Universality Relations in Non-solvable Quantum Spin Chains

2009/07/16 by G. Benfatto, V. Mastropietro · 22 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Critical exponent #Critical phenomena #Lattice (music) #Luttinger liquid #Quantum #Quantum many-body systems #Renormalization group #Spin (aerodynamics) #Topological Materials and Phenomena #Universality (dynamical systems) #cond-mat.stat-mech

paper · pdf · doi:10.1007/s10955-010-9920-0

published in Journal of Statistical Physics 138(6), 1084-1108 (Springer Science+Business Media)

arxiv created 2009/07/16 · openalex publication_date 2010/01/08 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We prove the exact relations between the critical exponents and the susceptibility, implied by the Haldane Luttinger liquid conjecture, for a generic lattice fermionic model or a quantum spin chain with short range weak interaction. The validity of such relations was only checked in some special solvable models, but there was up to now no proof of their validity in non-solvable models.

Citations

• On the Density-Density Critical Indices�in Interacting Fermi Systems
• Extended Scaling Relations for Planar Lattice Models
• Ward Identities and Chiral Anomaly in the Luttinger Liquid

Cited by

• Drude Weight in Non Solvable Quantum Spin Chains
• Canonical Drude Weight for Non-integrable Quantum Spin Chains