Hubbard ladders at small $U$ revisited

Abstract

We re-examine the zero temperature phase diagram of the two-leg Hubbard ladder in the small $U$ limit, both analytically and using density-matrix renormalization group (DMRG). We find a ubiquitous Luther-Emery phase, but with a crossover in behavior at a characteristic interaction strength, $U^{\star }$; for $U\gtrsim U^{\star }$, there is a single emergent correlation length $\log [\xi ]\sim 1/U$, characterizing the gapped modes of the system, but for $U\lesssim U^{\star }$ there is a hierarchy of length scales, differing parametrically in powers of $U$, reflecting a two-step renormalization group flow to the ultimate fixed point. Finally, to illustrate the versatility of the approach developed here, we sketch its implications for a half-filled triangular lattice Hubbard model on a cylinder, and find results in conflict with inferences concerning the small $U$ phase from recent DMRG studies of the same problem.

13+4 pages, 7+5 figures

References in corpus (36)

• Entanglement Entropy and Quantum Field Theory
• Spin-Gap Proximity Effect Mechanism of High Temperature Superconductivity
• Stripe order in the underdoped region of the two-dimensional Hubbard model
• Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
• Weak Coupling Phase Diagram of the Two Chain Hubbard Model
• Superconductivity in the repulsive Hubbard model: an asymptotically exact weak-coupling solution
• Many-body instability of Coulomb interacting bilayer graphene: RG approach
• Correlations in a two--chain Hubbard model
• Superconductivity in the Hubbard model and its interplay with charge stripes and next-nearest hopping t'
• Chiral spin liquid phase of the triangular lattice Hubbard model: a density matrix renormalization group study
• Phases of two coupled Luttinger liquids
• Competition Between Stripes and Pairing in a t-t'-J Model
• Friedel Oscillations and Charge Density Waves in Chains and Ladders
• The N-chain Hubbard Model in Weak Coupling
• Stripe order from the perspective of the Hubbard model
• Interacting fermions on the honeycomb bilayer: from weak to strong coupling
• Ground state phase diagram of the doped Hubbard model on the 4-leg cylinder
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• The ground state of the two-leg Hubbard ladder: a density--matrix renormalization group study
• Superconductivity from weak repulsion in hexagonal lattice systems
• Effects of disorder on two strongly correlated coupled chains
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Ground state phase diagram of the triangular lattice Hubbard model by density matrix renormalization group method
• Phases of the infinite U Hubbard model
• Pair Correlations in Doped Hubbard Ladders
• Superconductivity in the doped $t$-$J$ model: results for four-leg cylinders
• Intertwined Order in a Frustrated 4-leg $t-J$ Cylinder
• Pairing on striped $t$-$t^{\prime }$-$J$ lattices
• Ground State Phases of the Doped 4-Leg t-J Ladder
• Classification and Stability of Phases of the Multicomponent One-Dimensional Electron Gas
• A continuous Mott transition between a metal and a quantum spin liquid
• A DMRG Study of Superconductivity in the Triangular Lattice Hubbard Model
• Renormalization-Group Approach to a Three-Legs Fermionic Ladder
• Stripe Structures in the t-t'-J Model
• Coupled Luttinger Liquids
• Fractional charge and emergent mass hierarchy in diagonal two-leg t-J cylinders

Cited by in corpus (33)

• The Hubbard Model
• Robust d-wave superconductivity in the square-lattice $t$-$J$ model
• Cuprate superconductors as viewed through a striped lens
• Doped Mott Insulators in the Triangular Lattice Hubbard Model
• Phase diagram of the anisotropic triangular lattice Hubbard model
• Quantum Spin Liquid with Emergent Chiral Order in the Triangular-lattice Hubbard Model
• Doping the chiral spin liquid -- topological superconductor or chiral metal?
• Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators
• Topological chiral and nematic superconductivity by doping Mott insulators on triangular lattice
• Hole Spectral Function of a Chiral Spin Liquid in the Triangular Lattice Hubbard Model
• Quantum Phases of Transition Metal Dichalcogenide Moiré Systems
• Pair density wave and loop current promoted by van Hove singularities in moiré systems
• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• Ground-state phase diagram of the extended two-leg $t$-$J$ ladder
• Singlet, Triplet and Pair Density Wave Superconductivity in the Doped Triangular-Lattice Moiré System
• Robust superconducting correlation against inter-site interactions in the extended two-leg Hubbard ladder
• Phase Diagram, $d$-Wave Superconductivity, and Pseudogap of the $t$-$t^{\prime }$-$J$ Model at Finite Temperature
• Spectral properties of 1D extended Hubbard model from bosonization and time-dependent variational principle: applications to 1D cuprate
• Matrix product state recursion methods for strongly correlated quantum systems
• How quantum phases on cylinders approach the 2d limit
• Absence of Luther-Emery Superconducting Phase in the Three-Band Model for Cuprate Ladders
• Magnetic phases of the anisotropic triangular lattice Hubbard model
• Chiral superconductivity in the doped triangular-lattice Fermi-Hubbard model in two dimensions
• Robust d-wave superconductivity from the Su-Schrieffer-Heeger-Hubbard model: possible route to high-temperature superconductivity
• Doping asymmetry in the three-band Hamiltonian for cuprate ladders: failure of the standard model of superconductivity in cuprates
• Luther-Emery liquid and dominant singlet superconductivity in the hole-doped Haldane spin-1 chain
• Terminable Transitions in a Topological Fermionic Ladder
• Pair binding and enhancement of pairing correlations in asymmetric Hubbard ladders
• Strain-induced Aharonov-Bohm effect at nanoscale and ground state of a carbon nanotube with zigzag edges
• Valence Transition Theory of the Pressure-Induced Dimensionality Crossover in Superconducting Sr${}_{14-x}$Ca${}_x$Cu${}_{24}$O${}_{41}$
• Itinerant magnetism in Hubbard models with long-range interactions
• Functional renormalization of spinless triangular-lattice fermions: $N$-patch vs. truncated-unity scheme
• Competing instabilities of the extended Hubbard model on the triangular lattice: Truncated-unity functional renormalization group and application to moiré materials