Chiral liquid phase of simple quantum magnets

Wang, Zhentao; Feiguin, Adrian E.; Zhu, Wei; Starykh, Oleg A.; Chubukov, Andrey V.; Batista, Cristian D.

doi:10.1103/PhysRevB.96.184409

Title: Chiral liquid phase of simple quantum magnets

Journal Article · Tue Nov 07 00:00:00 EST 2017 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.96.184409· OSTI ID:1414150

Wang, Zhentao ^[1]; Feiguin, Adrian E. ^[2];

^[3]; Starykh, Oleg A. ^[4]; Chubukov, Andrey V. ^[5]; Batista, Cristian D. ^[6]

The Univ. of Tennessee, Knoxville, TN (United States)
Northeastern Univ., Boston, MA (United States)
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Univ. of Utah, Salt Lake City, UT (United States)
Univ. of Minnesota, Minneapolis, MN (United States)
The Univ. of Tennessee, Knoxville, TN (United States); Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

We study a T=0 quantum phase transition between a quantum paramagnetic state and a magnetically ordered state for a spin S=1 XXZ Heisenberg antiferromagnet on a two-dimensional triangular lattice. The transition is induced by an easy-plane single-ion anisotropy D. At the mean-field level, the system undergoes a direct transition at a critical D=D_c between a paramagnetic state at D>D_c and an ordered state with broken U(1) symmetry at D_c. We show that beyond mean field the phase diagram is very different and includes an intermediate, partially ordered chiral liquid phase. Specifically, we find that inside the paramagnetic phase the Ising (J_z) component of the Heisenberg exchange binds magnons into a two-particle bound state with zero total momentum and spin. This bound state condenses at D>D_c, before single-particle excitations become unstable, and gives rise to a chiral liquid phase, which spontaneously breaks spatial inversion symmetry, but leaves the spin-rotational U(1) and time-reversal symmetries intact. This chiral liquid phase is characterized by a finite vector chirality without long-range dipolar magnetic order. In our analytical treatment, the chiral phase appears for arbitrarily small J_z because the magnon-magnon attraction becomes singular near the single-magnon condensation transition. This phase exists in a finite range of D and transforms into the magnetically ordered state at some D_c. In conclusion, we corroborate our analytic treatment with numerical density matrix renormalization group calculations.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-06NA25396; AC02-05CH11231

OSTI ID:: 1414150

Alternate ID(s):: OSTI ID: 1407829

Report Number(s):: LA-UR-17-22905; PRBMDO; TRN: US1800673

Journal Information:: Physical Review B, Vol. 96, Issue 18; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 16 works

