Ground states of long-range interacting fermions in one spatial dimension

Abstract

We explore systematically the ground state properties of one dimensional fermions with long-range interactions decaying in a power law $\sim 1/r^{\alpha }$ through the density matrix renormalization group algorithm. By comparing values of Luttinger liquid parameters precisely measured in two different ways, we show convincing evidence that Luttinger liquid theory is valid if $\alpha$ is larger than some threshold, otherwise the theory breakdown. Combining analysis on structure factor, charge gap and charge stiffness, we determine how the metal-insulator transition point develops as the interaction range is continuously tuned. A region in the range of $0\le \alpha \le 1$ and small interactions has finite charge gaps, but, interestingly, it shows metallic nature at the same time. From these, we obtain approximate phase diagrams for the entire parameter space and for band fillings equal 1/2 and 1/3. Finally, we compare certain bosonization and field theory formula with our quasi-exact numerical results, from which disagreements are found.

arXiv comment10 pages, 16 figures

References in corpus (30)

• The density-matrix renormalization group in the age of matrix product states
• Area laws for the entanglement entropy - a review
• One-Dimensional Fermi liquids
• DMRG and periodic boundary conditions: a quantum information perspective
• From density-matrix renormalization group to matrix product states
• Wigner Crystal in One Dimension
• The one-dimensional Bose-Hubbard Model with nearest-neighbor interaction
• Applying matrix product operators to model systems with long-range interactions
• Friedel Oscillations and Charge Density Waves in Chains and Ladders
• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• Ferromagnetic transition and phase diagram of the one-dimensional Hubbard model with next-nearest-neighbor hopping
• Ground state properties of the one dimensional Coulomb gas
• Tensor operators: constructions and applications for long-range interaction systems
• Tomonaga-Luttinger parameters for doped Mott insulators
• Localization Transition in a Ballistic Quantum Wire
• Possible Exotic Phases in the One-Dimensional Extended Hubbard Model
• Phase diagram of the half-filled one-dimensional t-V-V' model
• Exact ground state properties of the one-dimensional Coulomb gas
• Insulator-Metal Transition in One Dimension Induced by Long-Range Electronic Interactions
• The Coulomb Luttinger liquid
• Effects of Long Range Electronic Interactions on a One-dimensional Electron System
• Correlation effects in quasi one dimensional electron wires
• Luttinger liquid physics from infinite-system DMRG
• Interaction-range effects for fermions in one dimension
• Unscreened Coulomb repulsion in the one dimensional electron gas
• Phase Diagram of the $t$--$U$--$V_1$--$V_2$ Model at Quarter Filling
• Conformal field theory in Tomonaga-Luttinger model with $1/r^{\beta }$ type long-range interactions
• Phase diagram of a quantum Coulomb wire
• Exact electronic Green functions in a Luttinger liquid with long-range interactions
• Conformal properties of 1D quantum systems with long-range interactions

Cited by in corpus (8)

• Entanglements and correlations of one-dimensional quantum spin-1/2 chain with anisotropic power-law long range interactions
• Effects of energy extensivity on the quantum phases of long-range interacting systems
• Pairing in spin chains and spinless fermions with next-nearest neighbour interactions
• Two-fluid coexistence and phase separation in a one dimensional model with pair hopping and density interactions
• Many-Body Physics in Small Systems: Observing the Onset and Saturation of Correlation in Linear Atomic Chains
• Wire width and density dependence of the crossover in the peak of the static structure factor from $2k_{\text{F}}$ $\to$ $4k_{\text{F}}$ in one-dimensional paramagnetic electron gases
• Slow transport and bound states for spinless fermions with long-range Coulomb interactions on one-dimensional lattices
• Long-Range Order and Quantum Criticality in Antiferromagnetic Chains with Long-Range Staggered Interactions