Self-dual $S_3$-invariant quantum chains

O'Brien, Edward; Fendley, Paul

doi:10.21468/SciPostPhys.9.6.088

SciPost Physics

Self-dual $S_3$-invariant quantum chains

Edward O'Brien, Paul Fendley

SciPost Phys. 9, 088 (2020) · published 16 December 2020

doi: 10.21468/SciPostPhys.9.6.088
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Abstract

We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and $S_3$, time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct "Fermi velocities". The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.9.6.088
TI  - Self-dual $S_3$-invariant quantum chains
PY  - 2020/12/16
UR  - https://scipost.org/SciPostPhys.9.6.088
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 9
IS  - 6
SP  - 088
A1  - O'Brien, Edward
AU  - Fendley, Paul
AB  - We investigate the self-dual three-state quantum chain with nearest-neighbor interactions and $S_3$, time-reversal, and parity symmetries. We find a rich phase diagram including gapped phases with order-disorder coexistence, integrable critical points with U(1) symmetry, and ferromagnetic and antiferromagnetic critical regions described by three-state Potts and free-boson conformal field theories respectively. We also find an unusual critical phase which appears to be described by combining two conformal field theories with distinct "Fermi velocities". The order-disorder coexistence phase has an emergent fractional supersymmetry, and we find lattice analogs of its generators.
ER  -

@Article{10.21468/SciPostPhys.9.6.088,
	title={{Self-dual $S_3$-invariant quantum chains}},
	author={Edward O'Brien and Paul Fendley},
	journal={SciPost Phys.},
	volume={9},
	pages={088},
	year={2020},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.9.6.088},
	url={https://scipost.org/10.21468/SciPostPhys.9.6.088},
}

Cited by 3

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¹ Edward O'Brien,
¹ ² Paul Fendley

Funder for the research work leading to this publication

Engineering and Physical Sciences Research Council [EPSRC]