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Yamamoto D, Morita K. Engineering of a Low-Entropy Quantum Simulator for Strongly Correlated Electrons Using Cold Atoms with SU(N)-Symmetric Interactions. PHYSICAL REVIEW LETTERS 2024; 132:213401. [PMID: 38856247 DOI: 10.1103/physrevlett.132.213401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2023] [Revised: 03/02/2024] [Accepted: 04/04/2024] [Indexed: 06/11/2024]
Abstract
An advanced cooling scheme, incorporating entropy engineering, is vital for isolated artificial quantum systems designed to emulate the low-temperature physics of strongly correlated electron systems. This study theoretically demonstrates a cooling method employing multicomponent Fermi gases with SU(N)-symmetric interactions, focusing on the case of ^{173}Yb atoms in a two-dimensional optical lattice. Adiabatically introducing a nonuniform state-selective laser gives rise to two distinct subsystems: a central low-entropy region, exclusively composed of two specific spin components, acts as a quantum simulator for strongly correlated electron systems, while the surrounding N-component mixture retains a significant portion of the entropy of the system. The total particle numbers for each component are good quantum numbers, creating a sharp boundary for the two-component region. The cooling efficiency is assessed through extensive finite-temperature Lanczos calculations. The results lay the foundation for quantum simulations of two-dimensional systems of Hubbard or Heisenberg type, offering crucial insights into intriguing low-temperature phenomena in condensed-matter physics.
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Affiliation(s)
- Daisuke Yamamoto
- Department of Physics, College of Humanities and Sciences, Nihon University, Sakurajosui, Setagaya, Tokyo 156-8550, Japan
| | - Katsuhiro Morita
- Department of Physics and Astronomy, Faculty of Science and Technology, Tokyo University of Science, Chiba 278-8510, Japan
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Lai HH, Hu WJ, Nica EM, Yu R, Si Q. Antiferroquadrupolar Order and Rotational Symmetry Breaking in a Generalized Bilinear-Biquadratic Model on a Square Lattice. PHYSICAL REVIEW LETTERS 2017; 118:176401. [PMID: 28498700 DOI: 10.1103/physrevlett.118.176401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/23/2016] [Indexed: 06/07/2023]
Abstract
The magnetic and nematic properties of the iron chalcogenides have recently been the subject of intense interest. Motivated by the proposed antiferroquadrupolar and Ising-nematic orders for the bulk FeSe, we study the phase diagram of an S=1 generalized bilinear-biquadratic model with multineighbor interactions. We find a large parameter regime for a (π, 0) antiferroquadrupolar phase, showing how quantum fluctuations stabilize it by lifting an infinite degeneracy of certain semiclassical states. Evidence for this C_{4}-symmetry-breaking quadrupolar phase is also provided by an unbiased density matrix renormalization group analysis. We discuss the implications of our results for FeSe and related iron-based superconductors.
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Affiliation(s)
- Hsin-Hua Lai
- Department of Physics and Astronomy & Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Wen-Jun Hu
- Department of Physics and Astronomy & Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Emilian M Nica
- Department of Physics and Astronomy & Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
| | - Rong Yu
- Department of Physics, Renmin University of China, Beijing 100872, China
- Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China and Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
| | - Qimiao Si
- Department of Physics and Astronomy & Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
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Dutta O, Gajda M, Hauke P, Lewenstein M, Lühmann DS, Malomed BA, Sowiński T, Zakrzewski J. Non-standard Hubbard models in optical lattices: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:066001. [PMID: 26023844 DOI: 10.1088/0034-4885/78/6/066001] [Citation(s) in RCA: 68] [Impact Index Per Article: 7.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Originally, the Hubbard model was derived for describing the behavior of strongly correlated electrons in solids. However, for over a decade now, variations of it have also routinely been implemented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the vast literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After giving an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so-called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighbor sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation for the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, the effects related to higher Bloch bands also become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis, Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher p orbitals, as well as models that dynamically couple spin and orbital degrees of freedom. Finally, we review mean-field nonlinear Schrödinger models of the Salerno type that share with the non-standard Hubbard models nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of consideration. We conclude by listing some open problems, to be addressed in the future.
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Affiliation(s)
- Omjyoti Dutta
- Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagielloński, Łojasiewicza 11, 30-348 Kraków, Poland
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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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Nataf P, Mila F. Exact Diagonalization of Heisenberg SU(N) models. PHYSICAL REVIEW LETTERS 2014; 113:127204. [PMID: 25279642 DOI: 10.1103/physrevlett.113.127204] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2014] [Indexed: 06/03/2023]
Abstract
Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the quantum permutation of N-color objects) takes an explicit and extremely simple form. Since the relative dimension of the full Hilbert space to that of the singlet space on n sites increases very fast with N, this formulation allows us to extend exact diagonalizations of finite clusters to much larger values of N than accessible so far. Using this method, we show that, on the square lattice, there is long-range color order for SU(5), spontaneous dimerization for SU(8), and evidence in favor of a quantum liquid for SU(10).
