Density of States of Quantum Spin Systems from Isotropic Entanglement

2011/08/26 by Ramis Movassagh, Alan Edelman
Computer Science · Physics and Astronomy · #Classical mechanics #Eigenvalues and eigenvectors #Entanglement witness #Interpolation (computer graphics) #Isotropy #Physics #Quantum #Quantum Information and Cryptography #Quantum and electron transport phenomena #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Quantum state #Spin (aerodynamics) #Squashed entanglement #Statistical physics #Theoretical physics #cond-mat.stat-mech #cond-mat.str-el #quant-ph

paper · pdf · doi:10.1103/physrevlett.107.097205

published as Phys. Rev. Lett. 107, 097205 (2011) · 4+ pages, content is as in the published version

openalex publication_date 2011/08/26 · arxiv created 2011/08/29 · arxiv updated 2018/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

Abstract

We propose a method that we call isotropic entanglement (IE), which predicts the eigenvalue distribution of quantum many body (spin) systems with generic interactions. We interpolate between two known approximations by matching fourth moments. Though such problems can be QMA-complete, our examples show that isotropic entanglement provides an accurate picture of the spectra well beyond what one expects from the first four moments alone. We further show that the interpolation is universal, i.e., independent of the choice of local terms.

Citations

• Computational Difficulty of Computing the Density of States
• Tensor-entanglement renormalization group approach as a unified method for symmetry breaking and topological phase transitions
• Unfrustrated Qudit Chains and their Ground States
• Efficient Simulation of One-Dimensional Quantum Many-Body Systems
• Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems