Chiral spin liquid and quantum criticality in extended 
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 Heisenberg models on the triangular lattice

Wietek, Alexander; Läuchli, Andreas M.

doi:10.1103/physrevb.95.035141

Cited by 125 publications

(115 citation statements)

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“…Previous exact diagonalization (ED) studies [Capriotti et al, 1999, Dagotto and Moreo, 1989, Deutscher and Everts, 1993, Hirsch and Tang, 1989, Jolicoeur et al, 1990, Wietek and Läuchli, 2016 Heisenberg model on other non-bipartite Archimedean lattices have been also studied in great detail [Farnell et al, 2014, Schollwöck et al, 2004. The expected groundstate for most of the phase diagram is quasiclassical frustrated Néel-type ordering.…”

Section: (B) It Is Widely Believed That the Celebratedmentioning

confidence: 99%

“…Chapter 4). Moreover, Chapter 5 and other precise numerical approaches' results [Hu et al, 2015, Iqbal et al, 2016, Kaneko et al, 2014, Li et al, 2015, Manuel and Ceccatto, 1999, Mishmash et al, 2013, Wietek and Läuchli, 2016, Zhu and White, 2015 demonstrate the existence of a SL state that stabilizes in a region ranging from J However, we suggest the detailed properties of the magnetic groundstates are still unclear in comparison to the well-understood counterparts in the classical THM (see Sec. 1.6) and the quantum model on the three-leg cylinders.…”

mentioning

confidence: 96%

“…Previous exact diagonalization (ED) studies [Capriotti et al, 1999, Dagotto and Moreo, 1989, Deutscher and Everts, 1993, Hirsch and Tang, 1989, Jolicoeur et al, 1990, Wietek and Läuchli, 2016 of the model could have only reached to a maximum system size of N = 36, which reflects the exponentially growing size problem of the Hilbert space. In addition, the geometrical frustration causes a sign problem for the conventional quantum Monte Carlo (QMC) calculations [Loh et al, 1990] (although, modern QMC approaches like bold-diagrammatic QMC [Kulagin et al, 2013], more or less, solved such difficulties).…”

Section: Declaration By Authormentioning

confidence: 99%

“…Perhaps, the most interesting realization for the J 1 -J 2 THM was that the addition of the NNN (J 2 ) term, eventually, stabilizes an SL groundstate (see Hu et al [2015], Iqbal et al [2016], Kaneko et al [2014], Li et al [2015], Manuel and Ceccatto [1999], Mishmash et al [2013], Wietek and Läuchli [2016], Zhu and White [2015] and also Chapter 5). So, roughly speaking, Anderson's prediction was correct.…”

Section: Triangular Heisenberg Modelmentioning

confidence: 99%

“…For the rest of the thesis, we mainly focus on the state-of-the-art MPS/DMRG studies of the J 1 -J 2 THM on cylinders to scrutinize properties of such emergent phases. There have been some historically important semi-classical spinwave theory (SWT) and ED studies [Chubukov and Jolicoeur, 1992, Dagotto and Moreo, 1989, Deutscher and Everts, 1993, Hirsch and Tang, 1989, Jolicoeur et al, 1990 Svistov et al [2003] and also below).Perhaps, the most interesting realization for the J 1 -J 2 THM was that the addition of the NNN (J 2 ) term, eventually, stabilizes an SL groundstate (see Hu et al [2015], Iqbal et al [2016], Kaneko et al [2014], Li et al [2015], Manuel and Ceccatto [1999], Mishmash et al [2013], Wietek and Läuchli [2016], Zhu and White [2015] and also Chapter 5). So, roughly speaking, Anderson's prediction was correct.…”

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confidence: 99%

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Frustrated spin systems, an MPS approach

Saadatmand¹

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In spin lattices, frustration happens when there exists a competition between different terms of the Hamiltonian, which cannot be simultaneously minimized in all local physical bases. Frustration can destabilize the bipartite Néel order, which is the conventional groundstate of antiferromagnetic Heisenberg-type models in two dimensions. Hence, the focus of two-dimensional quantum magnetism studies has been directed toward elucidating the zero-temperature properties of Heisenberg-type models on the Archimedean lattices that exhibit geometrical frustration. This type of frustration is of great interest since it can lead to exotic forms of the quantum matter, such as topological spin-liquid (SL) and many-sublattice long-range-ordered phases. The spin-1 2 triangular Heisenberg model (THM) is a prototypical model with geometrical frustration, which has the highest coordination number of all Archimedean lattices. However, there exist two major, distinct difficulties for numerical methods to efficiently determine the groundstate properties of the THM: the immense dimension of the Hilbert space and the geometrical frustration phenomenon. In this thesis, to deal with such difficulties, we employ the state-of-theart non-Abelian matrix product states (MPS) and density matrix renormalization group (DMRG) methods. We exploit the symmetries of the Hamiltonian to reduce the working dimension of the Hilbert space and, to lessen the effects of the geometrical frustration, we depend on the local entanglement (area-law) nature of the MPS as it scales with the size of a lattice subspace with reduced spatial dimensions. In such a way, we thoroughly examine the phase diagram of the THM with nearest and next-nearest neighbor (NN and NNN) exchange couplings on finite-and infinite-length cylinders of widths up to 12 sites.In addition, we develop new numerical tools to analyze topological and symmetry-broken phases in the context of the SU(2)-symmetric translation-invariant MPS algorithm. We establish that on infinite cylinders, the anyonic sectors of a topological order can be classified through the fractionalization of global symmetries and degeneracy patterns of the entanglement spectrum (ES). On the other hand, we detect symmetry-breaking phase transitions by a combination of the correlation lengths and second and fourth cumulants of the magnetic order parameters, even though symmetry implies that the order parameter itself is strictly zero. Furthermore, the appearance of Nambu-Goldstone modes in the excitation spectrum can be detected using "tower of states" (TOS) levels in the momentum-resolved ES. By applying the new tools to the THM, we discover a variety of exotic groundstates such as a Z 2 -gauge toric-code-type topological order (with vison and spinon excitations), a NNN Majumdar-Gosh, and a long-range 120• -ordered state. I acknowledge that an electronic copy of my thesis must be lodged with the University Library and, subject to the policy and procedures of The University of Queensland, the thesis be made available f...

