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Jażdżewska A, Mierzejewski M, Środa M, Nocera A, Alvarez G, Dagotto E, Herbrych J. Transition to the Haldane phase driven by electron-electron correlations. Nat Commun 2023; 14:8524. [PMID: 38129389 PMCID: PMC10740019 DOI: 10.1038/s41467-023-44135-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2023] [Accepted: 12/01/2023] [Indexed: 12/23/2023] Open
Abstract
One of the most famous quantum systems with topological properties, the spin [Formula: see text] antiferromagnetic Heisenberg chain, is well-known to display exotic [Formula: see text] edge states. However, this spin model has not been analyzed from the more general perspective of strongly correlated systems varying the electron-electron interaction strength. Here, we report the investigation of the emergence of the Haldane edge in a system of interacting electrons - the two-orbital Hubbard model-with increasing repulsion strength U and Hund interaction JH. We show that interactions not only form the magnetic moments but also form a topologically nontrivial fermionic many-body ground-state with zero-energy edge states. Specifically, upon increasing the strength of the Hubbard repulsion and Hund exchange, we identify a sharp transition point separating topologically trivial and nontrivial ground-states. Surprisingly, such a behaviour appears already at rather small values of the interaction, in a regime where the magnetic moments are barely developed.
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Affiliation(s)
- A Jażdżewska
- Faculty of Physics and Astronomy, University of Wrocław, 50-383, Wrocław, Poland
| | - M Mierzejewski
- Institute of Theoretical Physics, Wrocław University of Science and Technology, 50-370, Wrocław, Poland
| | - M Środa
- Institute of Theoretical Physics, Wrocław University of Science and Technology, 50-370, Wrocław, Poland
| | - A Nocera
- Department of Physics and Astronomy and Stewart Blusson Quantum Matter Institute, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada
| | - G Alvarez
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
| | - E Dagotto
- Department of Physics and Astronomy, University of Tennessee, Knoxville, TN, 37996, USA
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, TN, 37831, USA
| | - J Herbrych
- Institute of Theoretical Physics, Wrocław University of Science and Technology, 50-370, Wrocław, Poland.
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2
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Laurell P, Scheie A, Mukherjee CJ, Koza MM, Enderle M, Tylczynski Z, Okamoto S, Coldea R, Tennant DA, Alvarez G. Quantifying and Controlling Entanglement in the Quantum Magnet Cs_{2}CoCl_{4}. PHYSICAL REVIEW LETTERS 2021; 127:037201. [PMID: 34328778 DOI: 10.1103/physrevlett.127.037201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/19/2021] [Revised: 05/18/2021] [Accepted: 05/25/2021] [Indexed: 06/13/2023]
Abstract
The lack of methods to experimentally detect and quantify entanglement in quantum matter impedes our ability to identify materials hosting highly entangled phases, such as quantum spin liquids. We thus investigate the feasibility of using inelastic neutron scattering (INS) to implement a model-independent measurement protocol for entanglement based on three entanglement witnesses: one-tangle, two-tangle, and quantum Fisher information (QFI). We perform high-resolution INS measurements on Cs_{2}CoCl_{4}, a close realization of the S=1/2 transverse-field XXZ spin chain, where we can control entanglement using the magnetic field, and compare with density-matrix renormalization group calculations for validation. The three witnesses allow us to infer entanglement properties and make deductions about the quantum state in the material. We find QFI to be a particularly robust experimental probe of entanglement, whereas the one and two-tangles require more careful analysis. Our results lay the foundation for a general entanglement detection protocol for quantum spin systems.
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Affiliation(s)
- Pontus Laurell
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Computational Science and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Allen Scheie
- Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Chiron J Mukherjee
- Science Department, Drew School, San Francisco, California 94115, USA
- Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | | | | | | | - Satoshi Okamoto
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Quantum Science Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Radu Coldea
- Clarendon Laboratory, Oxford University, Parks Road, Oxford OX1 3PU, United Kingdom
| | - D Alan Tennant
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Quantum Science Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Shull-Wollan Center, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Gonzalo Alvarez
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Computational Science and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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Maeter H, Zvyagin AA, Luetkens H, Pascua G, Shermadini Z, Saint-Martin R, Revcolevschi A, Hess C, Büchner B, Klauss HH. Low temperature ballistic spin transport in the S = 1/2 antiferromagnetic Heisenberg chain compound SrCuO2. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:365601. [PMID: 23924574 DOI: 10.1088/0953-8984/25/36/365601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We report zero and longitudinal magnetic field muon spin relaxation (μSR) measurements of the spin S = 1/2 antiferromagnetic Heisenberg chain material SrCuO2. We find that in a weak applied magnetic field B0 the spin-lattice relaxation rate λ follows a power law λ is proportional to B(0)(-n) with n = 0.9(3). This result is temperature independent for 5 K ≤ T ≤ 300 K. Within conformal field theory and using the Müller ansatz we conclude ballistic spin transport in SrCuO2.
