topological insulators and superconductors based on $p$-wave magnets,electrical control and detection of a domain wall
• Bosonization of the interacting Su-Schrieffer-Heeger model
• Role of Bath-Induced Many-Body Interactions in the Dissipative Phases of the Su-Schrieffer-Heeger Model
• Many-body-localization induced protection of symmetry-protected topological order in a XXZ spin model
• Topological phases of the interacting Su-Schrieffer-Heeger model: An analytical study
• Corroborating the bulk-edge correspondence in weakly interacting 1D topological insulators
• Weakly interacting one-dimensional topological insulators: a bosonization approach
• Superfluid weight and polarization amplitude in the one-dimensional bosonic Hubbard model
• Lee-Yang formalism for phase transitions of interacting fermions using tensor networks
• Su-Schrieffer-Heeger-Hubbard model at quarter filling: effects of magnetic field and non-local interactions