Zero-Temperature Phases of the 2D Hubbard-Holstein Model: A Non-Gaussian Exact Diagonalization Study

Abstract

We propose a numerical method which embeds the variational non-Gaussian wavefunction approach within exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wavefunction that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wavefunction exactly, thus taking into account high-order correlation effects beyond the Gaussian level. Keeping the full electronic Hilbert space, the complexity is increased only by a polynomial scaling factor relative to the exact diagonalization calculation for pure electrons. As an example, we use this method to study ground-state properties of the two-dimensional Hubbard-Holstein model, providing evidence for the existence of intervening phases between the spin and charge-ordered states. In particular, we find one of the intervening phases has strong charge susceptibility and binding energy, but is distinct from a charge-density-wave ordered state, while the other intervening phase displays superconductivity at weak couplings. This method, as a general framework, can be extended to treat excited states and dynamics, as well as a wide range of systems with both electron-electron and electron-boson interactions.

arXiv comment19 pages, 17 figures

References in corpus (53)

• The density-matrix renormalization group in the age of matrix product states
• Correlated Electrons in High Temperature Superconductors
• Continuous-time Monte Carlo methods for quantum impurity models
• Real time evolution using the density matrix renormalization group
• Evidence for ubiquitous strong electron-phonon coupling in high-temperature superconductors
• Continuous Time Quantum Monte Carlo method for fermions
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Interplay of electron-lattice interactions and superconductivity in Bi2Sr2CaCu2O8+d
• Electron-phonon coupling reflecting dynamic charge inhomogeneity in copper-oxide superconductors
• Strongly correlated fermions after a quantum quench
• Missing Quasiparticles and the Chemical Potential Puzzle in the Doping Evolution of the Cuprate Superconductors
• The Holstein Polaron
• Numerical evidence of fluctuating stripes in the normal state of high-Tc cuprate superconductors
• Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
• Polaron in t-J model
• Ground-state phase diagram of the square lattice Hubbard model from density matrix embedding theory
• Rapid change of superconductivity and electron-phonon coupling through 19% doping in Bi2212
• Variational Study of Fermionic and Bosonic Systems with Non-Gaussian States: Theory and Applications
• Improved energy extrapolation with infinite projected entangled-pair states applied to the 2D Hubbard model
• Intermediate phase of the one dimensional half-filled Hubbard-Holstein model
• Geometry of variational methods: dynamics of closed quantum systems
• Competition among various charge-inhomogeneous states and d-wave superconducting state in Hubbard models on square lattices
• Competition between antiferromagnetic and charge density wave order in the half filled Hubbard-Holstein model
• Metallicity in the half-filled Holstein-Hubbard model
• Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model
• Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study
• Optical absorption and single-particle excitations in the 2D Holstein t-J model
• Variational study of U(1) and SU(2) lattice gauge theories with Gaussian states in 1+1 dimensions
• Phonon dispersion and the competition between pairing and charge order
• Ordered phases in the Holstein-Hubbard model: Interplay of strong Coulomb interaction and electron-phonon coupling
• Competition among Superconducting, Antiferromagnetic, and Charge Orders with Intervention by Phase Separation in the 2D Holstein-Hubbard Model
• Optimized phonon approach for the diagonalization of electron-phonon problems
• Superconductivity, charge-density waves, antiferromagnetism, and phase separation in the Hubbard-Holstein model
• Solving quantum impurity problems in and out of equilibrium with variational approach
• Excitation spectra and spin gap of the half-filled Holstein-Hubbard model
• Density-matrix renormalization group study of pairing when electron-electron and electron-phonon interactions coexist: effect of the electronic band structure
• Light-Enhanced Spin Fluctuations and d-Wave Superconductivity at a Phase Boundary
• Gaussian time dependent variational principle for the Bose-Hubbard model
• Dominant charge-density-wave correlations in the Holstein model on the half-filled square lattice
• Variational principle for quantum impurity systems in and out of equilibrium: application to Kondo problems
• Phonon Effects on Spin-Charge Separation in One Dimension
• Density matrix embedding theory for interacting electron-phonon systems
• Krylov-space approach to the equilibrium and the nonequilibrium single-particle Green's function
• Finite-size effects in Luther-Emery phases of Holstein and Hubbard models
• Renormalization of spectra by phase competition in the half-filled Hubbard-Holstein model
• Competing interactions and symmetry breaking in the Hubbard-Holstein model
• Density waves in strongly correlated quantum chains
• A variational approach for many-body systems at finite temperature
• Using Nonequilibrium Dynamics to Probe Competing Orders in a Mott-Peierls System
• Peierls-insulator Mott-insulator transition in 1D
• Ultrafast molecular dynamics in terahertz-STM experiments: Theoretical analysis using Anderson-Holstein model
• Study of supersolidity in the two-dimensional Hubbard-Holstein model
• Thermodynamic properties of Holstein polarons and the effects of disorder