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Affiliation(s)
- H Maeter
- Institute for Solid State Physics, TU Dresden, D-01069 Dresden, Germany
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Caux JS, Konno H, Sorrell M, Weston R. Tracking the effects of interactions on spinons in gapless Heisenberg chains. PHYSICAL REVIEW LETTERS 2011; 106:217203. [PMID: 21699336 DOI: 10.1103/physrevlett.106.217203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2010] [Revised: 04/27/2011] [Indexed: 05/31/2023]
Abstract
We consider the effects of interactions on spinon excitations in Heisenberg spin-1/2 chains. We compute the exact two-spinon part of the longitudinal structure factor of the infinite chain in zero field for all values of anisotropy in the gapless antiferromagnetic regime, via an exact algebraic approach. Our results allow us to quantitatively describe the behavior of these fundamental excitations throughout the observable continuum, for cases ranging from free to fully coupled chains, thereby explicitly mapping the effects of "turning on the interactions" in a strongly correlated system.
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Affiliation(s)
- Jean-Sébastien Caux
- Institute for Theoretical Physics, Universiteit van Amsterdam, Science Park 904, Amsterdam, The Netherlands
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Thielemann B, Rüegg C, Rønnow HM, Läuchli AM, Caux JS, Normand B, Biner D, Krämer KW, Güdel HU, Stahn J, Habicht K, Kiefer K, Boehm M, McMorrow DF, Mesot J. Direct observation of magnon fractionalization in the quantum spin ladder. PHYSICAL REVIEW LETTERS 2009; 102:107204. [PMID: 19392156 DOI: 10.1103/physrevlett.102.107204] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2008] [Indexed: 05/27/2023]
Abstract
We measure by inelastic neutron scattering the spin excitation spectra as a function of applied magnetic field in the quantum spin-ladder material (C5H12N)2CuBr4. Discrete magnon modes at low fields in the quantum disordered phase and at high fields in the saturated phase contrast sharply with a spinon continuum at intermediate fields characteristic of the Luttinger-liquid phase. By tuning the magnetic field, we drive the fractionalization of magnons into spinons and, in this deconfined regime, observe both commensurate and incommensurate continua.
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Affiliation(s)
- B Thielemann
- Laboratory for Neutron Scattering, ETH Zurich and Paul Scherrer Institute, CH-5232 Villigen, Switzerland
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Pereira RG, White SR, Affleck I. Exact edge singularities and dynamical correlations in spin-1/2 chains. PHYSICAL REVIEW LETTERS 2008; 100:027206. [PMID: 18232918 DOI: 10.1103/physrevlett.100.027206] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2007] [Indexed: 05/25/2023]
Abstract
Exact formulas for the singularities of the dynamical structure factor, Szz(q,omega), of the S=1/2 xxz spin chain at all q and any anisotropy and magnetic field in the critical regime are derived, expressing the exponents in terms of the phase shifts which are known exactly from the Bethe ansatz solution. We also study the long-time asymptotics of the self-correlation function 0|Sjz(t)Sjz(0)|0. Utilizing these results to supplement very accurate time-dependent density matrix renormalization group, for short to moderate times, we calculate Szz(q,omega) to very high precision.
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Affiliation(s)
- Rodrigo G Pereira
- Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, Canada V6T 1Z1
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Masuda T, Zheludev A, Uchinokura K, Chung JH, Park S. Dynamics and scaling in a quantum spin chain material with bond randomness. PHYSICAL REVIEW LETTERS 2004; 93:077206. [PMID: 15324273 DOI: 10.1103/physrevlett.93.077206] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2004] [Indexed: 05/24/2023]
Abstract
Single crystal inelastic neutron scattering is used to study dynamic spin correlations in the quasi-one-dimensional quantum antiferromagnet BaCu2(Si0.5Ge0.5)2O7, where the exchange constant fluctuates due to a random distribution of Si and Ge atoms. The measured low-energy spectrum is dominated by localized excitations and can be understood in the framework of the random singlet model. The observed scaling relations for the frequency dependencies of the correlation length and structure factor are in excellent agreement with recent theoretical predictions for the renormalization group fixed point.
