14 results on '"Liu, Wen-yuan"'
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2. Tensor network study of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ model: incommensurate spiral order, mixed valence-bond solids, and multicritical points
- Author
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Liu, Wen-Yuan, Poilblanc, Didier, Gong, Shou-Shu, Chen, Wei-Qiang, and Gu, Zheng-Cheng
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Condensed Matter - Strongly Correlated Electrons ,Condensed Matter - Superconductivity - Abstract
We use the finite projected entangled pair state (PEPS) method to investigate the global phase diagram of the spin-1/2 square-lattice $J_1$-$J_2$-$J_3$ antiferromagnetic (AFM) Heisenberg model. The ground state phase diagram is established with a rich variety of phases: AFM, gapless quantum spin liquid, valence-bond solid (VBS), stripe, and incommensurate spiral phases. The nature of the VBS region is revealed, containing a plaquette VBS and a mixed columnar-plaquette VBS, with the emergence of short-range incommensurate spin correlations in some region. The long-range incommensurate magnetic phase is also explicitly characterized as a planar spiral with incommensurate spatial periodicities. Most interestingly, there exists several multicritical points connecting different phases. These findings elucidate the true nature of the long-standing square-lattice $J_1$-$J_2$-$J_3$ antiferromagnet at zero-temperature. Our results also pave the way to accurately simulate complex two-dimensional quantum systems that may host nonuniform features by means of finite PEPS., Comment: 13 pages; 19 figures
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- 2023
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3. Quantum criticality with emergent symmetry in the extended Shastry-Sutherland model
- Author
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Liu, Wen-Yuan, Zhang, Xiao-Tian, Wang, Zhe, Gong, Shou-Shu, Chen, Wei-Qiang, and Gu, Zheng-Cheng
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Condensed Matter - Strongly Correlated Electrons ,Condensed Matter - Materials Science ,High Energy Physics - Theory - Abstract
Motivated by the novel phenomena observed in the layered material $\rm SrCu_2(BO_3)_2$, the Shastry-Sutherland model (SSM) has been extensively studied as the minimal model for $\rm SrCu_2(BO_3)_2$. However, the nature of its quantum phase transition from the plaquette valence-bond solid (PVBS) to antiferromagnetic (AFM) phase is under fierce debate, posing a challenge to understand the underlying quantum criticality. Via the state-of-the-art tensor network simulations, we study the ground state of the SSM on large-scale size up to $20 \times 20$ sites. We identify the continuous transition nature accompanied by an emergent O(4) symmetry between the PVBS and AFM phase, which strongly suggests a deconfined quantum critical point (DQCP). Furthermore, we map out the phase diagram of an extended SSM that can be continuously tuned to the SSM, which demonstrates the same DQCP phenomena along a whole critical line. Our results indicate a compelling scenario for understanding the origin of the proposed proximate DQCP in recent experiments of $\rm SrCu_2(BO_3)_2$., Comment: 5+6 pages; 4+5 figures; 3 tables
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- 2023
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4. Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid
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Liu, Wen-Yuan, Gong, Shou-Shu, Chen, Wei-Qiang, and Gu, Zheng-Cheng
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Condensed Matter - Strongly Correlated Electrons ,High Energy Physics - Theory - Abstract
The emergence of exotic quantum phenomena in frustrated magnets is rapidly driving the development of quantum many-body physics, raising fundamental questions on the nature of quantum phase transitions. Here we unveil the behaviour of emergent symmetry involving two extraordinarily representative phenomena, i.e., the deconfined quantum critical point (DQCP) and the quantum spin liquid (QSL) state. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, namely the $J_{1x}$-$J_{1y}$-$J_2$ model, which contains anisotropic nearest-neighbor couplings $J_{1x}$, $J_{1y}$ and the next nearest neighbor coupling $J_2$. For small $J_{1y}/J_{1x}$, by tuning $J_2$, a direct continuous transition between the AFM and valence bond solid phase is observed.(Of course, the possibility of weakly first order transition can not be fully excluded.) With growing $J_{1y}/J_{1x}$, a gapless QSL phase gradually emerges between the AFM and VBS phases. We observe an emergent O(4) symmetry along the AFM--VBS transition line, which is consistent with the prediction of DQCP theory. Most surprisingly, we find that such an emergent O(4) symmetry holds for the whole QSL--VBS transition line as well. These findings reveal the intrinsic relationship between the QSL and DQCP from categorical symmetry point of view, and strongly constrain the quantum field theory description of the QSL phase. The phase diagram and critical exponents presented in this paper are of direct relevance to future experiments on frustrated magnets and cold atom systems., Comment: 5+7 pages, 4+11 figures
