TY - JOUR

T1 - Spectral Gaps and Incompressibility in a ν = 1/3 Fractional Quantum Hall System

AU - Nachtergaele, Bruno

AU - Warzel, Simone

AU - Young, Amanda

N1 - Publisher Copyright:
© 2021, The Author(s).

PY - 2021/4

Y1 - 2021/4

N2 - We study an effective Hamiltonian for the standard ν= 1 / 3 fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States, which are labeled by a certain family of tilings of the one-dimensional lattice. We then prove that the model has a spectral gap above the ground states for a range of coupling constants that includes physical values. As a consequence of the gap we establish the incompressibility of the fractional quantum Hall states. We also show that all the ground states labeled by a tiling have a finite correlation length, for which we give an upper bound. We demonstrate by example, however, that not all superpositions of tiling states have exponential decay of correlations.

AB - We study an effective Hamiltonian for the standard ν= 1 / 3 fractional quantum Hall system in the thin cylinder regime. We give a complete description of its ground state space in terms of what we call Fragmented Matrix Product States, which are labeled by a certain family of tilings of the one-dimensional lattice. We then prove that the model has a spectral gap above the ground states for a range of coupling constants that includes physical values. As a consequence of the gap we establish the incompressibility of the fractional quantum Hall states. We also show that all the ground states labeled by a tiling have a finite correlation length, for which we give an upper bound. We demonstrate by example, however, that not all superpositions of tiling states have exponential decay of correlations.

UR - http://www.scopus.com/inward/record.url?scp=85101200248&partnerID=8YFLogxK

U2 - 10.1007/s00220-021-03997-0

DO - 10.1007/s00220-021-03997-0

M3 - Article

AN - SCOPUS:85101200248

SN - 0010-3616

VL - 383

SP - 1093

EP - 1149

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -