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Botzung T, Nataf P. Exact Diagonalization of SU(N) Fermi-Hubbard Models. PHYSICAL REVIEW LETTERS 2024; 132:153001. [PMID: 38682973 DOI: 10.1103/physrevlett.132.153001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Revised: 03/08/2024] [Accepted: 03/14/2024] [Indexed: 05/01/2024]
Abstract
We show how to perform exact diagonalizations of SU(N) Fermi-Hubbard models on L-site clusters separately in each irreducible representation (irrep) of SU(N). Using the representation theory of the unitary group U(L), we demonstrate that a convenient orthonormal basis, on which matrix elements of the Hamiltonian are very simple, is given by the set of semistandard Young tableaux (or, equivalently, the Gelfand-Tsetlin patterns) corresponding to the targeted irrep. As an application of this color factorization, we study the robustness of some SU(N) phases predicted in the Heisenberg limit upon decreasing the on-site interaction U on various lattices of size L≤12 and for 2≤N≤6. In particular, we show that a long-range color ordered phase emerges for intermediate U for N=4 at filling 1/4 on the triangular lattice.
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Affiliation(s)
- Thomas Botzung
- Laboratoire de Physique et Modélisation des Milieux Condensés, Université Grenoble Alpes and CNRS, 25 avenue des Martyrs, 38042 Grenoble, France
| | - Pierre Nataf
- Laboratoire de Physique et Modélisation des Milieux Condensés, Université Grenoble Alpes and CNRS, 25 avenue des Martyrs, 38042 Grenoble, France
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Chou YZ, Das Sarma S. Kondo Lattice Model in Magic-Angle Twisted Bilayer Graphene. PHYSICAL REVIEW LETTERS 2023; 131:026501. [PMID: 37505969 DOI: 10.1103/physrevlett.131.026501] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/25/2022] [Accepted: 06/02/2023] [Indexed: 07/30/2023]
Abstract
We systematically study emergent Kondo lattice models from magic-angle twisted bilayer graphene using the topological heavy fermion representation. At the commensurate fillings, we demonstrate a series of symmetric strongly correlated metallic states driven by the hybridization between a triangular lattice of SU(8) local moments and delocalized fermions. In particular, a (fragile) topological Dirac Kondo semimetal can be realized, providing a potential explanation for the symmetry-preserving correlated state at ν=0. We further investigate the stability of the Dirac Kondo semimetal by constructing a quantum phase diagram showing the interplay between Kondo hybridization and magnetic correlation. The destruction of Kondo hybridization suggests that the magic-angle twisted bilayer graphene may be on the verge of a solid-state quantum simulator for novel magnetic orders on a triangular lattice. Experimental implications are also discussed.
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Affiliation(s)
- Yang-Zhi Chou
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
| | - Sankar Das Sarma
- Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
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Keselman A, Bauer B, Xu C, Jian CM. Emergent Fermi Surface in a Triangular-Lattice SU(4) Quantum Antiferromagnet. PHYSICAL REVIEW LETTERS 2020; 125:117202. [PMID: 32976015 DOI: 10.1103/physrevlett.125.117202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2019] [Revised: 06/18/2020] [Accepted: 08/10/2020] [Indexed: 06/11/2023]
Abstract
Motivated by multiple possible physical realizations, we study the SU(4) quantum antiferromagnet with a fundamental representation on each site of the triangular lattice. We provide evidence for a gapless liquid ground state of this system with an emergent Fermi surface of fractionalized fermionic partons coupled with a U(1) gauge field. Our conclusions are based on numerical simulations using the density matrix renormalization group method, which we support with a field theory analysis.
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Affiliation(s)
- Anna Keselman
- Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
| | - Bela Bauer
- Microsoft Station Q, Santa Barbara, California 93106-6105, USA
| | - Cenke Xu
- Department of Physics, University of California, Santa Barbara, California 93106, USA
| | - Chao-Ming Jian
- Microsoft Station Q, Santa Barbara, California 93106-6105, USA
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Cazalilla MA, Rey AM. Ultracold Fermi gases with emergent SU(N) symmetry. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2014; 77:124401. [PMID: 25429615 DOI: 10.1088/0034-4885/77/12/124401] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We review recent experimental and theoretical progress on ultracold alkaline-earth Fermi gases with emergent SU(N) symmetry. Emphasis is placed on describing the ground-breaking experimental achievements of recent years. The latter include (1) the cooling to below quantum degeneracy of various isotopes of ytterbium and strontium, (2) the demonstration of optical Feshbach resonances and the optical Stern-Gerlach effect, (3) the realization of a Mott insulator of (173)Yb atoms, (4) the creation of various kinds of Fermi-Bose mixtures and (5) the observation of many-body physics in optical lattice clocks. On the theory side, we survey the zoo of phases that have been predicted for both gases in a trap and loaded into an optical lattice, focusing on two and three dimensional systems. We also discuss some of the challenges that lie ahead for the realization of such phases such as reaching the temperature scale required to observe magnetic and more exotic quantum orders. The challenge of dealing with collisional relaxation of excited electronic levels is also discussed.