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- 2022
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5. The emergence of gapless quantum spin liquid from deconfined quantum critical point
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Liu, Wen-Yuan, Hasik, Juraj, Gong, Shou-Shu, Poilblanc, Didier, Chen, Wei-Qiang, and Gu, Zheng-Cheng
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Condensed Matter - Strongly Correlated Electrons ,High Energy Physics - Lattice ,High Energy Physics - Theory - Abstract
A quantum spin liquid (QSL) is a novel phase of matter with long-range entanglement where localized spins are highly correlated with the vanishing of magnetic order. Such exotic quantum states provide the opportunities to develop new theoretical frameworks for many-body physics and have the potential application in realizing robust quantum computations. Here we show that a gapless QSL can naturally emerge from a deconfined quantum critical point (DQCP), which is originally proposed to describe Landau forbidden continuous phase transition between antiferromagnetic (AFM) and valence-bond solid (VBS) phases. Via large-scale tensor network simulations of a square-lattice spin-1/2 frustrated Heisenberg model, both QSL state and DQCP-type AFM-VBS transition are observed. With tuning coupling constants, the AFM-VBS transition vanishes and instead, a gapless QSL phase gradually develops in between. Remarkably, along the phase boundaries of AFM-QSL and QSL-VBS transitions, we always observe the same correlation length exponents $\nu\approx 1.0$, which is intrinsically different from the one of the DQCP-type transition, indicating new types of universality classes. Our results explicitly demonstrate a new scenario for understanding the emergence of gapless QSL from an underlying DQCP. The discovered QSL phase survives in a large region of tuning parameters and we expect its experimental realizations in solid state materials or quantum simulators.
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- 2021
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6. Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
- Author
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Liu, Wen-Yuan, Gong, Shou-Shu, Li, Yu-Bin, Poilblanc, Didier, Chen, Wei-Qiang, and Gu, Zheng-Cheng
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Condensed Matter - Strongly Correlated Electrons ,Condensed Matter - Superconductivity ,Physics - Computational Physics ,Quantum Physics - Abstract
The nature of the zero-temperature phase diagram of the spin-$1/2$ $J_1$-$J_2$ Heisenberg model on a square lattice has been debated in the past three decades, which may hold the key to understand high temperature superconductivity. By using the state-of-the-art tensor network method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram the $J_1$-$J_2$ Heisenberg model up to $24\times 24$ sites, we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region $0.56\lesssim J_2/J_1\leq0.61$ before the system enters the well known collinear antiferromagnetic phase. The physical nature of the discovered gapless QSL and potential experimental implications are also addressed. We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group (DMRG) method through one-to-one direct benchmark for small system sizes, and thus give rise to a very solid PEPS calculation beyond DMRG. Our numerical evidences explicitly demonstrate the huge power of PEPS for precisely capturing long-range physcis for highly frustrated systems, and also demonstrate the finite PEPS method is a very powerful approach to study strongly corrleated quantum many-body problems.
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- 2020
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7. Reply to comments on 'Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices'
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Liu, Wen-Yuan, Dong, Shaojun, Wang, Chao, Han, Yongjian, An, Hong, Guo, Guang-Can, and He, Lixin
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Condensed Matter - Strongly Correlated Electrons - Abstract
In a recent comments [arXiv:1909.12788 (2019)], Zhao et al. argue that the definition of dimer orders used in our paper [Phys. Rev. B 98, 241109 (2018)] may not rule out valence bond solid (VBS) orders of $J_1$-$J_2$ model on the open boundary conditions (OBC). In this reply, we show that their argument does not apply to our case.
