General Lieb–Schultz–Mattis Type Theorems for Quantum Spin Chains

We develop a general operator algebraic method which focuses on projective representations of symmetry group for proving Lieb–Schultz–Mattis type theorems, i.e., no-go theorems that rule out the existence of a unique gapped ground state (or, more generally, a pure split state), for quantum spin chai...

Full description

Saved in:
Bibliographic Details
Published in:Communications in mathematical physics 2021, Vol.385 (1), p.79-99
Main Authors: Ogata, Yoshiko, Tachikawa, Yuji, Tasaki, Hal
Format: Article
Language:English
Subjects:
Chain scission
Chains
Classical and Quantum Gravitation
Complex Systems
Existence theorems
Invariants
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Symmetry
Theoretical
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We develop a general operator algebraic method which focuses on projective representations of symmetry group for proving Lieb–Schultz–Mattis type theorems, i.e., no-go theorems that rule out the existence of a unique gapped ground state (or, more generally, a pure split state), for quantum spin chains with on-site symmetry. We first prove a theorem for translation invariant spin chains that unifies and extends two theorems proved by two of the authors (Ogata and Tasaki, Commun. Math. Phys. 372 951–962, (2019) https://doi.org/10.1007/s00220-019-03343-5 ). We then prove a Lieb–Schultz–Mattis type theorem for spin chains that are invariant under the reflection about the origin and not necessarily translation invariant.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-021-04116-9