Calogero model for the non-Abelian quantum Hall effect

被引：3

作者：

Bourgine, Jean-Emile ^{[1
]}

Matsuo, Yutaka ^{[2
,3
,4
]}

机构：

[1] Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia

[2] Univ Tokyo, Dept Phys, Hongo 7-3-1,Bunkyo Ku, Tokyo 1130033, Japan

[3] Univ Tokyo, Transscale Quantum Sci Inst, Hongo 7-3-1,Bunkyo Ku, Tokyo 1130033, Japan

[4] Univ Tokyo, Math & Informat Ctr, Hongo 7-3-1,Bunkyo Ku, Tokyo 1130033, Japan

来源：

PHYSICAL REVIEW B | 2024年 / 109卷 / 15期

关键词：

INTEGRABLE SYSTEMS; INFINITE SYMMETRY; BRANCHING-RULES; WZW MODELS; COMPUTATION; ALGEBRAS; DUALITY;

D O I：

10.1103/PhysRevB.109.155158

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

A model of the non-Abelian fractional quantum Hall effect is obtained from the diagonalization of the matrix model proposed by Dorey, Tong, and Turner (DTT). The Hamiltonian is reminiscent of a spin Calogero-Moser model but involves higher-order symmetric representations of the non-Abelian symmetry. We derive the energy spectrum and show that the Hamiltonian has a triangular action on a certain class of wave functions with a free-fermion expression. We deduce the expression of the ground-state eigenfunctions and show that they solve a Knizhnik-Zamolodchikov equation. Finally, we discuss the emergence of Kac-Moody symmetries in the large-N limit using the level-rank duality, and we confirm the results obtained previously by DTT.

引用

页数：23

共 54 条

[1] THE BRANCHING-RULES OF CONFORMAL EMBEDDINGS [J].

ALTSCHULER, D ;

BAUER, M ;

ITZYKSON, C .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 132 (02) :349-364

[2] Non-Abelian braiding of graph vertices in a superconducting processor [J].

Andersen, T. I. ;

Lensky, Y. D. ;

Kechedzhi, K. ;

Drozdov, I. K. ;

Bengtsson, A. ;

Hong, S. ;

Morvan, A. ;

Mi, X. ;

Opremcak, A. ;

Acharya, R. ;

Allen, R. ;

Ansmann, M. ;

Arute, F. ;

Arya, K. ;

Asfaw, A. ;

Atalaya, J. ;

Babbush, R. ;

Bacon, D. ;

Bardin, J. C. ;

Bortoli, G. ;

Bourassa, A. ;

Bovaird, J. ;

Brill, L. ;

Broughton, M. ;

Buckley, B. B. ;

Buell, D. A. ;

Burger, T. ;

Burkett, B. ;

Bushnell, N. ;

Chen, Z. ;

Chiaro, B. ;

Chik, D. ;

Chou, C. ;

Cogan, J. ;

Collins, R. ;

Conner, P. ;

Courtney, W. ;

Crook, A. L. ;

Curtin, B. ;

Debroy, D. M. ;

Del Toro Barba, A. ;

Demura, S. ;

Dunsworth, A. ;

Eppens, D. ;

Erickson, C. ;

Faoro, L. ;

Farhi, E. ;

Fatemi, R. ;

Ferreira, V. S. ;

Burgos, L. F. .

NATURE, 2023, 618 (7964) :264-+

[3] Chiral correlators of the Ising conformal field theory [J].

Ardonne, Eddy ;

Sierra, German .

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2010, 43 (50)

[4]

BAIS FA, 1987, NUCL PHYS B, V279, P561, DOI 10.1016/0550-3213(87)90010-1

[5] SPINONS IN CONFORMAL FIELD-THEORY [J].

BERNARD, D ;

PASQUIER, V ;

SERBAN, D .

NUCLEAR PHYSICS B, 1994, 428 (03) :612-628

[6] YANG-BAXTER EQUATION IN LONG-RANGE INTERACTING SYSTEMS [J].

BERNARD, D ;

GAUDIN, M ;

HALDANE, FDM ;

PASQUIER, V .

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1993, 26 (20) :5219-5236

[7]

Bernard D, 1994, Arxiv, DOI arXiv:hep-th/9412194

[8] MANY-BODY SYSTEMS WITH NON-ABELIAN STATISTICS [J].

BLOK, B ;

WEN, XG .

NUCLEAR PHYSICS B, 1992, 374 (03) :615-646

[9] SPINON BASIS FOR HIGHER-LEVEL SU(2) WZW MODELS [J].

BOUWKNEGT, P ;

LUDWIG, AWW ;

SCHOUTENS, K .

PHYSICS LETTERS B, 1995, 359 (3-4) :304-312

[10] The S(U(n))over-cap(1) WZW models - Spinon decomposition and yangian structure [J].

Bouwknegt, P ;

Schoutens, K .

NUCLEAR PHYSICS B, 1996, 482 (1-2) :345-372

← 1 2 3 4 5 6 →