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Section: (B) It Is Widely Believed That the Celebratedmentioning

confidence: 99%

mentioning

confidence: 96%

“…Previous exact diagonalization (ED) studies [Capriotti et al, 1999, Dagotto and Moreo, 1989, Deutscher and Everts, 1993, Hirsch and Tang, 1989, Jolicoeur et al, 1990, Wietek and Läuchli, 2016 of the model could have only reached to a maximum system size of N = 36, which reflects the exponentially growing size problem of the Hilbert space. In addition, the geometrical frustration causes a sign problem for the conventional quantum Monte Carlo (QMC) calculations [Loh et al, 1990] (although, modern QMC approaches like bold-diagrammatic QMC [Kulagin et al, 2013], more or less, solved such difficulties).…”

Section: Declaration By Authormentioning

confidence: 99%

Section: Triangular Heisenberg Modelmentioning

confidence: 99%

mentioning

confidence: 99%

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Frustrated spin systems, an MPS approach

Saadatmand¹

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YbMgGaO₄: A Triangular‐Lattice Quantum Spin Liquid Candidate

2019

Adv Quantum Tech

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Resonating valence bond ground state, the prototype of a quantum spin liquid (QSL), had been first proposed by P. W. Anderson back in 1973 on the triangular lattice. In such a 2D QSL, spinons created as unpaired spins can propagate by locally rearranging the uncorrelated valence bonds. However, the corresponding candidate materials are still rare to date. YbMgGaO4, first proposed in 2015 may fill this gap: the magnetic rare‐earth Yb3+ ions arrange on the triangular lattice with the perfect R‐3m symmetries and with a large interlayer distance. No conventional spin freezing is observed down to 40 mK without residual magnetic entropy, despite the significant antiferromagnetic coupling of ≈2 K. This report reviews and classifies the relevant experimental and theoretical progress on some (effective) spin‐1/2 triangular antiferromagnets, especially on YbMgGaO4, followed by discussion and outlook on some of the pending issues.

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Utilization of Renormalized Mean-Field Theory upon Novel Quantum Materials

2019

Springer Theses

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To finish a thesis co-advised by two parties is not a easy task. I can never accomplish this without being helped by a lot of people. Among them, first, I need to show my 100 percent gratitude to Dr. T.K. Lee, who granted me this opportunity of conducting research under his supervision. Besides the knowledge I have learned and the training I obtained, the most important spirits I learned from him are the integrity and diligence that a scientist should possess. After occupying a same position and doing the same job for a long time, it is easy for a person to feel exhausted and therefore lose interest. But as a scientist it is a sign of danger because what we are doing for lifetime is the pursuit for the truth and reality. That can be the burden but also the joy. In these days collaborating with Dr. Lee, despite the hard time when we tried to settle down on the same page, I have never saw him lose interest in Physics. Considering how busy he is with also a administrative position as the director of Institute of Physics, Academia Sinica, this is even more difficult to keep the passion like he does. Those spirits I learned from him will be my lifetime treasure no matter if I succeed in becoming a scholar in the future. Second, Dr. Didier Poilblanc also taught me a lot. The academic environment in Taiwan is not that open compared with Europe where scientists from difference countries can easily meet each other. Thanks for his acceptance of my request of a joint-degree thesis, I got the chance to conduct research in France and therefore obtained many opportunities discussing physical topics with other outstanding scientists. To learn how to express my idea properly v is crucial in becoming an independent physicist and during the time in France those are among all what I got to learn the most. I think it is fair to say that he led me on the track of becoming an independent researcher from just a apprentice of physics. Thus, I want to thank Didier for not only teaching me a lot of academic knowledge, but also those chances he granted me for interacting with other experts in this field. Plus, our co-workers mean a lot to me since they were willing to spare time collaborating with us upon certain issues. I would like to thank Dr.

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Chiral spin liquid and quantum criticality in extended S=12 Heisenberg models on the triangular lattice

Cited by 125 publications

References 66 publications

Frustrated spin systems, an MPS approach

Frustrated spin systems, an MPS approach

YbMgGaO₄: A Triangular‐Lattice Quantum Spin Liquid Candidate

Utilization of Renormalized Mean-Field Theory upon Novel Quantum Materials

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Chiral spin liquid and quantum criticality in extended S=12 Heisenberg models on the triangular lattice

Cited by 125 publications

References 66 publications

Frustrated spin systems, an MPS approach

Frustrated spin systems, an MPS approach

YbMgGaO4: A Triangular‐Lattice Quantum Spin Liquid Candidate

Utilization of Renormalized Mean-Field Theory upon Novel Quantum Materials

Contact Info

Product

Resources

About

YbMgGaO₄: A Triangular‐Lattice Quantum Spin Liquid Candidate