Density matrix renormalization group for bosonic quantum Hall effect

Abstract

We developed a density matrix renormalization-group technique to study quantum Hall fractions of fast rotating bosons. In this paper we present a discussion of the method together with the results which we obtain in three distinct cases of the narrow channel, cylinder and spherical geometries. In the narrow channel case, which is relevant to anisotropic confining traps in the limit of extremely fast rotation, we find a series of zero-temperature phase transitions in the strongly interacting regime as a function of the interaction strength between bosons. We compute energies and density profiles for different filling fractions on a cylinder and compare the convergence rates of the method in the cylinder and a sphere geometries.

8 pages, 7 figures, final version as published

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Cited by in corpus (16)

• Quantum Hall Physics - hierarchies and CFT techniques
• Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Fractional Quantum Hall States at 1/3 and 5/2 Filling: the Density-Matrix Renormalization Group Calculations
• Entanglement Scaling of Fractional Quantum Hall states through Geometric Deformations
• Comparison of the density-matrix renormalization group method applied to fractional quantum Hall systems in different geometries
• Probing the geometry of the Laughlin state
• Bulk-edge correspondence in fractional Chern insulators
• Quasiholes of 1/3 and 7/3 quantum Hall states: size estimates via exact diagonalization and density-matrix renormalization group
• Edge Mode Combinations in the Entanglement Spectra of Non-Abelian Fractional Quantum Hall States on the Torus
• Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
• Quantum Hall phase diagram of two-component Bose gases: Intercomponent entanglement and pseudopotentials
• Bubble phase at $\nu =1/3$ for a spinless hollow-core interaction
• Matrix-Product-State Algorithm for Finite Fractional Quantum Hall Systems
• Strange Metal to Insulator Transitions in the Lowest Landau Level
• Vortex and fractional quantum Hall phases in a rotating anisotropic Bose gas