Controlled bond expansion for DMRG ground state search at single-site costs

Abstract

DMRG ground state search algorithms employing symmetries must be able to expand virtual bond spaces by adding or changing symmetry sectors if these lower the energy. Traditional single-site DMRG does not allow bond expansion; two-site DMRG does, but at much higher computational costs. We present a controlled bond expansion (CBE) algorithm that yields two-site accuracy and convergence per sweep, at single-site costs. Given a matrix product state $\Psi$ defining a variational space, CBE identifies parts of the orthogonal space carrying significant weight in $H\Psi$ and expands bonds to include only these. CBE-DMRG uses no mixing parameters and is fully variational. Using CBE-DMRG, we show that the Kondo-Heisenberg model on a width 4 cylinder features two distinct phases differing in their Fermi surface volumes.

12 pages, 10 figures

References in corpus (19)

• The density-matrix renormalization group in the age of matrix product states
• Fermi-liquid instabilities at magnetic quantum phase transitions
• DMRG and periodic boundary conditions: a quantum information perspective
• Weak magnetism and non-Fermi liquids near heavy-fermion critical points
• Fractionalized Fermi liquids
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Fermi-surface collapse and dynamical scaling near a quantum critical point
• Ground State Phase Diagram of the $t$-$t^{\prime }$-$J$ model
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Real-Space Parallel Density Matrix Renormalization Group
• Phase diagram of the J1-J2 Heisenberg model on the kagome lattice
• Metallicity in the half-filled Holstein-Hubbard model
• Phase diagram for the one-dimensional Hubbard-Holstein model: A density-matrix renormalization group study
• T=0 heavy fermion quantum critical point as an orbital selective Mott transition
• Stripe order enhanced superconductivity in the Hubbard model
• Error estimates for extrapolations with matrix-product states
• Cellular Dynamical Mean Field Theory of the Periodic Anderson Model
• Zooming in on heavy fermions in Kondo lattice models
• Projector formalism for kept and discarded spaces of matrix product states

Cited by in corpus (19)

• A tensor network view of multilayer multiconfiguration time-dependent Hartree methods
• Measurement-induced transitions for interacting fermions
• Time-dependent variational principle with controlled bond expansion for matrix product states
• Density-matrix renormalization group: a pedagogical introduction
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Hund's Rule, Interorbital Hybridization, and High-$T_c$ Superconductivity in the Bilayer Nickelate
• Fractional Chern Insulator and Quantum Anomalous Hall Crystal in Twisted MoTe${}_2$
• SU($\mathbf{N}$) Kondo-Heisenberg chain: Phase diagram, Ising criticality, and the coexistence of heavy quasiparticles and valence bond solid order
• Searching for superconductivity in doped triangular lattice Kitaev magnets
• Thermal Tensor Network Simulations of Lattice Fermions with Fixed Filling
• Scaling up the transcorrelated density matrix renormalization group
• Dissipationless dynamics of spin supersolid states in a spin-1/2 triangular antiferromagnet with impurities
• The Software Landscape for the Density Matrix Renormalization Group
• Metal-insulator transition of spinless fermions coupled to dispersive optical bosons
• Matrix product states and first quantization
• Magnetically Mediated Cross-Layer Pairing in Pressurized Trilayer Nickelate La${}_4$Ni${}_3$O${}_{10}$
• Universal scaling of higher-order cumulants in quantum isotropic spin chains
• Probing Non-Fermi-Liquid Behaviour of Composite Fermi Liquid via Efficient Thermal Simulations
• paces: Parallelized Application of Co-Evolving Subspaces, a method for computing quantum dynamics on GPUs