Probing Quantum Frustrated Systems via Factorization of the Ground State

Abstract

The existence of definite orders in frustrated quantum systems is related rigorously to the occurrence of fully factorized ground states below a threshold value of the frustration. Ground-state separability thus provides a natural measure of frustration: strongly frustrated systems are those that cannot accommodate for classical-like solutions. The exact form of the factorized ground states and the critical frustration are determined for various classes of nonexactly solvable spin models with different spatial ranges of the interactions. For weak frustration, the existence of disentangling transitions determines the range of applicability of mean-field descriptions in biological and physical problems such as stochastic gene expression and the stability of long-period modulated structures.

4 pages, 2 figures. Replaced with published version

References in corpus (10)

• The density-matrix renormalization group
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Entanglement and factorized ground states in two-dimensional quantum antiferromagnets
• Theory of ground state factorization in quantum cooperative systems
• Separability and ground state factorization in quantum spin systems
• Entanglement of finite cyclic chains at factorizing fields
• Evidence for a floating phase of the transverse ANNNI model at high frustration
• Characterization of separability and entanglement in $(2\times D)$- and $(3\times D)$-dimensional systems by single-qubit and single-qutrit unitary transformations
• Determination of ground state properties in quantum spin systems by single qubit unitary operations and entanglement excitation energies

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