REVIEW 7 cited by
Bootstrapping the Quantum Hall problem
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
The bootstrap method aims to solve problems by imposing constraints on the space of physical observables, which often follow from physical assumptions such as positivity and symmetry. Here, we employ a bootstrap approach to study interacting electrons in the lowest Landau level by minimizing the energy as a function of the static structure factor subject to a set of constraints, bypassing the need to construct the full many-body wavefunction. This approach rigorously lower bounds the ground state energy, making it complementary to conventional variational upper bounds. We show that the lower bound we obtain is relatively tight, within at most 5\% from the ground state energy computed with exact diagonalization (ED) at small system sizes, and generally gets tighter as we include more constraints. In addition to energetics, our results reproduce the correct power law dependence of the pair correlation function at short distances and the existence of a large entanglement gap in the two-particle entanglement spectra for the Laughlin states at $\nu = 1/3$. We further identify signatures of the composite Fermi liquid state close to half-filling. This shows that the bootstrap approach is capable, in principle, of describing non-trivial gapped topologically ordered, as well as gapless, phases. At the end, we will discuss possible extensions and limitations of this approach. Our work establishes numerical bootstrap as a promising method to study many-body phases in topological bands, paving the way to its application in moir\'e platforms where the energetic competition between fractional quantum anomalous Hall, symmetry broken, and gapless states remains poorly understood.
Forward citations
Cited by 7 Pith papers
-
Bootstrapping Open Quantum Many-body Systems with Absorbing Phase Transitions
A bootstrap method using density-matrix positivity and steady-state conditions produces bounds on steady-state expectation values, the critical coupling, and the Liouvillian gap for the quantum contact process.
-
Static structure factor and the dispersion of the Girvin-MacDonald-Platzman density mode for fractional quantum Hall fluids on the Haldane sphere
GMP density-mode dispersion on the Haldane sphere accurately describes primary Jain states at long wavelength after deriving the sphere version of the LLL density-operator algebra.
-
Correlated Purification for Restoring $N$-Representability in Quantum Simulation
Correlated purification via bi-objective semidefinite programming restores N-representability to noisy 2-RDMs from fermionic shadow tomography and achieves chemical accuracy on hydrogen chain dissociation curves.
-
Bootstrapping Flat-band Superconductors: Rigorous Lower Bounds on Superfluid Stiffness
The reduced density matrix bootstrap yields rigorous lower bounds on superfluid stiffness for quantum geometric nesting models, relating stiffness to pair mass and showing enhancement from added magnetic interactions.
-
Ambiguity problem of the Bootstrap Method in Quantum Mechanics
Bootstrap method in quantum mechanics has an ambiguity problem for mixed potential and operator types, with three proposed resolutions.
-
Constrained Shadow Tomography for Molecular Simulation on Quantum Devices
A bi-objective SDP framework for constrained shadow tomography reconstructs N-representable 2-RDMs from noisy shadow data by balancing measurement fidelity with energy minimization for molecular quantum simulations.
-
Theory of magnetoroton bands in moir\'e materials
The authors derive an effective Hamiltonian for magnetoroton modes in moiré FQH and FCI systems via single-mode approximation and Monte Carlo three-point density correlations, predicting THz absorption trends and a so...
Discussion (0). Sign in to comment.