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- 2019
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8. Accurate simulation for finite projected entangled pair states in two dimensions
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Liu, Wen-Yuan, Huang, Yi-Zhen, Gong, Shou-Shu, and Gu, Zheng-Cheng
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Condensed Matter - Strongly Correlated Electrons ,Quantum Physics - Abstract
Based on the scheme of variational Monte Carlo sampling, we develop an accurate and efficient two-dimensional tensor-network algorithm to simulate quantum lattice models. We find that Monte Carlo sampling shows huge advantages in dealing with finite projected entangled pair states, which allows significantly enlarged system size and improves the accuracy of tensor network simulation. We demonstrate our method on the square-lattice antiferromagnetic Heisenberg model up to $32 \times 32$ sites, as well as a highly frustrated $J_1-J_2$ model up to $24\times 24$ sites. The results, including ground state energy and spin correlations, are in excellent agreement with those of the available quantum Monte Carlo or density matrix renormalization group methods. Therefore, our method substantially advances the calculation of 2D tensor networks for finite systems, and potentially opens a new door towards resolving many challenging strongly correlated quantum many-body problems.
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- 2019
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9. Solving frustrated quantum many-particle models with convolutional neural networks
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Liang, Xiao, Liu, Wen-Yuan, Lin, Pei-Ze, Guo, Guang-Can, Zhang, Yong-Sheng, and He, Lixin
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Condensed Matter - Strongly Correlated Electrons ,Physics - Computational Physics - Abstract
Recently, there has been significant progress in solving quantum many-particle problem via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning, which has not been demonstrated so far. In this work, we design a brand new convolutional neural network (CNN) to solve such quantum many-particle problems. We demonstrate, for the first time, of solving the highly frustrated spin-1/2 J$_1$-J$_2$ antiferromagnetic Heisenberg model on square lattices via CNN. The energy per site achieved by the CNN is even better than previous string-bond-state calculations. Our work therefore opens up a new routine to solve challenging frustrated quantum many-particle problems using machine learning.
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- 2018
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10. Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices
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Liu, Wen-Yuan, Dong, Shaojun, Wang, Chao, Han, Yongjian, An, Hong, Guo, Guang-Can, and He, Lixin
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Condensed Matter - Strongly Correlated Electrons - Abstract
The spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices are investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combining with Monte Carlo sampling techniques, we are able to obtain the ground states energies that are competitive to the best results. The calculations show that there is no N\'eel order, dimer order and plaquette order in the region of 0.42 $\lesssim J_2/J_1\lesssim$ 0.6, suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer and plaquette correlation functions all have power law decay behaviours, which provide strong evidences that the intermediate nonmagnetic phase is a single gapless spin liquid state.
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- 2018
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11. TNSPackage: A Fortran2003 library designed for tensor network state methods
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Dong, Shao-Jun, Liu, Wen-Yuan, Wang, Chao, Han, Yongjian, Guo, G-C, and He, Lixin
- Subjects
Condensed Matter - Strongly Correlated Electrons - Abstract
Recently, the tensor network states (TNS) methods have proven to be very powerful tools to investigate the strongly correlated many-particle physics in one and two dimensions. The implementation of TNS methods depends heavily on the operations of tensors, including contraction, permutation, reshaping tensors, SVD and son on. Unfortunately, the most popular computer languages for scientific computation, such as Fortran and C/C++ do not have a standard library for such operations, and therefore make the coding of TNS very tedious. We develop a Fortran2003 package that includes all kinds of basic tensor operations designed for TNS. It is user-friendly and flexible for different forms of TNS, and therefore greatly simplifies the coding work for the TNS methods.
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- 2017
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12. Gradient optimization of finite projected entangled pair states
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Liu, Wen-Yuan, Dong, Shao-Jun, Han, Yong-Jian, Guo, Guang-Can, and He, Lixin
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Quantum Physics ,Condensed Matter - Strongly Correlated Electrons - Abstract
The projected entangled pair states (PEPS) methods have been proved to be powerful tools to solve the strongly correlated quantum many-body problems in two-dimension. However, due to the high computational scaling with the virtual bond dimension $D$, in a practical application PEPS are often limited to rather small bond dimensions, which may not be large enough for some highly entangled systems, for instance, the frustrated systems. The optimization of the ground state using time evolution method with simple update scheme may go to a larger bond dimension. However, the accuracy of the rough approximation to the environment of the local tensors is questionable. Here, we demonstrate that combining the time evolution method with simple update, Monte Carlo sampling techniques and gradient optimization will offer an efficient method to calculate the PEPS ground state. By taking the advantages of massive parallel computing, we can study the quantum systems with larger bond dimensions up to $D$=10 without resorting to any symmetry. Benchmark tests of the method on the $J_1$-$J_2$ model give impressive accuracy compared with exact results.