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Affiliation(s)
- Pierre Nataf
- Institute of Theoretical Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Frédéric Mila
- Institute of Theoretical Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
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Lang TC, Meng ZY, Muramatsu A, Wessel S, Assaad FF. Dimerized solids and resonating plaquette order in SU(N)-Dirac fermions. PHYSICAL REVIEW LETTERS 2013; 111:066401. [PMID: 23971594 DOI: 10.1103/physrevlett.111.066401] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/19/2013] [Indexed: 06/02/2023]
Abstract
We study the quantum phases of fermions with an explicit SU(N)-symmetric, Heisenberg-like nearest-neighbor flavor exchange interaction on the honeycomb lattice at half filling. Employing projective (zero temperature) quantum Monte Carlo simulations for even values of N, we explore the evolution from a weak-coupling semimetal into the strong-coupling, insulating regime. Furthermore, we compare our numerical results to a saddle-point approximation in the large-N limit. From the large-N regime down to the SU(6) case, the insulating state is found to be a columnar valence bond crystal, with a direct transition to the semimetal at weak, finite coupling, in agreement with the mean-field result in the large-N limit. At SU(4) however, the insulator exhibits a subtly different valence bond crystal structure, stabilized by resonating valence bond plaquettes. In the SU(2) limit, our results support a direct transition between the semimetal and an antiferromagnetic insulator.
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Affiliation(s)
- Thomas C Lang
- Department of Physics, Boston University, Boston, Massachusetts 02215, USA.
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Messio L, Mila F. Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets. PHYSICAL REVIEW LETTERS 2012; 109:205306. [PMID: 23215503 DOI: 10.1103/physrevlett.109.205306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/05/2012] [Indexed: 06/01/2023]
Abstract
Motivated by the possibility to load multicolor fermionic atoms in optical lattices, we study the entropy dependence of the properties of the one-dimensional antiferromagnetic SU(N) Heisenberg model, the effective model of the SU(N) Hubbard model with one particle per site (filling 1/N) in the large U/t limit. Using continuous-time world-line Monte Carlo simulations for N=2-5, we show that characteristic short-range correlations develop at low temperature as a precursor of the ground state algebraic correlations. We also calculate the entropy as a function of temperature, and we show that the first sign of short-range order appears at an entropy per particle that increases with N and already reaches 0.8k(B) at N=4, in the range of experimentally accessible values.
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Affiliation(s)
- Laura Messio
- Institut de Physique Théorique (IPhT), CEA, CNRS, URA 2306, F-91191 Gif-sur-Yvette, France
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Bonnes L, Hazzard KRA, Manmana SR, Rey AM, Wessel S. Adiabatic loading of one-dimensional SU(N) alkaline-earth-atom fermions in optical lattices. PHYSICAL REVIEW LETTERS 2012; 109:205305. [PMID: 23215502 DOI: 10.1103/physrevlett.109.205305] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2012] [Indexed: 06/01/2023]
Abstract
Ultracold fermionic alkaline earth atoms confined in optical lattices realize Hubbard models with internal SU(N) symmetries, where N can be as large as ten. Such systems are expected to harbor exotic magnetic physics at temperatures below the superexchange energy scale. Employing quantum Monte Carlo simulations to access the low-temperature regime of one-dimensional chains, we show that after adiabatically loading a weakly interacting gas into the strongly interacting regime of an optical lattice, the final temperature decreases with increasing N. Furthermore, we estimate the temperature scale required to probe correlations associated with low-temperature SU(N) magnetism. Our findings are encouraging for the exploration of exotic large-N magnetic states in ongoing experiments.
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Affiliation(s)
- Lars Bonnes
- Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck, Austria.
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Li P, Kou SP. Topological edge states in the spin 1 bilinear-biquadratic model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:446001. [PMID: 23053205 DOI: 10.1088/0953-8984/24/44/446001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
The spin 1 bilinear-biquadratic model H = ∑(ij)[cosφS(i)·S(j) + sinφ(S(i)·S(j))(2)] on a square lattice in the region 0 < φ < π/4 is studied in a fermion representation with a p-wave pairing Bardeen-Cooper-Schrieffer type of mean-field theory. Our results show there may exist a non-trivial gapped spin liquid with time-reversal symmetry spontaneously breaking. This exotic state manifests its topological nature by forming chiral states at the edges. To show this more clearly, we set up and solved a ribbon system. We got a gapless dispersion representing the edge modes beneath the bulk modes. The edge modes with nonzero longitudinal momentum (k(x) ≠ 0) convect in opposite directions at the two edges, which leads to a twofold degeneracy, while the modes with zero longitudinal momentum (k(x) = 0) turn out to be Majorana fermion states. The edge spin correlation functions are found to decay following a power law with increasing distance. We also calculated the contribution of the edge modes to the specific heat and obtained a linear law at low temperatures.
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Affiliation(s)
- Peng Li
- Center for Theoretical Physics, Department of Physics, Sichuan University, Chengdu 610064, People's Republic of China.
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Corboz P, Läuchli AM, Penc K, Troyer M, Mila F. Simultaneous dimerization and SU(4) symmetry breaking of 4-color fermions on the square lattice. PHYSICAL REVIEW LETTERS 2011; 107:215301. [PMID: 22181892 DOI: 10.1103/physrevlett.107.215301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/14/2011] [Indexed: 05/31/2023]
Abstract
Using infinite projected entangled-pair states, exact diagonalization, and flavor-wave theory, we show that the SU(4) Heisenberg model undergoes a spontaneous dimerization on the square lattice, in contrast with its SU(2) and SU(3) counterparts, which develop Néel and three-sublattice stripelike long-range order. Since the ground state of a dimer is not a singlet for SU(4) but a 6-dimensional irreducible representation, this leaves the door open for further symmetry breaking. We provide evidence that, unlike in SU(4) ladders, where dimers pair up to form singlet plaquettes, here the SU(4) symmetry is additionally broken, leading to a gapless spectrum in spite of the broken translational symmetry.
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