Gauging defects in quantum spin systems

A case study

authored by: Jacob C. Bridgeman, Alexander Hahn, Tobias J. Osborne, Ramona Wolf
Abstract: The goal of this work is to build a dynamical theory of defects for quantum spin systems. This is done by explicitly giving an exhaustive case study of a one-dimensional spin chain with Vec(Z/2Z) fusion rules, which can easily be extended to more general settings. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by allowing the defects to become mobile via a microscopic Hamiltonian. This construction is extended to topologically ordered systems by restricting to the ground state eigenspace of Hamiltonians generalizing the golden chain. Technically, this is done by employing generalized tube algebra techniques to model the defects in the chain. We illustrate this approach for the Vec(Z/2Z) spin chain, in whose case the resulting dynamical defect model is equivalent to the critical transverse Ising model.
Organisation(s): Institute of Theoretical Physics
QuantumFrontiers
CRC 1227 Designed Quantum States of Matter (DQ-mat)
External Organisation(s): Perimeter Institute for Theoretical Physics
Type: Article
Journal: Physical Review B
Volume: 101
ISSN: 2469-9950
Publication date: 27.04.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Electronic, Optical and Magnetic Materials, Condensed Matter Physics
Electronic version(s): https://doi.org/10.1103/PhysRevB.101.134111 (Access: Closed)

BibTeX

@article{b6cfed5fe6f44d88981724d534221358,
title = "Gauging defects in quantum spin systems: A case study",
abstract = "The goal of this work is to build a dynamical theory of defects for quantum spin systems. This is done by explicitly giving an exhaustive case study of a one-dimensional spin chain with Vec(Z/2Z) fusion rules, which can easily be extended to more general settings. A kinematic theory for an indefinite number of defects is first introduced exploiting distinguishable Fock space. Dynamics are then incorporated by allowing the defects to become mobile via a microscopic Hamiltonian. This construction is extended to topologically ordered systems by restricting to the ground state eigenspace of Hamiltonians generalizing the golden chain. Technically, this is done by employing generalized tube algebra techniques to model the defects in the chain. We illustrate this approach for the Vec(Z/2Z) spin chain, in whose case the resulting dynamical defect model is equivalent to the critical transverse Ising model.",
author = "Bridgeman, {Jacob C.} and Alexander Hahn and Osborne, {Tobias J.} and Ramona Wolf",
note = "Funding information: J.C.B. thanks Daniel Barter for many useful discussions. This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through SFB 1227 (DQ-mat), the RTG 1991, and under Germanys Excellence Strategy EXC-2123 QuantumFrontiers, Grant No. 390837967. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade.",
year = "2020",
month = apr,
day = "27",
doi = "10.1103/PhysRevB.101.134111",
language = "English",
volume = "101",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Institute of Physics",
number = "13",
}