Understanding repulsively mediated superconductivity of correlated electrons via massively parallel DMRG

Abstract

The so-called minimal models of unconventional superconductivity are lattice models of interacting electrons derived from materials in which electron pairing arises from purely repulsive interactions. Showing unambiguously that a minimal model actually can have a superconducting ground state remains a challenge at nonperturbative interactions. We make a significant step in this direction by computing ground states of the 2D \mbox{U-V} Hubbard model - the minimal model of the quasi-1D superconductors - by parallelized DMRG, which allows for systematic control of any bias and that is sign-problem-free. Using distributed-memory supercomputers and leveraging the advantages of the \mbox{U-V} model, we can treat unprecedented sizes of 2D strips and extrapolate their spin gap both to zero approximation error and the thermodynamic limit. Our results for the spin gap are shown to be compatible with a spin excitation spectrum that is either fully gapped or has zeros only in discrete points, and conversely that a Fermi liquid or magnetically ordered ground state is incompatible with them. Coupled with the enhancement to short-range correlations that we find exclusively in the $d_{xy}$ pairing-channel, this allows us to build an indirect case for the ground state of this model having superconducting order in the full 2D limit, and ruling out the other main possible phases, magnetic orders and Fermi liquids.

arXiv commentFinal published version: 18 pages including appendix, 11 figures

References in corpus (43)

• The density-matrix renormalization group in the age of matrix product states
• Angle-resolved photoemission spectroscopy of the cuprate superconductors
• Surprises on the Way from 1D to 2D Quantum Magnets: the Novel Ladder Materials
• A Common Thread: the pairing interaction for the unconventional superconductors
• Scanning tunneling spectroscopy of high-temperature superconductors
• Functional renormalization group approach to correlated fermion systems
• The ALPS project release 1.3: open source software for strongly correlated systems
• Magnetism, superconductivity, and pairing symmetry in Fe-based superconductors
• The ALPS project release 2.0: Open source software for strongly correlated systems
• Heavy Fermions and Quantum Phase Transitions
• 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
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Neel order in square and triangular lattice Heisenberg models
• Evolution of the resonance and incommensurate spin fluctuations in superconducting YBa${}_2$Cu${}_3$O${}_{6+x}$
• Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator
• Truncation of a 2-dimensional Fermi surface due to quasiparticle gap formation at the saddle points
• Phase diagram of the one-dimensional extended Hubbard model at quarter filling
• Spin gap and magnetic coherence in a clean high-T_c superconductor
• Dimensional Crossover in Quasi One-Dimensional and High T_c Superconductors
• Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice
• Matrix Product State applications for the ALPS project
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Phases of the infinite U Hubbard model
• Pair Correlations in Doped Hubbard Ladders
• Emergent BCS regime of the two-dimensional fermionic Hubbard model: ground-state phase diagram
• Triplet superconducting pairing and density-wave instabilities in organic conductors
• Pairing on striped $t$-$t^{\prime }$-$J$ lattices
• Evolution from a nodeless gap to d(x2-y2) form in underdoped La(2-x)SrxCuO4
• Multigrid Algorithms for Tensor Network States
• Band-structure effects on superconductivity in Hubbard models
• Superconducting pairing and density-wave instabilities in quasi-one-dimensional conductors
• d-Mott phases in one and two dimensions
• Dynamic spin susceptibility of superconducting cuprates: A microscopic theory of the magnetic resonance mode
• Knight shifts, nuclear spin-relaxation rates, and spin echo decay times in the pseudogap regime of the cuprates: Simulation and relation to experiment
• Nodal Superconducting Order Parameter and Thermodynamic Phase Diagram of (TMTSF)2ClO4
• Stripe Structures in the t-t'-J Model
• Enhanced Pairing in the "Checkerboard" Hubbard Ladder
• Extended quantum criticality of low-dimensional superconductors near a spin-density-wave instability
• Organic Superconductors: when correlations and magnetism walk in
• Phase Diagram of the $t$--$U$--$V_1$--$V_2$ Model at Quarter Filling
• Superconductivity and antiferromagnetism as interfering orders in organic conductors
• Density of States and NMR Relaxation Rate in Anisotropic Superconductivity with Intersecting Line Nodes

Cited by in corpus (13)

• Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs
• Magnetically mediated hole pairing in fermionic ladders of ultracold atoms
• Fractional quantum Hall states for moiré superstructures in the Hofstadter regime
• Parallel time-dependent variational principle algorithm for matrix product states
• Transcorrelated Density Matrix Renormalization Group
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Hilbert curve vs Hilbert space: exploiting fractal 2D covering to increase tensor network efficiency
• Nature of quantum spin liquids of the S=1/2 Heisenberg antiferromagnet on the triangular lattice: A parallel DMRG study
• Dimensional crossover and phase transitions in coupled chains: Density matrix renormalization group results
• Hubbard models and state preparation in an optical Lieb lattice
• Distributed-Memory DMRG via Sparse and Dense Parallel Tensor Contractions
• Dimensional crossover on multileg attractive-$U$ Hubbard ladders
• Geometric and computational aspects of chiral topological quantum matter