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Affiliation(s)
- Miguel A Cazalilla
- Department of Physics, National Tsing Hua University and National Center for Theoretical Sciences, Hsinchu City, Taiwan. Donostia International Physics Center (DIPC), Manuel de Lardizabal, 4. 20018 San Sebastian, Spain
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Clark BK, Kinder JM, Neuscamman E, Chan GKL, Lawler MJ. Striped spin liquid crystal ground state instability of kagome antiferromagnets. PHYSICAL REVIEW LETTERS 2013; 111:187205. [PMID: 24237558 DOI: 10.1103/physrevlett.111.187205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2012] [Indexed: 06/02/2023]
Abstract
The Dirac spin liquid ground state of the spin 1/2 Heisenberg kagome antiferromagnet has potential instabilities. This has been suggested as the reason why it does not emerge as the ground state in large-scale numerical calculations. However, previous attempts to observe these instabilities have failed. We report on the discovery of a projected BCS state with lower energy than the projected Dirac spin liquid state which provides new insight into the stability of the ground state of the kagome antiferromagnet. The new state has three remarkable features. First, it breaks spatial symmetry in an unusual way that may leave spinons deconfined along one direction. Second, it breaks the U(1) gauge symmetry down to Z(2). Third, it has the spatial symmetry of a previously proposed "monopole" suggesting that it is an instability of the Dirac spin liquid. The state described herein also shares a remarkable similarity to the distortion of the kagome lattice observed at low Zn concentrations in Zn-paratacamite and in recently grown single crystals of volborthite suggesting it may already be realized in these materials.
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Affiliation(s)
- Bryan K Clark
- Station Q, Microsoft Research, Santa Barbara, California 93106, USA and Princeton University and Princeton Center for Theoretical Science, Department of Physics, Princeton, New Jersey 08544, USA
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Rau JG, Kee HY. Emergence of superconductivity, valence bond order, and Mott insulators in Pd[(dmit)2] based organic salts. PHYSICAL REVIEW LETTERS 2011; 106:056405. [PMID: 21405417 DOI: 10.1103/physrevlett.106.056405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/01/2010] [Indexed: 05/30/2023]
Abstract
The EtMe(3)P and EtMe(3)Sb triangular organic salts are distinguished from other Pd[(dmit)(2)] based salts, as they display valence bond and no long-range order, respectively. Under pressure, a superconducting phase is revealed in EtMe(3)P near the boundary of valence bond order. We use slave-rotor theory with an enlarged unit cell to study competition between uniform and broken translational symmetry states, offering a theoretical framework capturing the superconducting, valence bond order, spin liquid, and metallic phases on an isotropic triangular lattice. Our finite temperature phase diagram manifests a remarkable resemblance to the phase diagram of the EtMe(3)P salt, where the reentrant transition of insulator-metal-insulator type can be explained by an entropy difference between the metal and U(1) spin liquid. We predict different temperature dependence of the specific heat between the spin liquid and metal.
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Affiliation(s)
- Jeffrey G Rau
- Department of Physics, University of Toronto, Toronto, Ontario M5S 1A7, Canada
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Misguich G. Quantum Spin Liquids and Fractionalization. INTRODUCTION TO FRUSTRATED MAGNETISM 2011. [DOI: 10.1007/978-3-642-10589-0_16] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
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Hermele M, Gurarie V, Rey AM. Mott insulators of ultracold fermionic alkaline Earth atoms: underconstrained magnetism and chiral spin liquid. PHYSICAL REVIEW LETTERS 2009; 103:135301. [PMID: 19905520 DOI: 10.1103/physrevlett.103.135301] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2009] [Revised: 08/13/2009] [Indexed: 05/28/2023]
Abstract
We study Mott insulators of fermionic alkaline earth atoms, described by Heisenberg spin models with enhanced SU(N) symmetry. In dramatic contrast to SU(2) magnetism, more than two spins are required to form a singlet. On the square lattice, the classical ground state is highly degenerate and magnetic order is thus unlikely. In a large-N limit, we find a chiral spin liquid ground state with topological order and Abelian fractional statistics. We discuss its experimental detection. Chiral spin liquids with non-Abelian anyons may also be realizable with alkaline earth atoms.
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Affiliation(s)
- Michael Hermele
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
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Zeng C, Elser V. Quantum dimer calculations on the spin-1/2 kagome-acute Heisenberg antiferromagnet. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:8318-8324. [PMID: 9977441 DOI: 10.1103/physrevb.51.8318] [Citation(s) in RCA: 39] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Sachdev S. Kagomé- and triangular-lattice Heisenberg antiferromagnets: Ordering from quantum fluctuations and quantum-disordered ground states with unconfined bosonic spinons. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:12377-12396. [PMID: 10001275 DOI: 10.1103/physrevb.45.12377] [Citation(s) in RCA: 242] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Harris AB, Kallin C, Berlinsky AJ. Possible Néel orderings of the Kagomé antiferromagnet. PHYSICAL REVIEW. B, CONDENSED MATTER 1992; 45:2899-2919. [PMID: 10001839 DOI: 10.1103/physrevb.45.2899] [Citation(s) in RCA: 83] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Freericks JK, Falicov LM, Rokhsar DS. Exact solutions of frustrated ordinary and chiral eight-site Hubbard models. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:1458-1474. [PMID: 9999678 DOI: 10.1103/physrevb.44.1458] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Marston JB. Absence of instanton-induced spin-Peierls order in the flux phase. PHYSICAL REVIEW. B, CONDENSED MATTER 1990; 42:10804-10806. [PMID: 9995354 DOI: 10.1103/physrevb.42.10804] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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