Abelian SU(N)1 chiral spin liquids on the square lattice

Chen, Ji-Yao; Li, Jheng-Wei; Nataf, Pierre; Capponi, Sylvain; Mambrini, Matthieu; Totsuka, Keisuke; Tu, Hong-Hao; Weichselbaum, Andreas; von Delft, Jan; Poilblanc, Didier

doi:10.1103/physrevb.104.235104

Title: Abelian SU(N)₁ chiral spin liquids on the square lattice

Journal Article · Fri Dec 03 00:00:00 EST 2021 · Physical Review B

DOI:https://doi.org/10.1103/physrevb.104.235104· OSTI ID:1841111

^[1];

^[2]; Nataf, Pierre ^[3];

^[4];

^[4]; Totsuka, Keisuke ^[5];

^[6];

^[7]; von Delft, Jan ^[2]; Poilblanc, Didier ^[4]

Max Planck Society, Garching (Germany). Max Planck Inst. of Quantum Optics; Munich Center for Quantum Science and Technology (MCQST), Munich (Germany)
Munich Center for Quantum Science and Technology (MCQST), Munich (Germany); Ludwig Maximilian Univ. of Munich, Munich (Germany)
Maison des Magistères (CNRS), Grenoble (France)
Univ. of Toulouse (France)
Kyoto Univ. (Japan)
Technische Universität Dresden (Germany)
Brookhaven National Lab. (BNL), Upton, NY (United States)

In the physics of the Fractional Quantum Hall (FQH) effect, a zoo of Abelian topological phases can be obtained by varying the magnetic field. Aiming to reach the same phenomenology in spin-like systems, in this work we propose a family of SU(N)-symmetric models in the fundamental representation, on the square lattice with short-range interactions restricted to triangular units, a natural generalization for arbitrary N of an SU(3) model studied previously where time-reversal symmetry is broken explicitly. Guided by the recent discovery of SU(2)₁ and SU(3)₁ chiral spin liquids (CSL) on similar models we search for topological SU(N)₁ CSL in some range of the Hamiltonian parameters via a combination of complementary numerical methods such as exact diagonaliza- tions (ED), infinite density matrix renormalization group (iDMRG) and infinite Projected Entangled Pair State (iPEPS). Extensive ED on small (periodic and open) clusters up to N = 10 and an innovative SU(N)-symmetric version of iDMRG to compute entanglement spectra on (infinitely-long) cylinders in all topological sectors pro- vide unambiguous signatures of the SU(N)₁ character of the chiral liquids. An SU(4)-symmetric chiral PEPS, constructed in a manner similar to its SU(2) and SU(3) analogs, is shown to give a good variational ansatz of the N = 4 ground state, with chiral edge modes originating from the PEPS holographic bulk-edge correspondence. Finally, we discuss the possible observation of such Abelian CSL in ultracold atom setups where the possibility of varying N provides a tuning parameter similar to the magnetic field in the physics of the FQH effect.

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Research Organization:: Brookhaven National Laboratory (BNL), Upton, NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: SC0012704

OSTI ID:: 1841111

Report Number(s):: BNL-222604-2022-JAAM; TRN: US2301454

Journal Information:: Physical Review B, Vol. 104, Issue 23; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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