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- 2016
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13. Emergent Symmetry in Frustrated Magnets: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid
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Liu, Wen-Yuan, Gong, Shou-Shu, Chen, Wei-Qiang, and Gu, Zheng-Cheng
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High Energy Physics - Theory ,Condensed Matter - Strongly Correlated Electrons ,Strongly Correlated Electrons (cond-mat.str-el) ,High Energy Physics - Theory (hep-th) ,FOS: Physical sciences - Abstract
Emergent symmetry is a unique feature of identifying quantum phase transitions beyond the Landau paradigm. Via large-scale tensor network simulations, we study a spatially anisotropic spin-1/2 square-lattice frustrated antiferromagnetic (AFM) model, i.e., the $J_{1x}$-$J_{1y}$-$J_2$ model, which contains anisotropic nearest-neighbour couplings $J_{1x}$ and $J_{1y}$, and next nearest-neighbour coupling $J_2$. For small $J_{1y}/J_{1x}$, by tuning $J_2$, a direct continuous transition between the AFM and valence-bond solid (VBS) phase is observed. With growing $J_{1y}/J_{1x}$, a gapless quantum spin liquid (QSL) phase gradually emerges in between the AFM and VBS phase. We observe an emergent O(4) symmetry along the AFM-VBS transition line, which is consistent with the prediction of the deconfined quantum critical point (DQCP) theory. Most surprisingly, we find that such an emergent O(4) symmetry still holds for the whole QSL-VBS transition line. These findings reveal the intrinsic relationship between QSL and DQCP, which also provide us with a very strong constraint on quantum field theory description of the QSL phase. The phase diagram and critical exponents therein are also of direct relevance to future experiments on frustrated magnets., Comment: 5+7 pages, 4+11 figures
- Published
- 2022
- Full Text
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14. Gapless quantum spin liquid and global phase diagram of the spin-1/2 J1-J2 square antiferromagnetic Heisenberg model
- Author
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Liu, Wen-Yuan, Gong, Shou-Shu, Li, Yu-Bin, Poilblanc, Didier, Chen, Wei-Qiang, Gu, Zheng-Cheng, Laboratoire de Physique Théorique (LPT), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Institut de Recherche sur les Systèmes Atomiques et Moléculaires Complexes (IRSAMC), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), and Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)
- Subjects
deconfinement ,Frustrated magnets ,FOS: Physical sciences ,collinear ,Heisenberg model ,Quantum spin liquid ,spin ,Superconductivity (cond-mat.supr-con) ,Condensed Matter - Strongly Correlated Electrons ,solids ,benchmark ,effective field theory ,Tensor network state ,site ,[INFO]Computer Science [cs] ,liquid ,Deconfined quantum critical point ,density matrix ,lattice ,Quantum Physics ,Strongly Correlated Electrons (cond-mat.str-el) ,Condensed Matter - Superconductivity ,critical phenomena ,Computational Physics (physics.comp-ph) ,magnet ,[PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph] ,correlation ,network ,many-body problem ,Condensed Matter::Strongly Correlated Electrons ,renormalization group ,[PHYS.COND.CM-SCE]Physics [physics]/Condensed Matter [cond-mat]/Strongly Correlated Electrons [cond-mat.str-el] ,Quantum Physics (quant-ph) ,entanglement ,Physics - Computational Physics - Abstract
International audience; The nature of the zero-temperature phase diagram of the spin-1/2J1-J2 Heisenberg model on a square lattice has been debated in the past three decades, and it remains one of the fundamental problems unsettled in the study of quantum many-body theory. By using the state-of-the-art tensor network method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram of the J1-J2 Heisenberg model up to 24×24 sites, we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region 0.56≲J2/J1≤0.61 before the system enters the well known collinear antiferromagnetic phase. We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group (DMRG) method through one-to-one direct benchmark for small system sizes, and thus give rise to a very solid PEPS calculation beyond DMRG. Our numerical evidences explicitly demonstrate the huge power of PEPS for highly frustrated spin systems. Finally, an effective field theory is also proposed to understand the physical nature of the discovered gapless QSL and its relation to deconfined quantum critical point (DQCP).
- Published
- 2022
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