Cited by in corpus (38)

• Phonon-Mediated Long-Range Attractive Interaction in One-Dimensional Cuprates
• Phase Diagram of the Su-Schrieffer-Heeger-Hubbard model on a square lattice
• Antiferromagnetism induced by electron-phonon-coupling
• Robustness of Antiferromagnetism in the Su-Schrieffer-Heeger-Hubbard model
• Variational Lang-Firsov approach plus Møller-Plesset perturbation theory with applications to ab initio polariton chemistry
• Nonperturbative Waveguide Quantum Electrodynamics
• A perspective on machine learning and data science for strongly correlated electron problems
• Gaussian time-dependent variational principle for the finite-temperature anharmonic lattice dynamics
• Magnetism and charge order in the honeycomb lattice
• Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
• Fluctuating Nature of Light-Enhanced $d$-Wave Superconductivity: A Time-Dependent Variational Non-Gaussian Exact Diagonalization Study
• Charge Density Wave and Superconductivity in the Disordered Holstein Model
• Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
• Attractive Su-Schrieffer-Heeger-Hubbard Model on a Square Lattice Away from Half-Filling
• Phonon-induced pairing in quantum dot quantum simulator
• Generalization of group-theoretic coherent states for variational calculations
• A Hybrid Quantum-Classical Method for Electron-Phonon Systems
• Competing Correlated Insulators in multi-orbital systems coupled to phonons
• Robust d-wave superconductivity from the Su-Schrieffer-Heeger-Hubbard model: possible route to high-temperature superconductivity
• Mixed-state phase transitions in spin-Holstein models
• Phonon Induced Instabilities in Correlated Electron Hamiltonians
• Steady-state Peierls transition in nanotube quantum simulator
• High-temperature superconductivity induced by the Su-Schrieffer-Heeger electron-phonon coupling
• Quantum simulation of extended electron-phonon coupling models in a hybrid Rydberg atom setup
• Phonon renormalization and Pomeranchuk instability in the Holstein model
• Collective modes in the charge-density wave state of K${}_{0.3}$MoO${}_3$: The role of long-range Coulomb interactions revisited
• Variational theory of angulons and their rotational spectroscopy
• Full configuration interaction quantum Monte Carlo for coupled electron--boson systems and infinite spaces
• Antiferromagnetic and bond-order-wave phases in the half-filled two-dimensional optical Su-Schrieffer-Heeger-Hubbard model
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• Magnetic impurities in a charge-ordered background
• Tuning competition between charge order and superconductivity in the square-lattice $t$-$t^{\prime }$-$J$ model
• Role of Matter Interactions in Superradiant Phenomena
• Electron addition spectral functions of low-density polaron liquids
• Charge-Density-Wave State in Extremely Overdoped Cuprates Driven by Phonons
• Algorithm for initializing a generalized fermionic Gaussian state on a quantum computer
• Simulating electron-vibron energy transfer with quantum dots and resonators
• Bootstrap Embedding for Interacting Electrons in Phonon Coherent-state Mean Field