Citation information provided by
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M.; Chubukov, A. V.; Knolle, J.</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1110.1893" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1110.1893<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2011-01-01">January 2011</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1207.1725" target="_blank" rel="noopener noreferrer" class="title" data-title="Chiral Mott insulator with staggered loop currents in the fully frustrated Bose Hubbard model">Chiral Mott insulator with staggered loop currents in the fully frustrated Bose Hubbard model<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Dhar, Arya; Mishra, Tapan; Maji, Maheswar</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1207.1725" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1207.1725<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2012-01-01">January 2012</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1301.2025" target="_blank" rel="noopener noreferrer" class="title" data-title="Phase Diagram and Magnetic Excitations of Anisotropic SpinOne Magnets">Phase Diagram and Magnetic Excitations of Anisotropic Spin-One Magnets<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Zhang, Zhifeng; Wierschem, Keola; Yap, Ian</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1301.2025" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1301.2025<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2013-01-01">January 2013</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1303.3519" target="_blank" rel="noopener noreferrer" class="title" data-title="Spincurrent order in anisotropic triangular antiferromagnets">Spin-current order in anisotropic triangular antiferromagnets<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Chubukov, Andrey V.; Starykh, Oleg A.</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1303.3519" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1303.3519<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2013-01-01">January 2013</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1307.7731" target="_blank" rel="noopener noreferrer" class="title" data-title="Generalized spinwave theory application to the bilinearbiquadratic model">Generalized spin-wave theory: application to the bilinear-biquadratic model<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Muniz, Rodrigo A.; Kato, Yasuyuki; Batista, Cristian D.</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1307.7731" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1307.7731<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2013-01-01">January 2013</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1308.0823" target="_blank" rel="noopener noreferrer" class="title" data-title="Vector Chiral Phases in the Frustrated 2D XY Model and Quantum Spin Chains">Vector Chiral Phases in the Frustrated 2D XY Model and Quantum Spin Chains<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Schenck, H.; Pokrovsky, V. L.; Nattermann, T.</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1308.0823" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1308.0823<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2013-01-01">January 2013</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1312.3461" target="_blank" rel="noopener noreferrer" class="title" data-title="Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model">Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">He, Yin-Chen; Sheng, D. N.; Chen, Yan</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1312.3461" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1312.3461<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2013-01-01">January 2013</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1406.4959" target="_blank" rel="noopener noreferrer" class="title" data-title="Emergent loop current order from pair density wave superconductivity">Emergent loop current order from pair density wave superconductivity<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Agterberg, Daniel F.; Melchert, Drew S.; Kashyap, Manoj K.</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1406.4959" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1406.4959<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2014-01-01">January 2014</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.1510.00380" target="_blank" rel="noopener noreferrer" class="title" data-title="BoseEinstein condensation in a frustrated triangular optical lattice">Bose-Einstein condensation in a frustrated triangular optical lattice<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Janzen, Peter; Huang, Wen-Min; Mathey, Ludwig</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.1510.00380" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.1510.00380<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2015-01-01">January 2015</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.cond-mat/0010283" target="_blank" rel="noopener noreferrer" class="title" data-title="Ground State Phase Diagrams of Frustrated SpinS XXZ Chains Chiral Ordered Phases">Ground State Phase Diagrams of Frustrated Spin-S XXZ Chains: Chiral Ordered Phases<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Hikihara, T.; Kaburagi, M.; Kawamura, H.</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.cond-mat/0010283" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.cond-mat/0010283<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2000-01-01">January 2000</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.cond-mat/0412319" target="_blank" rel="noopener noreferrer" class="title" data-title="Spin current and magnetoelectric effect in noncollinear magnets">Spin current and magneto-electric effect in non-collinear magnets<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Katsura, Hosho; Nagaosa, Naoto; Balatsky, Alexander V.</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.cond-mat/0412319" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.cond-mat/0412319<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2004-01-01">January 2004</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.cond-mat/0510692" target="_blank" rel="noopener noreferrer" class="title" data-title="Ferroelectricity in spiral magnets">Ferroelectricity in spiral magnets<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Mostovoy, Maxim</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.cond-mat/0510692" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.cond-mat/0510692<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="2005-01-01">January 2005</span></td> </tr><tr> <td> <a href="https://doi.org/10.48550/arxiv.cond-mat/9708141" target="_blank" rel="noopener noreferrer" class="title" data-title="Possible chiral phase transition in twodimensional solid 3He">Possible chiral phase transition in two-dimensional solid $^3$He<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; padding-left: 0; line-height:1.8em;"> <li class="authors">Momoi, Tsutomu; Kubo, Kenn; Niki, Koji</li> <li class="mb-0-5 source"> <span class="mr-1">arXiv</span> <span class="text-muted"><a href="https://doi.org/10.48550/arxiv.cond-mat/9708141" class="text-muted" target="_blank" rel="noopener noreferrer">https://doi.org/10.48550/arxiv.cond-mat/9708141<span class="fa fa-external-link" aria-hidden="true"></span></a></span> </li> </ul> </td> <td class="small text-muted biblio-refs-td-secondary"> <span class="biblio-refs-type-badge ml-1 type" data-type="text">text</span> </td> <td class="small text-muted biblio-refs-td-secondary biblio-refs-td-secondary-date"><span class="date" data-date="1997-01-01">January 1997</span></td> </tr></tbody></table> </div> </div> </section> <hr class="mt-2 mb-2"/> <section id="section-citations" data-list="list_cite" class="tab-content-sec osti-curated biblio-section section-scroll" style="scroll-margin-top:110px;"> <div class="biblio-section-navbar active row"> <div class="col"> <h2 class="abstract biblio-section-title mt-0 mb-0-5" style="cursor:pointer;"><span class="fa indicator"></span> Cited By (4) <span class="text-muted list-table-filternum"></span></h2> </div> <div class="col-md-12 col-lg-auto"> <form class="pure-form reference-filter d-print-none"> <div class="small biblio-section-navbar-tool"> <label for="list-table-search-citations" class="sr-only">Search citations: </label> <input type="text" class="list-table-search mt-0 mb-0-5 ml-1" id="list-table-search-citations" placeholder="Search citations ..."> </div> <div class="small biblio-section-navbar-tool"> <select class="list-table-type mt-0 mb-0-5"> <option value="">Resource Types</option> <option value="journal">Journal</option><option value="text">Text</option> </select> </div> <div class="small biblio-section-navbar-tool"> <select class="list-table-sort mt-0 mb-0-5"> <option value="date">Sort by Date</option> <option value="title">Sort by Title</option> </select> </div> <div class="small biblio-section-navbar-tool"> <button type="reset" class="pure-button list-table-reset mt-0 mb-0-5">↺</button> </div> </form> </div> </div> <div class="row"> <div class="col-sm-12"> <table id="list-table-citations" class="truncate-rows list-table table-striped" data-rows="5" style="width:100%;"><tbody class="list"><tr> <td> <a href="https://doi.org/10.1038/s42005-020-0323-5" target="_blank" rel="noopener noreferrer" class="title" data-title="Frustrated quantum magnetism with Bose gases in triangular optical lattices at negative absolute temperatures">Frustrated quantum magnetism with Bose gases in triangular optical lattices at negative absolute temperatures<span class="fa fa-external-link" aria-hidden="true"></span></a> <ul class="small references-list mb-0 mt-0" style="list-style-type:none; 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Title: Chiral liquid phase of simple quantum magnets

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