Pith. sign in

REVIEW 4 cited by

Variational-Correlations Approach to Quantum Many-body Problems

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

arxiv 2001.06510 v1 pith:GNWC5XLG submitted 2020-01-17 cond-mat.str-el quant-ph

classification cond-mat.str-elquant-ph
keywords approachcorrelationboundenergyfunctionsground-statemany-bodymatrix
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix, order-by-order, in a way that keeps track of a limited set of correlation functions. In particular, the density-matrix description is replaced by a correlation matrix whose dimension is kept linear in system size, to all orders of the approximation. Unlike the conventional variational principle which provides an upper bound on the ground-state energy, in this approach one obtains a lower bound instead. By treating several one-dimensional spin $1/2$ Hamiltonians, we demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result. Possible extensions, including to higher-excited states are discussed.

Discussion (0). Sign in to comment.

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Exact models of chiral flat-band superconductors

    cond-mat.str-el 2025-08 conditional novelty 8.0 of 10

    For a single-flavor flat band with inversion symmetry, a local attraction between opposite-parity orbitals yields exact superconducting ground states, including topological pairing.

  2. Bootstrapping ground state properties of classical frustrated magnets

    cond-mat.stat-mech 2026-05 unverdicted novelty 7.0 of 10

    Semidefinite programming hierarchy yields rigorous two-sided bounds on ground state properties of translation-invariant classical spin models.

  3. Representability for Quantum Theory beyond Particle-Number Conservation

    quant-ph 2026-04 unverdicted novelty 7.0 of 10

    A hierarchy of representability conditions for 2-RDMs in non-particle-number-conserving quantum systems is obtained from the polar cone of the p-positive cone, unified with conserving cases by adding particle-number variance.

  4. Bootstrapping Flat-band Superconductors: Rigorous Lower Bounds on Superfluid Stiffness

    cond-mat.str-el 2025-06 unverdicted novelty 6.0 of 10

    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.

Pith tools