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Affiliation(s)
- T Masuda
- Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393, USA
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Biegel D, Karbach M, M ller G. Transition rates via Bethe ansatz for the spin-1/2 planarXXZantiferromagnet. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/20/301] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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9
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Zheludev A, Kenzelmann M, Raymond S, Ressouche E, Masuda T, Kakurai K, Maslov S, Tsukada I, Uchinokura K, Wildes A. Energy separation of single-particle and continuum states in an S = 1/2 weakly coupled chains antiferromagnet. PHYSICAL REVIEW LETTERS 2000; 85:4799-4802. [PMID: 11082655 DOI: 10.1103/physrevlett.85.4799] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2000] [Indexed: 05/23/2023]
Abstract
Inelastic neutron scattering is used to study transverse-polarized magnetic excitations in the quasi-one-dimensional S = 1/2 antiferromagnet BaCu2Si2O7, where the saturation value for the Neel order parameter is m(0) = 0.12&mgr;(B) per spin. At low energies the spectrum is totally dominated by resolution-limited spin-wave-like excitations. An excitation continuum sets in above a well-defined threshold frequency. Experimental results are discussed in the context of current theories for weakly interacting quantum half-integer-spin chains.
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Affiliation(s)
- A Zheludev
- Physics Department, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
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Derzhko O, Krokhmalskii T, Stolze J. Dynamics of the spin-½ isotropicXYchain in a transverse field. ACTA ACUST UNITED AC 2000. [DOI: 10.1088/0305-4470/33/16/301] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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11
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Fledderjohann A, Gerhardt C, Mütter KH, Schmitt A, Karbach M. Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:7168-7176. [PMID: 9984338 DOI: 10.1103/physrevb.54.7168] [Citation(s) in RCA: 28] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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12
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Fledderjohann A, Karbach M, Mütter K. Numerical evaluation of frequency-moment sum rules for dynamical structure factors. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:11543-11549. [PMID: 9982774 DOI: 10.1103/physrevb.53.11543] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Viswanath VS, Zhang S, Müller G, Stolze J. Zero-temperature dynamics of the one-dimensional XXZ and t-J models: A weak-coupling continued-fraction analysis. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:368-380. [PMID: 9977097 DOI: 10.1103/physrevb.51.368] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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14
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Karbach M, Mütter K, Schmidt M. Finite-size analysis of the structure factors in the one-dimensional spin-1/2 antiferromagnetic XXZ model. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:9281-9292. [PMID: 9974974 DOI: 10.1103/physrevb.50.9281] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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15
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Viswanath VS, Zhang S, Stolze J, Müller G. Ordering and fluctuations in the ground state of the one-dimensional and two-dimensional S=1/2 XXZ antiferromagnets: A study of dynamical properties based on the recursion method. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:9702-9715. [PMID: 10009771 DOI: 10.1103/physrevb.49.9702] [Citation(s) in RCA: 20] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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16
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Deisz J, Jarrell M, Cox DL. Dynamical properties of one-dimensional antiferromagnets: A Monte Carlo study. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:10227-10239. [PMID: 10007299 DOI: 10.1103/physrevb.48.10227] [Citation(s) in RCA: 31] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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17
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Ma S, Broholm C, Reich DH, Sternlieb BJ, Erwin RW. Dominance of long-lived excitations in the antiferromagnetic spin-1 chain NENP. PHYSICAL REVIEW LETTERS 1992; 69:3571-3574. [PMID: 10046855 DOI: 10.1103/physrevlett.69.3571] [Citation(s) in RCA: 42] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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18
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Gagliano ER, Balseiro CA. Dynamical properties of quantum many-body systems at zero temperature. PHYSICAL REVIEW LETTERS 1987; 59:2999-3002. [PMID: 10035707 DOI: 10.1103/physrevlett.59.2999] [Citation(s) in RCA: 60] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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19
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Parkinson JB, Bonner JC. Spin chains in a field: Crossover from quantum to classical behavior. PHYSICAL REVIEW. B, CONDENSED MATTER 1985; 32:4703-4724. [PMID: 9937653 DOI: 10.1103/physrevb.32.4703] [Citation(s) in RCA: 108] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/11/2023]
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