Density waves in strongly correlated quantum chains

Abstract

We review exact numerical results for one-dimensional quantum systems with half-filled bands. The topics covered include Peierls transitions in Holstein, Fröhlich, Su-Schrieffer-Heeger, and Heisenberg models with quantum phonons, competing fermion-boson and fermion-fermion interactions, as well as symmetry-protected topological states in fermion and anyon models.

15 pages, 17 figures; focused review article for an EPJ B topical issue on "Coexistence of long-range orders in low-dimensional systems". Comments welcome!

References in corpus (42)

• Many-Body Physics with Ultracold Gases
• Classification of topological insulators and superconductors in three spatial dimensions
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Hidden order in 1D Bose insulators
• Rise and fall of hidden string order of lattice bosons
• Correlation effects in two-dimensional topological insulators
• Topological invariants and interacting one-dimensional fermionic systems
• Diagrammatic Determinantal methods: projective schemes and applications to the Hubbard-Holstein model
• Phase diagram of the one-dimensional half-filled extended Hubbard model
• Infinite size density matrix renormalization group, revisited
• Metallicity in the half-filled Holstein-Hubbard model
• Ground-state phase diagram of the one-dimensional half-filled extended Hubbard model
• Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study
• Phase diagram of the one dimensional Hubbard-Holstein Model at 1/2 and 1/4 filling
• Bound state formation and nature of the excitonic insulator phase in the extended Falicov-Kimball model
• Functional Renormalization Group Analysis of the Half-filled One-dimensional Extended Hubbard Model
• Quantum lattice dynamical effects on the single-particle excitations in 1D Mott and Peierls insulators
• Spectral and Entanglement Properties of the Bosonic Haldane Insulator
• Excitation spectra and spin gap of the half-filled Holstein-Hubbard model
• Spin and charge dynamics of the one-dimensional extended Hubbard model
• Comparative density-matrix renormalization group study of symmetry-protected topological phases in spin-1 chain and Bose-Hubbard models
• Identifying a bath-induced Bose liquid in interacting spin-boson models
• Excitation spectra and correlation functions of quantum Su-Schrieffer-Heeger models
• Boson-controlled quantum transport
• Coupling-dependent rates of energy transfers from photoexcited Mott insulators to lattice vibrations
• Effect of Electron-Phonon Interaction Range for a Half-Filled Band in One Dimension
• The quantum vs classical aspects of one dimensional electron-phonon systems revisited by the renormalization group method
• Anyonic Haldane insulator in one dimension
• Nature of ground states in one-dimensional electron-phonon Hubbard models at half-filling
• Dynamic charge correlations near the Peierls transition
• Quantum phase transition in a 1D transport model with boson affected hopping: Luttinger liquid versus charge-density-wave behavior
• Phonon spectral function of the one-dimensional Holstein-Hubbard model
• Interplay of Site and Bond Electron-Phonon Coupling in One Dimension
• Phase diagram of the asymmetric Hubbard model
• Bosonization study of quantum phase transitions in the one-dimensional asymmetric Hubbard model
• Directed-Loop Quantum Monte Carlo Method for Retarded Interactions
• Phase diagram of the spin-Peierls chain with local coupling
• Correlation-induced metal insulator transition in a two-channel fermion-boson model
• Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
• Phase diagram and isotope effects of the quasi-one-dimensional electron gas coupled to phonons
• Analytical approach to the quantum-phase transition in the one-dimensional spinless Holstein model
• Optical phonons for Peierls chains with long-range Coulomb interactions

Cited by in corpus (17)

• Charge Order in the Holstein Model on a Honeycomb Lattice
• Symmetry-Breaking Topological Insulators in the ${\mathbb{Z}}_2$ Bose-Hubbard Model
• Valence-bond solid to antiferromagnet transition in the two-dimensional Su-Schrieffer-Heeger model by Langevin dynamics
• Strong Coupling Limit of the Holstein-Hubbard Model
• Zero-Temperature Phases of the 2D Hubbard-Holstein Model: A Non-Gaussian Exact Diagonalization Study
• Dominant charge-density-wave correlations in the Holstein model on the half-filled square lattice
• Competing Orders and Unconventional Criticality in the Su-Schrieffer-Heeger Model
• Cooperative enhancement of superconducting correlations by electron-electron and electron-phonon interactions in the quarter-filled band
• Thermal and quantum lattice fluctuations in Peierls chains
• Theory of electron-phonon interactions in extended correlated systems probed by resonant inelastic x-ray scattering
• Importance of coupling strength in shaping electron energy loss and phonon spectra of phonon-plasmon systems
• The one-dimensional Holstein model revisited
• Metal-insulator transition of spinless fermions coupled to dispersive optical bosons
• Grand-canonical Peierls theory for atomic wires on substrates
• Topological analog of the magnetic bit within the Su-Schrieffer-Heeger-Holstein model
• Phase diagram of the two-dimensional Hubbard-Holstein model: enhancement of $s$-wave pairing between charge and magnetic orders
• Insulating and metallic phases in the one-dimensional Hubbard-Su-Schrieffer-Heeger model: Insights from a backflow-inspired variational wave function